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1.34 ! takayama 1: /* $OpenXM: OpenXM/src/asir-contrib/packages/src/os_muldif.rr,v 1.33 2018/08/30 00:52:44 takayama Exp $ */
1.6 takayama 2: /* The latest version will be at ftp://akagi.ms.u-tokyo.ac.jp/pub/math/muldif
3: scp os_muldif.[dp]* ${USER}@lemon.math.kobe-u.ac.jp:/home/web/OpenXM/Current/doc/other-docs
4: */
5: #define USEMODULE 1
6: /* #undef USEMODULE */
7:
8: /* os_muldif.rr (Library for Risa/Asir)
1.31 takayama 9: * Toshio Oshima (Nov. 2007 - Jun. 2018)
1.6 takayama 10: *
11: * For polynomials and differential operators with coefficients
12: * in rational funtions (See os_muldif.pdf)
13: *
14: * "Tab = 4 column" is best
15: */
16:
17: ord([zz,dz,dy,dx])$
18:
19: #ifdef USEMODULE
20: module os_md;
21: static Muldif.rr$
22: static TeXEq$
23: static TeXLim$
24: static DIROUT$
1.16 takayama 25: static DIROUTD$
1.6 takayama 26: static DVIOUTL$
27: static DVIOUTA$
28: static DVIOUTB$
29: static DVIOUTH$
30: static DVIOUTF$
31: static LCOPT$
32: static COLOPT$
33: static LPOPT$
34: static LFOPT$
35: static ErMsg$
36: static FLIST$
37: static IsYes$
38: static XYPrec$
39: static XYcm$
40: static TikZ$
41: static XYLim$
42: static Canvas$
43: static ID_PLOT$
44: static Rand$
45: static LQS$
46: localf spType2$
47: localf erno$
48: localf chkfun$
49: localf makev$
50: localf shortv$
51: localf makenewv$
52: localf vweyl$
53: localf mycat$
54: localf mycat0$
1.9 takayama 55: localf fcat$
1.6 takayama 56: localf findin$
57: localf countin$
58: localf mycoef$
59: localf mydiff$
60: localf myediff$
61: localf m2l$
62: localf m2ll$
63: localf mydeg$
64: localf pfctr$
65: localf mymindeg$
66: localf m1div$
67: localf mulsubst$
68: localf cmpsimple$
69: localf simplify$
70: localf monotos$
71: localf minustos$
72: localf monototex$
73: localf vnext$
74: localf ldict$
75: localf ndict$
76: localf nextsub$
77: localf nextpart$
78: localf transpart$
79: localf trpos$
80: localf sprod$
81: localf sinv$
82: localf slen$
83: localf sord$
84: localf vprod$
85: localf dvangle$
86: localf dvprod$
87: localf dnorm$
88: localf mulseries$
89: localf pluspower$
90: localf vtozv$
91: localf dupmat$
92: localf matrtop$
93: localf mytrace$
94: localf mydet$
95: localf mperm$
96: localf mtranspose$
97: localf mtoupper$
98: localf mydet2$
99: localf myrank$
100: localf meigen$
101: localf transm$
102: localf vgen$
103: localf mmc$
104: localf lpgcd$
105: localf mdivisor$
106: localf mdsimplify$
107: localf m2mc$
108: localf easierpol$
109: localf paracmpl$
110: localf mykernel$
111: localf myimage$
112: localf mymod$
113: localf mmod$
114: localf ladd$
115: localf lchange$
116: localf llsize$
117: localf llbase$
118: localf lsort$
1.22 takayama 119: localf lpair$
1.6 takayama 120: localf lmax$
121: localf lmin$
122: localf lgcd$
123: localf llcm$
124: localf ldev$
125: localf lsol$
126: localf lnsol$
127: localf l2p$
128: localf m2v$
129: localf lv2m$
130: localf m2lv$
131: localf s2m$
132: localf c2m$
133: localf m2diag$
134: localf myinv$
135: localf madjust$
136: localf mpower$
137: localf mrot$
138: localf texlen$
139: localf isdif$
140: localf fctrtos$
141: localf texlim$
142: localf fmult$
143: localf radd$
144: localf getel$
145: localf ptol$
146: localf rmul$
147: localf mtransbys$
148: localf drawopt$
149: localf execdraw$
150: localf execproc$
151: localf myswap$
152: localf mysubst$
153: localf evals$
154: localf myval$
155: localf myeval$
156: localf mydeval$
157: localf myfeval$
158: localf myf2eval$
159: localf myf3eval$
160: localf myfdeval$
161: localf myf2deval$
162: localf myf3deval$
163: localf myexp$
164: localf mycos$
165: localf mysin$
166: localf mytan$
167: localf myarg$
168: localf myasin$
169: localf myacos$
170: localf myatan$
171: localf mylog$
172: localf mypow$
1.13 takayama 173: localf scale$
1.6 takayama 174: localf arg$
175: localf sqrt$
176: localf gamma$
177: localf lngamma$
178: localf digamma$
179: localf dilog$
180: localf zeta$
181: localf eta$
182: localf jell$
183: localf frac$
184: localf erfc$
1.20 takayama 185: localf orthpoly$
186: localf schurpoly$
1.6 takayama 187: localf fouriers$
188: localf todf$
189: localf f2df$
190: localf df2big$
191: localf compdf$
192: localf fzero$
193: localf fmmx$
194: localf flim$
195: localf fcont$
196: localf fresidue$
197: localf mmulbys$
198: localf appldo$
199: localf appledo$
200: localf muldo$
201: localf jacobian$
202: localf hessian$
203: localf wronskian$
204: localf adj$
205: localf laplace1$
206: localf laplace$
207: localf mce$
208: localf mc$
209: localf rede$
210: localf ad$
211: localf add$
212: localf vadd$
213: localf addl$
214: localf cotr$
215: localf rcotr$
216: localf muledo$
217: localf mulpdo$
218: localf transpdosub$
219: localf transpdo$
220: localf translpdo$
221: localf rpdiv$
222: localf mygcd$
223: localf mylcm$
224: localf sftpexp$
225: localf applpdo$
226: localf tranlpdo$
227: localf divdo$
228: localf qdo$
229: localf sqrtdo$
230: localf ghg$
231: localf ev4s$
232: localf b2e$
233: localf sftpow$
234: localf sftpowext$
235: localf polinsft$
236: localf pol2sft$
237: localf polroots$
238: localf fctri$
239: localf binom$
240: localf expower$
241: localf seriesHG$
242: localf seriesMc$
243: localf seriesTaylor$
1.27 takayama 244: localf mulpolyMod$
1.26 takayama 245: localf taylorODE$
1.6 takayama 246: localf evalred$
247: localf toeul$
248: localf fromeul$
249: localf sftexp$
250: localf fractrans$
251: localf soldif$
252: localf chkexp$
253: localf sqrtrat$
254: localf getroot$
255: localf expat$
256: localf polbyroot$
257: localf polbyvalue$
258: localf pcoef$
259: localf prehombf$
260: localf prehombfold$
261: localf sub3e$
262: localf fuchs3e$
263: localf okubo3e$
264: localf eosub$
265: localf even4e$
266: localf odd5e$
267: localf extra6e$
268: localf rigid211$
269: localf solpokuboe$
270: localf stoe$
271: localf dform$
272: localf polinvsym$
273: localf polinsym$
274: localf tohomog$
275: localf substblock$
276: localf okuboetos$
277: localf heun$
278: localf fspt$
279: localf abs$
1.20 takayama 280: localf sgn$
1.6 takayama 281: localf calc$
282: localf isint$
283: localf israt$
284: localf iscrat$
285: localf isalpha$
286: localf isnum$
287: localf isalphanum$
1.8 takayama 288: localf isdecimal$
1.6 takayama 289: localf isvar$
290: localf isyes$
291: localf isall$
292: localf iscoef$
293: localf iscombox$
294: localf sproot$
295: localf spgen$
296: localf chkspt$
297: localf cterm$
298: localf terms$
299: localf polcut$
300: localf redgrs$
301: localf cutgrs$
302: localf mcgrs$
303: localf mc2grs$
304: localf mcmgrs$
305: localf anal2sp$
306: localf delopt$
307: localf str_char$
308: localf str_pair$
309: localf str_cut$
310: localf str_str$
311: localf str_subst$
312: localf str_times$
313: localf str_tb$
314: localf strip$
315: localf i2hex$
316: localf sjis2jis$
317: localf jis2sjis$
318: localf s2os$
319: localf l2os$
320: localf r2os$
321: localf s2euc$
322: localf s2sjis$
323: localf r2ma$
324: localf evalma$
325: localf ssubgrs$
326: localf verb_tex_form$
327: localf tex_cuteq$
328: localf my_tex_form$
329: localf texket$
330: localf smallmattex$
331: localf divmattex$
332: localf dviout0$
333: localf myhelp$
334: localf isMs$
335: localf showbyshell$
336: localf readcsv$
337: localf tocsv$
338: localf getbyshell$
339: localf show$
340: localf dviout$
341: localf rtotex$
342: localf mtotex$
343: localf ltotex$
344: localf texbegin$
345: localf texcr$
346: localf texsp$
347: localf getbygrs$
348: localf mcop$
349: localf shiftop$
350: localf conf1sp$
1.34 ! takayama 351: localf confexp$
1.6 takayama 352: localf pgen$
353: localf diagm$
354: localf mgen$
355: localf madj$
356: localf newbmat$
357: localf unim$
358: localf pfrac$
359: localf cfrac$
360: localf cfrac2n$
361: localf sqrt2rat$
362: localf s2sp$
363: localf sp2grs$
364: localf fimag$
365: localf trig2exp$
366: localf intpoly$
367: localf integrate$
1.22 takayama 368: localf rungeKutta$
1.6 takayama 369: localf simplog$
370: localf fshorter$
371: localf isshortneg$
372: localf intrat$
373: localf powsum$
374: localf bernoulli$
375: localf lft01$
376: localf linfrac01$
377: localf nthmodp$
378: localf issquaremodp$
379: localf rootmodp$
380: localf rabin$
381: localf primroot$
382: localf varargs$
383: localf ptype$
384: localf pfargs$
385: localf average$
1.23 takayama 386: localf tobig$
1.6 takayama 387: localf sint$
388: localf frac2n$
389: localf xyproc$
390: localf xypos$
391: localf xyput$
392: localf xybox$
393: localf xyline$
394: localf xylines$
395: localf xycirc$
396: localf xybezier$
397: localf lbezier$
398: localf draw_bezier$
399: localf tobezier$
400: localf velbezier$
401: localf ptbezier$
402: localf cutf$
403: localf fsum$
404: localf fint$
405: localf periodicf$
406: localf cmpf$
407: localf areabezier$
408: localf saveproc$
409: localf xygraph$
410: localf xy2graph$
1.22 takayama 411: localf addIL$
1.19 takayama 412: localf xy2curve$
1.18 takayama 413: localf xygrid$
1.6 takayama 414: localf xyarrow$
415: localf xyarrows$
416: localf xyang$
417: localf xyoval$
1.33 takayama 418: localf xypoch$
1.6 takayama 419: localf ptcommon$
420: localf ptcopy$
421: localf ptaffine$
422: localf ptlattice$
423: localf ptpolygon$
424: localf ptwindow$
425: localf ptbbox$
426: localf lninbox$
427: localf ptcombezier$
428: localf ptcombz$
429: localf lchange$
430: localf init$
431: localf powprimroot$
432: localf distpoint$
433: localf ntable$
434: localf keyin$
435: localf mqsub$
436: localf msort$
437: #else
438: extern Muldif.rr$
439: extern TeXEq$
440: extern TeXLim$
441: extern DIROUT$
1.16 takayama 442: extern DIROUTD$
1.6 takayama 443: extern DVIOUTL$
444: extern DVIOUTA$
445: extern DVIOUTB$
446: extern DVIOUTH$
447: extern DVIOUTF$
448: static LCOPT$
449: static COLOPT$
450: static LPOPT$
451: static LFOPT$
452: extern TikZ$
453: extern ErMsg$
454: extern FLIST$
455: extern IsYes$
456: extern XYPrec$
457: extern XYcm$
458: extern TikZ$
459: extern XYLim$
460: extern Canvas$
461: extern ID_PLOT$
462: extern Rand$
463: extern LQS$
464: #endif
465: static S_Fc,S_Dc,S_Ic,S_Ec,S_EC,S_Lc$
1.16 takayama 466: static S_FDot$
1.6 takayama 467: extern AMSTeX$
1.34 ! takayama 468: Muldif.rr="00180921"$
1.6 takayama 469: AMSTeX=1$
470: TeXEq=5$
471: TeXLim=80$
472: TikZ=0$
473: XYcm=0$
474: XYPrec=3$
475: XYLim=4$
476: Rand=0$
477: DIROUT="%HOME%\\tex"$
478: DVIOUTL="%ASIRROOT%\\bin\\risatex0.bat"$
479: DVIOUTA="%ASIRROOT%\\bin\\risatex.bat"$
480: DVIOUTB="%ASIRROOT%\\bin\\risatex1%TikZ%.bat"$
481: DVIOUTH="start dviout -2 -hyper=0x90 \"%ASIRROOT%\\help\\os_muldif.dvi\" #%LABEL%"$
482: DVIOUTF=0$
483: LCOPT=["red","green","blue","yellow","cyan","magenta","black","white","gray"]$
484: COLOPT=[0xff,0xff00,0xff0000,0xffff,0xffff00,0xff00ff,0,0xffffff,0xc0c0c0]$
485: LPOPT=["above","below","left","right"]$
486: LFOPT=["very thin","thin","dotted","dashed"]$
487: Canvas=[400,400]$
488: LQS=[[1,0]]$
489:
490: ErMsg = newvect(3,[
491: "irregal argument", /* 0 */
492: "too big size", /* 1 */
493: "irregal option" /* 2 */
494: ])$
495: FLIST=0$
496: IsYes=[]$
497: ID_PLOT=-1$
498:
499: def erno(N)
500: {
501: /* extern ErMsg; */
502: print(ErMsg[N]);
503: }
504:
505: def chkfun(Fu, Fi)
506: {
507: /* extern FLIST; */
508: /* extern Muldif.rr; */
509:
510: if(type(Fu) <= 1){
511: if(Fu==1)
512: mycat(["Loaded os_muldif Ver.", Muldif.rr, "(Toshio Oshima)"]);
513: else
514: mycat(["Risa/Asir Ver.", version()]);
515: return 1;
516: }
517: if(type(FLIST) < 4)
518: FLIST = flist();
519: if(type(Fu) == 4){
520: for(; Fu != [] ;Fu = cdr(Fu))
521: if(chkfun(car(Fu),Fi) == 0) return 0;
522: return 1;
523: }
524: if(findin(Fu, FLIST) >= 0)
525: return 1;
526: FLIST = flist();
527: if(findin(Fu, FLIST) >= 0)
528: return 1;
529: if(type(Fi)==7){
530: mycat0(["load(\"", Fi,"\") -> try again!\n"],1);
531: load(Fi);
532: }
533: return 0;
534: /*
535: if(type(Fi) == 7)
536: Fi = [Fi];
537: for( ; Fi != []; Fi = cdr(Fi))
538: load(car(Fi));
539: FLIST = flist();
540: return (findin(Fu,FLIST)>=0)?1:0;
541: */
542: }
543:
544: def makev(L)
545: {
546: S = "";
547: Num=getopt(num);
548: while(length(L) > 0){
549: VL = car(L); L = cdr(L);
550: if(type(VL) == 7)
551: S = S+VL;
552: else if(type(VL) == 2 || VL < 10)
553: S = S+rtostr(VL);
554: else if(VL<46 && Num!=1)
555: S = S+asciitostr([VL+87]);
556: else
557: S = S+rtostr(VL);
558: }
559: return strtov(S);
560: }
561:
562: def makenewv(L)
563: {
564: if((V=getopt(var))<2) V="z_";
565: else if(isvar(V)) V=rtostr(V);
566: if(type(N=getopt(num))!=1) N=0;
1.21 takayama 567: Var=varargs(L|all=2);
1.6 takayama 568: for(XX=[],I=J=0;;I++){
569: X=strtov(V+rtostr(I));
570: if(findin(X,Var)<0){
571: XX=cons(X,XX);
572: if(++J>N) return X;
573: else if(J==N) return reverse(XX);
574: }
575: }
576: }
577:
578: def shortv(P,L)
579: {
580: V=vars(P);
581: if(type(T=getopt(top))==2) T=strtoascii(rtostr(T))[0]-87;
582: else T=10;
583: for(;L!=[];L=cdr(L)){
584: for(J=0;J<36;J++){
585: if(findin(X=makev([car(L),J]|num=1),V)>=0){
586: while(findin(Y=makev([T]),V)>=0) T++;
587: if(T>35) return P;
588: P=subst(P,X,Y);
589: T++;
590: }else if(J>0) break;
591: }
592: }
593: return P;
594: }
595:
596: def vweyl(L)
597: {
598: if(type(L) == 4){
599: if(length(L) == 2)
600: return L;
601: else
602: return [L[0],makev(["d",L[0]])];
603: }
604: /* else if(type(L)<2) return L; */
605: return [L,makev(["d", L])];
606: }
607:
608: def mycat(L)
609: {
610: if(type(L) != 4){
611: print(L);
612: return;
613: }
614: Opt = getopt(delim);
615: Del = (type(Opt) >= 0)?Opt:" ";
616: Opt = getopt(cr);
617: CR = (type(Opt) >= 0)?0:1;
618: while(L != []){
619: if(Do==1)
620: print(Del,0);
621: print(car(L),0);
622: L=cdr(L);
623: Do = 1;
624: }
625: if(CR) print("");
626: }
627:
1.9 takayama 628: def fcat(S,X)
629: {
630: if(type(S)!=7){
1.18 takayama 631: if(type(DIROUTD)!=7){
632: DIROUTD=str_subst(DIROUT,["%HOME%","%ASIRROOT%","\\"],
633: [getenv("HOME"),get_rootdir(),"/"])+"/";
634: if(isMs()) DIROUTD=str_subst(DIROUTD,"/","\\"|sjis=1);
635: }
636: if(S==-1) return;
1.16 takayama 637: T="fcat";
638: if(S>=2&&S<=9) T+=rtostr(S);
639: T=DIROUTD+T+".txt";
640: if(S==-1) return T;
641: if(S!=0&&access(T)) remove_file(T);
642: S=T;
1.9 takayama 643: }
1.19 takayama 644: R=output(S);
1.9 takayama 645: print(X);
646: output();
1.16 takayama 647: if(getopt(exe)==1) shell("\""+S+"\"");
1.19 takayama 648: return R;
1.9 takayama 649: }
650:
1.6 takayama 651: def mycat0(L,T)
652: {
653: Opt = getopt(delim);
654: Del = (type(Opt) >= 0)?Opt:"";
1.20 takayama 655: if(type(L)!=4) L=[L];
1.6 takayama 656: while(L != []){
657: if(Do==1)
658: print(Del,0);
659: print(car(L),0);
660: L=cdr(L);
661: Do = 1;
662: }
663: if(T) print("");
664: }
665:
666: def findin(M,L)
667: {
668: if(type(L)==4){
669: for(I = 0; L != []; L = cdr(L), I++)
670: if(car(L) == M) return I;
671: }else if(type(L)==5){
672: K=length(L);
673: for(I = 0; I < K; I++)
674: if(L[I] == M) return I;
675: }else return -2;
676: return -1;
677: }
678:
679: def countin(S,M,L)
680: {
1.10 takayama 681: Step=getopt(step);
682: if(type(Step)==1){
683: N=(Step>0)?Step:-Step;
1.7 takayama 684: if(type(L)==5) L=vtol(L);
685: L=qsort(L);
686: while(car(L)<S&&L!=[]) L=cdr(L);
687: S+=M;
1.10 takayama 688: for(R=[],C=I=0;L!=[];){
689: if(car(L)<S||(Step>0&&car(L)==S)){
1.7 takayama 690: C++;
691: L=cdr(L);
692: }else{
693: R=cons(C,R);C=0;S+=M;
1.10 takayama 694: if(N>1&&++I>=N) break;
1.7 takayama 695: }
696: }
697: if(C>0) R=cons(C,R);
1.10 takayama 698: if(N>1&&(N-=length(R))>0) while(N-->0) R=cons(0,R);
1.7 takayama 699: return reverse(R);
700: }
1.6 takayama 701: if(type(L)==4){
702: for(N=0; L!=[]; L=cdr(L))
703: if(car(L)>=S && car(L)<=M) N++;
704: }else if(type(L)==5){
705: K=length(L);
706: for(I = 0; I < K; I++)
707: if(L[I]>=S && L[I]<=M) N++;
708: }else return -2;
709: return N;
710: }
711:
712: def mycoef(P,N,X)
713: {
714: if(type(P)<3 && type(N)<3)
715: return coef(P,N,X);
716: if(type(P) >= 4)
717: #ifdef USEMODULE
718: return map(os_md.mycoef,P,N,X);
719: #else
720: return map(mycoef,P,N,X);
721: #endif
722: if(type(N)==4){
723: for(;N!=[];N=cdr(N),X=cdr(X))
724: P=mycoef(P,car(N),car(X));
725: return P;
726: }
727: if(deg(dn(P), X) > 0){
728: P = red(P);
729: if(deg(dn(P), X) > 0)
730: return 0;
731: }
732: return red(coef(nm(P),N,X)/dn(P));
733: }
734:
735: def mydiff(P,X)
736: {
737: if(X == 0)
738: return 0;
739: if(type(P)<3 && type(X)<3)
740: return diff(P,X);
741: if(type(P) >= 4)
742: #ifdef USEMODULE
743: return map(os_md.mydiff,P,X);
744: #else
745: return map(mydiff,P,X);
746: #endif
747: if(type(X)==4){
748: for(;X!=[];X=cdr(X)) P=mydiff(P,car(X));
749: return P;
750: }
1.19 takayama 751: if(ptype(dn(P),X)<2)
1.6 takayama 752: return red(diff(nm(P),X)/dn(P));
753: return red(diff(P,X));
754: }
755:
756: def myediff(P,X)
757: {
758: if(X == 0)
759: return 0;
760: if(type(P) < 3)
761: return ediff(P,X);
762: if(type(P) >= 4)
763: #ifdef USEMODULE
764: return map(os_md.myediff,P,X);
765: #else
766: return map(myediff,P,X);
767: #endif
768: if(deg(dn(P),X) == 0)
769: return red(ediff(nm(P),X)/dn(P));
770: return red(X*diff(P,X));
771: }
772:
773: def m2l(M)
774: {
775: if(type(M) < 4)
776: return [M];
777: if(type(M) == 4){
778: if(type(car(M))==4 && getopt(flat)==1){
779: for(MM = []; M!=[]; M=cdr(M))
780: MM = append(MM,car(M));
781: return MM;
782: }
783: return M;
784: }
785: if(type(M) == 5)
786: return vtol(M);
787: S = size(M);
788: for(MM = [], I = S[0]-1; I >= 0; I--)
789: MM = append(vtol(M[I]), MM);
790: return MM;
791: }
792:
793: def mydeg(P,X)
794: {
795: if(type(P) < 3)
796: return deg(P,X);
797: II = -1;
798: Opt = getopt(opt);
799: if(type(P) >= 4){
800: S=(type(P) == 6)?size(P)[0]:0;
801: P = m2l(P);
802: for(I = 0, Deg = -3; P != []; P = cdr(P), I++){
803: if( (DT = mydeg(car(P),X)) == -2)
804: return -2;
805: if(DT > Deg){
806: Deg = DT;
807: II = I;
808: }
809: }
810: return (Opt==1)?([Deg,(S==0)?II:[idiv(II,S),irem(II,S)]]):Deg;
811: }
812: P = red(P);
813: if(deg(dn(P),X) == 0)
814: return deg(nm(P),X);
815: return -2;
816: }
817:
818: def pfctr(P,X)
819: {
820: P=red(P);
821: if((T=ptype(P,X))>3) return [];
822: if(T==3){
823: G=pfctr(dn(P),X);
824: F=pfctr(nm(P),X);
825: R=[[car(F)[0]/car(G)[0],1]];
826: for(F=cdr(F);F!=[];F=cdr(F)) R=cons(car(F),R);
827: for(G=cdr(G);G!=[];G=cdr(G)) R=cons([car(G)[0],-car(G)[1]],R);
828: return reverse(R);
829: }
830: F=fctr(nm(P));
831: for(R=[],C=1/dn(P);F!=[];F=cdr(F))
832: if(mydeg(car(F)[0],X)>0) R=cons(car(F),R);
833: else C*=car(F)[0]^car(F)[1];
834: return cons([C,1],reverse(R));
835: }
836:
837: def mymindeg(P,X)
838: {
839: if(type(P) < 3)
840: return mindeg(P,X);
841: II = -1;T=60;
842: Opt = getopt(opt);
843: if(type(P) >= 4){
844: S=(type(P) == 6)?size(P)[0]:0;
845: P = m2l(P);
846: for(I = 0, Deg = -3; P != []; P = cdr(P), I++){
847: if(car(P) == 0)
848: continue;
849: if( (DT = mydeg(car(P),X)) == -2)
850: return -2;
851: if(DT < Deg || Deg == -3){
852: if(DT==0){
853: if(type(car(P))>=T) continue;
854: T=type(car(P));
855: }
856: Deg = DT;
857: II = I;
858: }
859: }
860: return (Opt==1)?([Deg,(S==0)?II:[idiv(II,S),irem(II,S)]]):Deg;
861: }
862: P = red(P);
863: if(deg(dn(P),X) == 0)
864: return mindeg(nm(P),X);
865: return -2;
866: }
867:
868: def m1div(M,N,L)
869: {
870: L = (type(L) <= 3)?[0,L]:vweyl[L];
871: DX = L[1]; X = L[0];
872: if(mydeg(N,DX) != 0)
873: return 0;
874: DD = mydeg(M,DX);
875: MM = M;
876: while( (Deg=mydeg(MM,DX)) > 0){
877: MC = mycoef(MM,Deg,DX)*DX^(Deg-1);
878: MS = radd(MC, MS);
879: MM = radd(MM, muldo(MC,radd(-DX,N),L));
880: }
881: return [MM, MS];
882: }
883:
884:
885: def mulsubst(F,L)
886: {
887: N = length(L);
888: if(N == 0)
889: return F;
890: if(type(L[0])!=4) L=[L];
891: if(getopt(inv)==1){
892: for(R=[];L!=[];L=cdr(L)) R=cons([car(L)[1],car(L)[0]],R);
893: L=reverse(R);
894: }
895: if(length(L)==1) return mysubst(F,L);
896: L1 = newvect(N);
897: for(J = 0; J < N ; J++)
898: L1[J] = uc();
899: L2 = newvect(N);
900: for(J = 0; J < N; J++){
901: S = L[J][1];
902: for(I = 0; I < N; I++)
903: S = mysubst(S,[L[I][0],L1[I]]);
904: L2[J] = S;
905: }
906: for(J = 0; J < N; J++)
907: F = mysubst(F, [L[J][0],L2[J]]);
908: for(J = 0; J < N; J++)
909: F = mysubst(F, [L1[J],L[J][0]]);
910: return F;
911: }
912:
913: def cmpsimple(P,Q)
914: {
915: T = getopt(comp);
916: if(P == Q)
917: return 0;
918: D = 0;
919: if(type(T) < 0)
920: T = 7;
921: if(iand(T,1))
922: D = length(vars(P)) - length(vars(Q));
923: if(!D && iand(T,2))
924: D = nmono(P) - nmono(Q);
925: if(!D && iand(T,4))
926: D = str_len(rtostr(P)) - str_len(rtostr(Q));
927: if(!D){
928: if(P > Q) D++;
929: else D--;
930: }
931: return D;
932: }
933:
934: def simplify(P,L,T)
935: {
936: if(type(P) > 3)
937: #ifdef USEMODULE
938: return map(os_md.simplify,P,L,T);
939: #else
940: return map(simplify,P,L,T);
941: #endif
942: if(type(L[0]) == 4){
943: if(length(L[0]) > 1)
944: #if USEMODULE
945: return fmult(os_md.simplify,P,L,[T]);
946: #else
947: return fmult(simplify,P,L,[T]);
948: #endif
949: L = L[0];
950: }
951: if(type(Var=getopt(var)) == 4 && Var!=[]){
952: if(type(P) == 3)
953: return simplify(nm(P),P,L,T|var=Var)/simplify(dn(P),P,L,T|var=Var);
954: V = car(Var);
955: if((I = mydeg(P,V)) > 0){
956: Var = cdr(Var);
957: for(Q=0; I>=0 ; I--)
958: Q += simplify(mycoef(P,I,V), L, T|var=Var)*V^I;
959: return Q;
960: }
961: }
962: if(length(L) == 1){
963: L = car(L);
964: for(V = vars(L); V != []; V = cdr(V)){
965: VT = car(V);
966: if(deg(L,VT) != 1) continue;
967: P = simplify(P, [VT, -red(coef(L,0,VT)/coef(L,1,VT))], T);
968: }
969: return P;
970: }
971: Q = mysubst(P,[L[0],L[1]]);
972: return (cmpsimple(P,Q|comp=T) <= 0)?P:Q;
973: }
974:
975: def monotos(P)
976: {
977: if(nmono(P) <= 1)
978: return rtostr(P);
979: return "("+rtostr(P)+")";
980: }
981:
982:
983: def monototex(P)
984: {
985: Q=my_tex_form(P);
986: if(nmono(P)<2 && (getopt(minus)!=1 || str_str(Q,"-"|top=0,end=0)<0))
987: return Q;
988: return "("+Q+")";
989: }
990:
991: def minustos(S)
992: {
993: if(str_str(S,"-"|top=0,end=0)<0) return S;
994: return "("+S+")";
995: }
996:
997: def vnext(V)
998: {
999: S = length(V);
1000: for(I = S-1; I > 0; I--){
1001: if(V[I-1] < V[I]){
1002: V0 = V[I-1];
1003: for(J = I+1; J < S; J++)
1004: if(V0 >= V[J]) break;
1005: V[I-1] = V[--J];
1006: V[J] = V0;
1007: for(J = S-1; I < J; I++, J--){
1008: V0 = V[I];
1009: V[I] = V[J];
1010: V[J] = V0;
1011: }
1012: return 1;
1013: }
1014: }
1015: return 0;
1016: }
1017:
1018: def ldict(N, M)
1019: {
1020: Opt = getopt(opt);
1021: R = S = [];
1022: for(I = 2; N > 0; I++){
1023: R = cons(irem(N,I), R);
1024: N = idiv(N,I);
1025: }
1026: L = LL = length(R);
1027: T=newvect(LL+1);
1028: while(L-- > 0){
1029: V = car(R); R = cdr(R);
1030: for(I = J = 0; J <= V ; I++){
1031: if(T[I] == 0)
1032: J++;
1033: }
1034: T[I-1] = 1;
1035: S = cons(LL-I+1, S);
1036: }
1037: for(I = 0; I <= LL; I++){
1038: if(T[I] == 0){
1039: S = cons(LL-I, S);
1040: break;
1041: }
1042: }
1043: if(M == 0)
1044: return S;
1045: if(M <= LL){
1046: print("too small size");
1047: return 0;
1048: }
1049: T = [];
1050: for(I = --M; I > LL; I--)
1051: T = cons(I,T);
1052: S = append(S,T);
1053: if(Opt == 2 || Opt == 3)
1054: S = reverse(S);
1055: if(Opt != 1 && Opt != 3)
1056: return S;
1057: for(T = []; S != []; S = cdr(S))
1058: T = cons(M-car(S),T);
1059: return T;
1060: }
1061:
1062: def ndict(L)
1063: {
1064: Opt = getopt(opt);
1065: R = [];
1066: if(Opt != 1 && Opt != 2)
1067: L = reverse(L);
1068: T = (Opt == 1 || Opt == 3)?1:0;
1069: for( ; L != []; L = cdr(L)){
1070: for(I = 0, V = car(L), LT = cdr(L); LT != []; LT = cdr(LT))
1071: if(T == 0){
1072: if(V < car(LT)) I++;
1073: }else if (V > car(LT)) I++;
1074: R = cons(I, R);
1075: }
1076: R = reverse(R);
1077: for(V = 0, I = length(R); I > 0; R = cdr(R), I--)
1078: V = V*I + car(R);
1079: return V;
1080: }
1081:
1082: def nextsub(L,N)
1083: {
1084: if(type(L) == 1){
1085: for(LL = [], I = L-1; I >= 0; I--)
1086: LL = cons(I,LL);
1087: return LL;
1088: }
1089: M = length(L = ltov(L));
1090: K = N-M;
1091: for(I = M-1; I >= 0; I--)
1092: if(L[I] < I+K) break;
1093: if(I < 0)
1094: return 0;
1095: for(J = L[I]+1; I < M; I++, J++)
1096: L[I] = J;
1097: return vtol(L);
1098: }
1099:
1100: def nextpart(L)
1101: {
1102: if(car(L) <= 1)
1103: return 0;
1104: for(I = 0, L = reverse(L); car(L) == 1; L=cdr(L))
1105: I++;
1106: I += (K = car(L));
1107: R = irem(I,--K);
1108: R = (R==0)?[]:[R];
1109: for(J = idiv(I,K); J > 0; J--)
1110: R = cons(K,R);
1111: L = cdr(L);
1112: while(L!=[]){
1113: R = cons(car(L), R);
1114: L = cdr(L);
1115: }
1116: return R;
1117: }
1118:
1119: def transpart(L)
1120: {
1121: L = reverse(L);
1122: for(I=1, R=[]; L!= []; I++){
1123: R = cons(length(L), R);
1124: while(L != [] && car(L) <= I)
1125: L = cdr(L);
1126: }
1127: return reverse(R);
1128: }
1129:
1130: def trpos(A,B,N)
1131: {
1132: S = newvect(N);
1133: for(I = 0; I < N; I++)
1134: S[I]=(I==A)?B:((I==B)?A:I);
1135: return S;
1136: }
1137:
1138: def sprod(S,T)
1139: {
1140: L = length(S);
1141: V = newvect(L);
1142: while(--L >= 0)
1143: V[L] = S[T[L]];
1144: return V;
1145: }
1146:
1147: def sinv(S)
1148: {
1149: L = length(S);
1150: V = newvect(L);
1151: while(--L >= 0)
1152: V[S[L]] = L;
1153: return V;
1154: }
1155:
1156: def slen(S)
1157: {
1158: L = length(S);
1159: for(V = 0, J = 2; J < L; i++){
1160: for(I = 0; I < J; I++)
1161: if(S[I] > S[J]) V++;
1162: }
1163: return V;
1164: }
1165:
1166: def sord(W,V)
1167: {
1168: L = length(W);
1169: W0 = nevect(L);
1170: V0 = newvect(L);
1171: for(I = F = C = 0; I < L; I++){
1172: C = 0;
1173: if( (W1 = W[I]) > (V1 = V[I]) ){
1174: if(F < 0) C = 1;
1175: else if(F==0) F = 1;
1176: }else if(W1 < V1){
1177: if(F > 0) C = 1;
1178: else if(F==0) F = -1;
1179: }
1180: for(J = I;--J >= 0 && W0[J] > W1; ) W0[J+1] = W0[J];
1181: W0[J+1] = W1;
1182: for(J = I;--J >= 0 && V0[J] > V1; ) V0[J+1] = V0[J];
1183: V0[J+1] = V1;
1184: if(C){
1185: for(J = I; J >= 0; J--){
1186: if((W1=W0[J]) == (V1=V0[J])) continue;
1187: if(W1 > V1){
1188: if(F < 0) return 2;
1189: }
1190: else if(F > 0) return 2;
1191: }
1192: }
1193: }
1194: return F;
1195: }
1196:
1197: def vprod(V1,V2)
1198: {
1199: for(R = 0, I = length(V1)-1; I >= 0; I--)
1200: R = radd(R, rmul(V1[I], V2[I]));
1201: return R;
1202: }
1203:
1204: def dnorm(V)
1205: {
1206: if(type(V)<2) return dabs(V);
1207: R=0;
1208: if(type(V)!=4)
1209: for (I = length(V)-1; I >= 0; I--) R+= V[I]^2;
1210: else{
1211: if(type(V[0])>3){
1212: V=ltov(V[0])-ltov(V[1]);
1213: return dnorm(V);
1214: }
1215: for(;V!=[]; V=cdr(V)) R+=car(V)^2;
1216: }
1217: return dsqrt(R);
1218: }
1219:
1220: def dvprod(V1,V2)
1221: {
1222: if(type(V1)<2) return V1*V2;
1223: R=0;
1224: if(type(V1)!=4)
1225: for(I = length(V1)-1; I >= 0; I--)
1226: R += V1[I]*V2[I];
1227: else{
1228: for(; V1!=[]; V1=cdr(V1),V2=cdr(V2))
1229: R+=car(V1)*car(V2);
1230: }
1231: return R;
1232: }
1233:
1234: def dvangle(V1,V2)
1235: {
1236: if(V2==0 && type(V1)==4 && length(V1)==3 &&
1237: (type(V1[0])==4 || type(V1[0])==5 || type(V1[1])==4 || type(V1[1])==5 ||
1238: type(V1[2])==4 || type(V1[2])==5) ){
1239: if(V1[0]==0 || V1[1]==0 || V1[2]==0) return 1;
1240: PV2=V1[1];
1241: if(type(PV2)==4){
1242: PV2=ltov(PV2);
1243: return dvangle(PV2-ltov(V1[0]),ltov(V1[2])-PV2);
1244: }else
1245: return dvangle(PV2-V1[0],V1[2]-PV2);
1246: }
1247: if((L1=dnorm(V1))==0 || (L2=dnorm(V2))==0) return 1;
1248: return dvprod(V1,V2)/(L1*L2);
1249: }
1250:
1251: def mulseries(V1,V2)
1252: {
1253: L = length(V1);
1254: if(size(V2) < L)
1255: L = size(V2);
1256: VV = newvect(L);
1257: for(J = 0; J < L; J++){
1258: for(K = R = 0; K <= J; K++)
1259: R = radd(R,rmul(V1[K],V2[J-K]));
1260: VV[J] = R;
1261: }
1262: return VV;
1263: }
1264:
1.13 takayama 1265: def scale(L)
1266: {
1.23 takayama 1267: T=F=0;LS=1;
1.18 takayama 1268: Pr=getopt(prec);
1.23 takayama 1269: Inv=getopt(inv);
1270: Log10=dlog(10);
1271: if(type(L)==7){
1272: V=findin(L,["CI","DI","CIF","CIF'","DIF","DIF'","SI","TI1","TI2","STI"]);
1273: if(V>=0){
1274: L=["C","D","CF","CF'","DF","DF'","S","T1","T2","ST"];
1275: Inv=1;L=L[V];
1276: }
1277: V=findin(L,["C","A","K","CF","CF'","S","T1","T2","ST","LL0","LL1","LL2","LL3","LL00",
1278: "LL01","LL02","LL03"])+1;
1279: if(V==0) V=findin(L,["D","B","K","DF","DF'"])+1;
1280: if(V>0) L=V;
1281: }
1282: if(type(OL=L)!=4){
1.15 takayama 1283: if(L==2){
1.23 takayama 1284: L=(Pr==0)?
1.18 takayama 1285: [[[1,2,1/20],[2,5,1/10],[5,10,1/5], [10,20,1/2],[20,50,1],[50,100,2]],
1.15 takayama 1286: [[1,2,1/10],[2,5,1/2], [10,20,1],[20,50,5]],
1.18 takayama 1287: [[1,2,1/2],[2,10,1], [10,20,5],[20,100,10]]]:
1288: [[[1,2,1/50],[2,5,1/20],[5,10,1/10], [10,20,1/5],[20,50,1/2],[50,100,1]],
1289: [[1,5,1/10],[5,10,1/2], [10,20,1],[50,100,5]],
1290: [[1,5,1/2],[5,10,1], [10,50,5],[50,100,10]]];
1.23 takayama 1291: LS=2;M2=[[1,10,1],[10,100,10]];
1.15 takayama 1292: }else if(L==3){
1.23 takayama 1293: L=(Pr==0)?
1.18 takayama 1294: [[[1,2,1/20],[2,5,1/10],[5,10,1/5], [10,20,1/2],[20,50,1],[50,100,2],
1295: [100,200,5],[200,500,10],[500,1000,20]],
1.15 takayama 1296: [[1,2,1/10],[2,5,1/2], [10,20,1],[20,50,5], [100,200,10],[200,500,50]],
1.18 takayama 1297: [[1,2,1/2],[2,10,1], [10,20,5],[20,100,10], [100,200,50],[200,1000,100]]]:
1298: [[[1,2,1/50],[2,5,1/20],[5,10,1/10],[10,20,1/5],[20,50,1/2],[50,100,1],
1299: [100,200,2],[200,500,5],[500,1000,10]],
1300: [[1,5,1/10],[5,10,1/2], [10,50,1],[50,100,5], [100,500,10],[500,1000,50]],
1.23 takayama 1301: [[1,5,1/2],[5,10,1],[10,50,5],[50,100,10], [100,500,50],[500,1000,100]]];
1302: LS=3;M2=[[1,5,1],[10,50,10],[100,500,100],[500,1000,500]];
1303: }else if(L>9&&L<18){
1.26 takayama 1304: if(L<18){ /* LL0 - LL3, LL00 - LL03 */
1.23 takayama 1305: if(L==10){
1306: L=[ [[1.001,1.002,0.00001],[1.002,1.005,0.00002],[1.005,1.0105,0.00005]],
1307: [[1.001,1.002,0.00005],[1.002,1.005,0.0001], [1.005,1.0105,0.0001]],
1308: [[1.001,1.002,0.0001],[1.002,1.005,0.0005], [1.005,1.0105,0.0005]]];
1309: M2=[1.001,1.0015,1.002,1.003,1.004,1.005,1.006,1.007,1.008,1.009,1.01];
1310: }
1311: if(L==11){
1312: L=[ [[1.01,1.02,0.0001],[1.02,1.05,0.0002],[1.05,1.105,0.0005]],
1313: [[1.01,1.02,0.0005],[1.02,1.05,0.001], [1.05,1.105,0.001]],
1314: [[1.01,1.02,0.001],[1.02,1.05,0.005], [1.05,1.105,0.005]]];
1315: M2=[1.01,1.015,1.02,1.03,1.04,1.05,1.06,1.07,1.08,1.09,1.10];
1316: }else if(L==12){
1317: L=[ [[1.105,1.2,0.001],[1.2,1.4,0.002],[1.4,1.8,0.005],[1.8,2.5,0.01],
1318: [2.5,2.72,0.02]],
1319: [[1.105,1.2,0.005],[1.2,1.4,0.01],[1.4,1.8,0.01],[1.8,2.5,0.05],
1320: [2.5,2.72,0.1]],
1321: [[1.105,1.2,0.01],[1.2,1.4,0.05],[1.4,1.8,0.05],[1.8,2.5,0.1],
1322: [2.5,2.72,0.1]]];
1.26 takayama 1323: M2=[1.11,1.15,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.0,2.2,2.5];
1.23 takayama 1324: }else if(L==13){
1325: L=[ [[2.72,4,0.02],[4,6,0.05],[6,10,0.1],[10,15,0.2],[15,30,0.5],[30,50,1],
1326: [50,100,2],[100,200,5],[200,400,10],[400,500,20],[500,1000,50],
1327: [1000,2000,100],[2000,5000,200],[5000,10000,500],[10000,22000,1000]],
1328: [[2.7,4,0.1],[4,6,0.1],[6,10,0.5],[10,15,1],[15,30,1],[30,50,5],
1329: [50,100,10],[100,200,10],[200,400,50],[400,500,100],[500,1000,100],
1330: [1000,2000,500],[2000,5000,1000],[5000,10000,1000],[10000,22000,5000]],
1331: [[3,4,0.5],[4,6,0.5],[6,10,1],[10,15,5],[15,30,5],[30,50,10],
1332: [50,100,50],[100,200,50],[200,400,100],[400,500,100],[500,1000,500],
1333: [1000,2000,1000],[2000,5000,3000],[5000,10000,5000],[10000,22000,10000]]];
1334: M2=[3,4,5,6,7,8,9,10,15,20,30,40,50,100,200,500,1000,2000,5000,10000,20000];
1335: }else if(L==14){
1.26 takayama 1336: L=[ [[0.998,0.999,0.00001],[0.995,0.998,0.00002],[0.99,0.995,0.00005]],
1337: [[0.998,0.999,0.00005],[0.995,0.998,0.0001],[0.99,0.995,0.0001]],
1338: [[0.998,0.999,0.0001],[0.995,0.998,0.0005],[0.99,0.995,0.0005]]];
1.23 takayama 1339: M2=[0.999,0.9985,0.998,0.997,0.996,0.995,0.994,0.993,0.992,0.991,0.99];
1340: }else if(L==15){
1.26 takayama 1341: L=[ [[0.98,0.9901,0.0001],[0.95,0.98,0.0002],[0.905,0.95,0.0005]],
1342: [[0.98,0.99,0.0005],[0.95,0.98,0.001], [0.905,0.95,0.001]],
1.23 takayama 1343: [[0.98,0.99,0.001],[0.95,0.98,0.005], [0.91,0.95,0.005]]];
1344: M2=[0.99,0.985,0.98,0.97,0.96,0.95,0.94,0.93,0.92,0.91];
1345: }else if(L==16){
1.26 takayama 1346: L=[ [[0.8,0.906,0.001],[0.6,0.8,0.002],[0.37,0.6,0.005]],
1347: [[0.8,0.906,0.005],[0.6,0.8,0.01],[0.37,0.6,0.01]],
1348: [[0.8,0.9,0.01],[0.6,0.8,0.05],[0.4,0.6,0.05]]];
1349: M2=[0.9,0.85,0.8,0.75,0.7,0.65,0.6,0.55,0.5,0.45,0.4];
1.23 takayama 1350: }else{
1.26 takayama 1351: L=[ [[0.05,0.37,0.002],[0.02,0.05,0.001],[0.01,0.02,0.0005],
1352: [0.005,0.01,0.0002],[0.001,0.005,0.0001],
1353: [0.0005,0.001,0.00002],[0.0001,0.0005,0.00001],[0.00005,0.0001,0.000002]],
1354: [[0.05,0.37,0.01],[0.02,0.05,0.002],[0.01,0.02,0.001],
1355: [0.005,0.01,0.001],[0.001,0.005,0.0002],
1356: [0.0005,0.001,0.0001],[0.0001,0.0005,0.00002],[0.00005,0.0001,0.00001]],
1357: [[0.05,0.37,0.05],[0.02,0.05,0.01],[0.01,0.02,0.005],
1358: [0.005,0.01,0.005],[0.002,0.005,0.001],
1359: [0.0005,0.001,0.0005],[0.0001,0.0005,0.0001],[0.00005,0.0001,0.00005]]];
1360: M2=[0.3,0.2,0.1,0.05,0.03,0.02,0.01,0.005,0.002,0.001,0.0005,0.0002,0.0001];
1.23 takayama 1361: }
1362: }
1.15 takayama 1363: }else{
1.23 takayama 1364: if(L==6){ /* S */
1365: L=[ [[6-3/12,15,1/12],[15,30,1/6],[30,50,1/3],[50,70,1/2],[70,80,1],[80,90,5]],
1366: [[6-1/6,15,1/6],[15,30,1/2],[30,70,1],[70,80,5],[80,90,10]],
1367: [[6,15,1/2],[15,30,1],[30,70,5],[70,90,10]] ];
1368: M2=[6,7,8,9,10,15,20,30,40,50,60,70,90];
1369: }else if(L==7){ /* T1 */
1370: F=log(tan(x*3.1416/180))/Log10+1;
1371: L=[ [[6-1/3,15,1/12],[15,45,1/6]],
1372: [[6-1/3,15,1/6],[15,45,1/2]],
1373: [[6,45,1]] ];
1374: M2=[6,7,8,9,10,15,20,30,40,45];
1375: }else if(L==8){ /* T2 */
1376: L=[ [[45,75,1/6],[75,84+1/6,1/12]],
1377: [[45,75,1],[75,84+1/6,1/6]],
1378: [[45,84,1]] ];
1379: M2=[45,50,60,70,75,80,81,82,83,84];
1380: }else if(L==9){ /* ST */
1381: L=[ [[35/60,1,1/120],[1,2,1/60],[2,5+9/12,1/30]],
1382: [[35/60,1,1/60],[1,2,1/6],[2,5+9/12,1/6]],
1383: [[40/60,1,1/6],[1,2,1/2],[2,5+9/12,1]] ];
1384: M2=[1,2,3,4,5];
1385: }else{
1386: M2=(L==4||L==5)?[[1,2,1/2],[2,9,1]]:[[1,2,1/2],[2,10,1]];
1387: L=(Pr==0)?
1388: [ [[1,2,1/50],[2,5,1/20],[5,10,1/10]],
1389: [[1,5,1/10],[5,10,1/2]],
1390: [[1,5,1/2],[5,10,1]] ]:
1391: [[[1,2,1/100],[2,5,1/50],[5,10,1/20]],
1392: [[1,2,1/20],[2,10,1/10]],
1393: [[1,2,1/10],[2,10,1/2]] ];
1394: }
1.15 takayama 1395: }
1396: }else if(type(L[0])!=4){
1397: L=[L];
1398: if(length(L)!=3||L[0]+L[2]>L[1]) T=L;
1.13 takayama 1399: }
1.15 takayama 1400: if(T==0){
1401: if(type(L[0][0])!=4) L=[L];
1402: for(R=[];L!=[];L=cdr(L)){
1403: for(RR=[],LT=car(L);LT!=[];LT=cdr(LT))
1404: for(I=car(LT)[0];I<=car(LT)[1];I+=car(LT)[2]) RR=cons(I,RR);
1405: RR=lsort(RR,[],1);
1406: R=cons(RR,R);
1407: }
1408: R=reverse(R);
1409: for(T=[];R!=[];R=cdr(R)){
1410: if(length(R)>1) T=cons(lsort(R[0],R[1],"setminus"),T);
1411: else T=cons(R[0],T);
1412: }
1.13 takayama 1413: }
1414: V0=dlog(10);
1415: S0=S1=1;D0=D1=0;
1416: SC=getopt(scale);
1417: if(type(SC)==4){
1418: S0=SC[0];S1=SC[1];
1.18 takayama 1419: }else if(type(SC)==1){
1420: S0=SC;S1=0;
1.13 takayama 1421: }else return T;
1422: if(type(D=getopt(shift))==4){
1423: D0=D[0];D1=D[1];
1.31 takayama 1424: }else if(type(D)<2&&type(D)>=0){
1.23 takayama 1425: D0=0;D1=D;
1.31 takayama 1426: };
1.23 takayama 1427: if(Inv==1){
1428: D0+=S0;S0=-S0;
1.13 takayama 1429: }
1.23 takayama 1430: if(type(TF=getopt(f))>1) F=TF;
1431: if(F) F=f2df(F);
1432: if(type(I=getopt(ol))==1&&OL>3) OL=I;
1.18 takayama 1433: for(M=M0=[],I=length(T);T!=[];T=cdr(T),I--){
1.13 takayama 1434: for(S=car(T);S!=[];S=cdr(S)){
1.23 takayama 1435: VS=car(S);
1436: if(F) V=myfdeval(F,car(S));
1437: else if(OL==4) V=frac(dlog(VS)/Log10+0.5);
1438: else if(OL==5) V=frac(dlog(VS*3.1416)/Log10);
1439: else if(OL>5&&OL<10){
1440: VS=VS*3.1416/180;
1441: if(OL==6) V=dlog(dsin(VS))/Log10+1;
1442: else if(OL==9) V=dlog(VS)/Log10+2;
1443: else V=dlog(dtan(VS))/Log10+8-OL;
1444: }
1445: else if(OL>9&&OL<14) V=dlog(dlog(VS))/Log10+13-OL;
1446: else if(OL>13&&OL<18) V=dlog(-dlog(VS))/Log10+17-OL;
1447: else V=dlog(VS)/Log10/LS;
1448: V*=S0;
1.13 takayama 1449: if(S1!=0){
1450: M=cons([V+D0,D1],M);
1.23 takayama 1451: M=cons([V+D0,((length(SC)>2)?SC[I]:(I*S1))+D1],M);
1.13 takayama 1452: M=cons(0,M);
1.18 takayama 1453: }else M0=cons(V+D0,M0);
1.13 takayama 1454: }
1.18 takayama 1455: if(S1==0) M=cons(reverse(M0),M);
1.13 takayama 1456: }
1457: if(S1!=0) M=cdr(M);
1.18 takayama 1458: if(S1==0||getopt(TeX)!=1) return M;
1.13 takayama 1459: M=reverse(M);
1.23 takayama 1460: if(type(U=getopt(line))==4){
1461: if(Inv==1) U=[U[0]+S0,U[1]+S0];
1.18 takayama 1462: M=cons([U[0]+D0,D1],cons([U[1]+D0,D1],cons(0,M)));
1.23 takayama 1463: }
1464: if((VT=getopt(vert))==1){
1465: for(N=[];M!=[];M=cdr(M)){
1466: if(type(TM=car(M))==4) N=cons([TM[1],TM[0]],N);
1467: else N=cons(TM,N);
1468: }
1469: M=reverse(N);
1470: }
1.18 takayama 1471: if(type(Col=getopt(col))<1) S=xylines(M);
1472: else S=xylines(M|opt=Col);
1473: if(type(Mes=getopt(mes))==4){
1.23 takayama 1474: if(length(Mes)==1&&type(M2)==4) Mes=cons(car(Mes),M2);
1.18 takayama 1475: S3=car(Mes);
1476: if(type(S3)==4){
1477: Col=S3[1];
1478: S3=car(S3);
1479: }else Col=0;
1480: V=car(scale(cdr(Mes)));
1.23 takayama 1481: if(!F) Mes=scale(cdr(Mes)|scale=[S0/LS,0],shift=[D0,D1],ol=OL);
1.18 takayama 1482: else Mes=scale(cdr(Mes)|f=F,scale=[S0,0],shift=[D0,D1]);
1483: for(M=car(Mes);M!=[];M=cdr(M),V=cdr(V)){
1.23 takayama 1484: TV=deval(car(V));
1485: if(Col!=0) TV=[Col,TV];
1486: S+=(VT==1)?xyput([S3+D1,car(M),TV]):xyput([car(M),S3+D1,TV]);
1487: }
1488: }
1489: if(type(Mes=getopt(mes2))==4){
1490: if(type(car(Mes))!=4) Mes=[Mes];
1491: for(;Mes!=[];Mes=cdr(Mes)){
1492: TM=car(Mes);
1493: if(!F) V=scale([car(TM)]|scale=[S0/LS,0],shift=[D0,D1],ol=OL);
1494: else V=scale([car(TM)]|f=F,scale=[S0,0],shift=[D0,D1]);
1495: V=car(car(V));
1496: TM=cdr(TM);
1497: if(type(Col=car(TM))==4){
1498: C0=Col[0];C1=Col[1];
1499: if(length(Col)==3){
1500: S+=(VT==1)?xyline([D1+C0,V],[D1+C1,V]|opt=Col[2])
1501: :xyline([V,D1+C0],[V,D1+C1]|opt=Col[2]);
1502: }else S+=(VT==1)?xyline([D1+C0,V],[D1+C1,V]):xyline([V,D1+C0],[V,D1+C1]);
1503: }
1504: if(type(TM[1]<2)){
1505: TM=cdr(TM);
1506: S3=car(TM);
1507: }
1508: S+=(VT==1)?xyput([S3+D1,V,TM[1]]):xyput([V,S3+D1,TM[1]]);
1.13 takayama 1509: }
1510: }
1.18 takayama 1511: return S;
1.13 takayama 1512: }
1513:
1.6 takayama 1514: def pluspower(P,V,N,M)
1515: {
1516: RR = 1;
1517: for(K = R = 1; K < M-1; I++){
1518: R = R*(N-K+1)*P/K;
1519: RR = radd(RR,R);
1520: }
1521: VV = newvect(M);
1522: for(K = 0; K < M-1; K++)
1523: VV[K] = red(mycoef(RR,K,V));
1524: }
1525:
1526: def vtozv(V)
1527: {
1528: if(type(V)<4) V=newvect(1,[V]);
1529: S = length(V);
1530: VV = newvect(S);
1531: Lcm = 1;
1532: for(K = 0; K < S; K++){
1533: VV[K] = red(V[K]);
1534: Lcm = lcm(Lcm,dn(VV[K]));
1535: C = ptozp(nm(VV[K])|factor=0);
1536: if(K == 0){
1537: Dn = dn(C[1]);
1538: Nm = nm(C[1]);
1539: PNm = nm(C[0]);
1540: }else{
1541: Dn = ilcm(Dn,dn(C[1]));
1542: Nm = igcd(Nm,nm(C[1]));
1543: PNm = gcd(PNm,nm(C[0]));
1544: }
1545: }
1546: if(!(M=Nm*PNm)) return [VV,0];
1547: Mul = (Lcm*Dn)/M;
1548: for(K = 0; K < S; K++)
1549: VV[K] = rmul(VV[K],Mul);
1550: return [VV,Mul];
1551: }
1552:
1553: def dupmat(M)
1554: {
1555: if(type(M) == 6){
1556: Size = size(M);
1557: MM = newmat(Size[0],Size[1]);
1558: for(I = 0; I < Size[0]; I++){
1559: for(J = 0; J < Size[1]; J++)
1560: MM[I][J] = M[I][J];
1561: }
1562: return MM;
1563: }
1564: if(type(M) == 5)
1565: return ltov(vtol(M));
1566: return M;
1567: }
1568:
1569: def matrtop(M)
1570: {
1571: S = size(M);
1572: MM = dupmat(M);
1573: Lcm = newvect(S[0]);
1574: for(J = 0; J < S[0]; J++){
1575: U = vtozv(M[J]);
1576: for(K = -1, I = 0; I < S[1]; I++)
1577: MM[J][I] = U[0][I];
1578: Lcm[J] = U[1];
1579: }
1580: return [MM,Lcm];
1581: }
1582:
1583: def mytrace(M)
1584: {
1585: S=size(M);
1586: if(S[0]!=S[1]) return 0;
1587: for(I=V=0; I<S[0]; I++){
1588: V+=M[I][I];
1589: }
1590: return V;
1591: }
1592:
1593: def mydet(M)
1594: {
1595: MM = matrtop(M);
1596: if(type(MM[0]) == 6){
1597: S = size(M);
1598: for(Dn = 1, I = 0; I < S[0]; I++)
1599: Dn *= MM[1][I];
1600: return (!Dn)?0:red(det(MM[0])/Dn);
1601: }
1602: }
1603:
1604: def mperm(M,P,Q)
1605: {
1606: if(type(M) == 6){
1607: S = size(M);
1608: if(type(P) <= 1)
1609: P=(P==1)?Q:trpos(0,0,S[0]);
1610: if(type(P) > 3 && type(P[0]) >= 4)
1611: P = trpos(P[0][0],P[0][1],S[0]);
1612: else if(type(P) == 4){
1613: if(length(P)==2 && type(P[1])==4){
1614: P0=P[0];P1=car(P[1]);P=newvect(P1);
1615: for(I=0;I<P1;I++) P[I]=P0+I;
1616: }else P = ltov(P);
1617: }
1618: if(type(Q) <= 1)
1619: Q=(Q==1)?P:trpos(0,0,S[1]);
1620: if(type(Q) > 3 && type(Q[0]) >= 4)
1621: Q = trpos(Q[0][0],Q[0][1],S[1]);
1622: if(type(Q) == 4){
1623: if(length(Q)==2 && type(Q[1])==4){
1624: P0=Q[0];P1=car(Q[1]);Q=newvect(P1);
1625: for(I=0;I<P1;I++) Q[I]=P0+I;
1626: }else Q = ltov(Q);
1627: }
1628: MM = newmat(S0=length(P),S1=length(Q));
1629: for(I = 0; I < S0; I++){
1630: MMI = MM[I]; MPI = M[P[I]];
1631: for(J = 0; J < S1; J++)
1632: MMI[J] = MPI[Q[J]];
1633: }
1634: return MM;
1635: }
1636: if((type(M) == 5 || type(M) == 4) && type(P) >= 4){
1637: if(length(P) == 1 && type(car(P)) == 4)
1638: P = trpos(car(P)[0],car(P)[1],length(M));
1639: MM = newvect(S = length(P));
1640: for(I = 0; I < S; I++)
1641: MM[I] = M[P[I]];
1642: if(type(M) == 4)
1643: MM = vtol(MM);
1644: return MM;
1645: }
1646: return M;
1647: }
1648:
1649: def mtranspose(M)
1650: {
1651: if(type(M)==4){
1652: MV=ltov(M);
1653: II=length(MV);
1654: for(I=L=0; I<II; I++){
1655: if(type(MV[I])!=4) return M;
1656: MV[I]=ltov(MV[I]);
1657: }
1658: for(R=[],J=0; ;J++){
1659: for(T=[],I=F=0; I<II; I++){
1660: if(length(MV[I])>J){
1661: F=1;
1662: T=cons(MV[I][J],T);
1663: }
1664: }
1665: if(F==0) return reverse(R);
1666: if(F==1) R=cons(reverse(T),R);
1667: }
1668: }
1669: if(type(M) != 6)
1670: return M;
1671: S = size(M);
1672: MM = newmat(S[1],S[0]);
1673: for(I = 0; I < S[0]; I++){
1674: for(J = 0; J < S[1]; J++)
1675: MM[J][I] = M[I][J];
1676: }
1677: return MM;
1678: }
1679:
1680: def mtoupper(MM, F)
1681: {
1682: TeXs=["\\ -=\\ ","\\ +=\\ "];
1683: Lins=[" -= line"," += line"];
1684: Assume=["If","Assume"];
1685: if(type(St = getopt(step))!=1) St=0;
1686: Opt = getopt(opt);
1687: if(type(Opt)!=1) Opt=0;
1688: TeX=getopt(dviout);
1689: if(type(Tab=getopt(tab))!=1 && Tab!=0) Tab=2;
1690: Line="\\text{line}";
1691: if(type(TeX)!=1 || !St) TeX=0;
1692: Size = size(MM);
1693: if(F==-1){
1694: M = newmat(Size[0], Size[1]+1);
1695: for(I = 0; I < Size[0]; I++){
1696: for(J = 0; J < Size[1]; J++)
1697: M[I][J] = MM[I][J];
1698: M[I][Size[1]] = zz^I;
1699: }
1700: Size = size(M);
1701: F = 1;
1702: }else if(F<0){
1703: F=Size[0];
1704: M = newbmat(1,2,[[MM,mgen(F,0,[1],0)]]);
1705: Size=[Size[0],F+Size[1]];
1706: }else
1707: M = dupmat(MM);
1708: if(St){
1709: if(TeX) Lout=[[dupmat(M)]];
1710: else mycat0([M,"\n\n"],0);
1711: }
1712: Top="";
1713: if(Opt>3){
1714: for(I=Opt; I>4; I--)
1715: Top+=(TeX)?"\\ ":" ";
1716: }
1717: PC=IF=1;
1718: for(K = JJ = 0; K < Size[1] - F; K++){
1719: for(J = JJ; J < Size[0]; J++){
1720: if(M[J][K] != 0){ /* search simpler element */
1721: if(Opt>2 && (Mul=M[J][K])!=1){
1722: for(FF=0,JT=J; JT<Size[0]; JT++){
1723: if((Val=M[JT][K])==1){ /* 1 */
1724: Mul=1;J=JT; break;
1725: }
1726: if(Val==0 || type(Val)>type(Mul)) continue;
1727: if(type(Val)<type(Mul) || (Val==-1 && Mul!=-1)){
1728: Mul=Val; J=JT; /* smaller type */
1729: }
1730: else if(Opt>3){
1731: if(isint(Val)==1){ /* integer elememt */
1732: if(isint(Mul)!=1){
1733: Mul=Val; J=JT; /* integer */
1734: }
1735: if(FF<3||(FF==3&&Val>0)){
1736: for(JK=K+1;;){
1737: if(JK>=Size[1]-F){
1738: J=JT;
1739: FF=((Mul=Val)>0)?4:3;
1740: break; /* divisible int => 4: pos_int 3: neg_int */
1741: }
1742: if(isint(M[JT][JK++]/Val)!=1) break;
1743: }
1744: }
1745: }else if(!FF){
1746: for(JK=K+1; JK<Size[1]-F; JK++){
1747: if(isint(M[JT][JK]/Val)!=1) break;
1748: J=JT; FF=1; /* divisible => 1: non integer */
1749: }
1750: }
1751: }
1752: }
1753: if(FF==0 && Opt>3 && Mul!=1 && Mul!=-1){ /* FF > 0 => divisible */
1754: for(FF=0,J0=J; J0<Size[0]-1 && FF!=9; J0++){
1755: VV0=M[J0][K];
1756: if(VV0==0 || isint(VV0)==0) continue;
1757: for(J1=J0+1;J1<Size[0] && FF!=9; J1++){
1758: VV1=M[J1][K];
1759: if(VV1==0 || isint(VV1)==0) continue;
1760: for(C=FT=0,V0=VV0,V1=VV1; C<2 && FF!=10; C++,V1=V0,V0=VV1){
1761: for(CC=0,RC=ceil(V0/V1);CC<2;CC++,RC--){
1762: if((CD=V0-RC*V1)==0 && (RC==1 || RC==-1)){
1763: FT=1; FF=10; /* 10: vanish by +- */
1764: }else if(CD==1){
1765: FV=(vars(M[J0])==[]&&vars(M[J1])==[])?1:0;
1766: if((RC==1 || RC==-1) && FF<8+FV){
1767: FT=1; FF=8+FV; /* 8/9: 1 by +- */
1768: }else if(FF<6+VF){
1769: FT=1; FF=6+FV; /* 6/7: 1 by times */
1770: }
1771: }else if(CD==-1){
1772: FV=(vars(M[J0])==[]&&vars(M[J1])==[])?1:0;
1773: if((RC==1 || RC==-1) && FF<4+FV){
1774: FT=1; FF=4+FV; /* 4/5: 1 by +- */
1775: }else if(FF<2+VF){
1776: FT=1; FF=2+FV; /* 2/3: 1 by times */
1777: }
1778: }
1779: if(FT==1){
1780: FT=0; KRC=RC;
1781: if(C==0){
1782: KJ0=J0; KJ1=J1;
1783: }else{
1784: KJ0=J1; KJ1=J0;
1785: }
1786: }
1787: }
1788: }
1789: }
1790: }
1791: if(FF>0){
1792: for(I=K;I<Size[1];I++)
1793: M[KJ0][I]=radd(M[KJ0][I],rmul(M[KJ1][I],-KRC));
1794: if(KRC<0){
1795: KRC=-KRC;Sgn=1;
1796: }else
1797: Sgn=0;
1798: if(St){
1799: if(TeX){
1800: if(KRC==1)
1801: Lout=cons([Top+"\\xrightarrow{", Line,KJ0+1,TeXs[Sgn],
1802: Line,KJ1+1,"}",dupmat(M)],Lout);
1803: else
1804: Lout=cons([Top+"\\xrightarrow{", Line,KJ0+1,TeXs[Sgn],
1805: Line,KJ1+1,"\\times\\left(",KRC,"\\right)}",
1806: dupmat(M)],Lout);
1807:
1808: }else{
1809: if(KRC==1)
1810: mycat([Top+"line",KJ0+1,Lins[Sgn],KJ1+1,"\n",M,"\n"]); else
1811: mycat([Top+"line",KJ0+1,Lins[Sgn],KJ1+1," * (",KRC,")\n",M,"\n"]);
1812: }
1813: }
1814: Mul=M[KJ0][K]; J=KJ0;
1815: if(FF==10){
1816: J--; continue;
1817: }
1818: }
1819: }
1820: }
1821: /* a parameter Var */
1822: Var=0;
1823: if(St && Opt>4 && length(Var=vars(nm(M[J][K])))==1){
1824: J0=J;Jv=mydeg(nm(M[J0][K]),car(Var));
1825: for(I=JJ;I<Size[0]; I++){
1826: if((MIK=M[I][K])==0) continue;
1827: if((T=vars(MIK=nm(MIK)))==[]){ /* 1/poly */
1828: J=I;Var=[]; break;
1829: }
1830: if(length(T)>1) continue;
1831: if(mydeg(MIK,T[0])<Jv){
1832: J0=I;Jv=mydeg(MIK);Var=T; /* search minimal degree */
1833: }
1834: }
1835: if(length(Var)==1){
1836: Var=car(Var);
1837: Q=nm(M[J0][K]);
1838: for(I=JJ; I<Size[0]; I++){
1839: if(I==J0 || mydeg(nm(M[I][K]),Var)<0) continue;
1840: T=rpdiv(nm(M[I][K]),Q,Var);
1841: if(T[0]!=0 && (vars(T)==[] || vars(T)==[Var])) break; /* dec. deg */
1842: }
1843: }
1844: }
1845: if(type(Var)==2){ /* 1 variable */
1846: if(I==Size[0]){
1847: for(QF=0,Q0=1,QR=getroot(Q,Var|mult=1);QR!=[];QR=cdr(QR)){
1848: if(deg(T=QR[0][1],Var)>0){
1849: QF=1;Q0*=T; continue;
1850: }
1851: if(subst(PC,Var,T)==0) continue;
1852: Q0*=(Var-(T=QR[0][1]));
1853: if(type(T)<2){
1854: M0=subst(M,Var,T);
1855: if(TeX){
1856: Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{If }",
1857: Var,"=",T,","] ,Lout);
1858: Lout=append(mtoupper(M0,F|step=St+1,opt=Opt,dviout=-2,tab=Tab),Lout);
1859: }else{
1860: mycat([str_times(" ",St-1)+"If",Var,"=",T,","]);
1861: mtoupper(M0,F|step=St+1,opt=Opt);
1862: }
1863: }
1864: }
1865: if(Q0!=1){
1866: if(TeX)
1867: Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{"+Assume[QF]+" }",
1868: Q0/=fctr(Q0)[0][0],"\\ne0,"],Lout);
1869: else
1870: mycat([str_times(" ",St-1)+Assume[QF],Q0,"!=0,"]);
1871: PC*=Q0;
1872: }
1873: IF=0;St++;
1874: }else{
1875: KRC=-red((T[2]*dn(M[J0][K]))/(T[1]*dn(M[I][K])));
1876: for(II=K;II<Size[1];II++)
1877: M[I][II]=radd(M[I][II],rmul(M[J0][II],KRC));
1878: if(TeX)
1879: Lout=cons([Top+"\\xrightarrow{", Line,I+1,"\\ +=\\ ",Line,
1880: J0+1,"\\times\\left(",KRC,"\\right)}",dupmat(M)],Lout);
1881: else
1882: mycat([Top+"line",I+1,"+=",Line,J0+1," * (",KRC,")\n",M,"\n"]);
1883: J=JJ-1;
1884: continue;
1885: }
1886: }
1887: if(J != JJ){
1888: for(I = K; I < Size[1]; I++){
1889: Temp = M[JJ][I];
1890: M[JJ][I] = M[J][I];
1891: M[J][I] = (Opt>=2)?Temp:-Temp;
1892: }
1893: if(St){
1894: if(TeX)
1895: Lout=cons([Top+"\\xrightarrow{",Line,JJ+1,"\\ \\leftrightarrow\\ ",
1896: Line,J+1,"}",dupmat(M)],Lout);
1897: else
1898: mycat0([Top+"line",JJ+1," <-> line",J+1,"\n",M,"\n\n"],0);
1899: }
1900: }
1901: /* Assume PC != 0 */
1902: if(Opt>1){
1903: Mul = M[JJ][K];
1904: if(Opt > 5 && St && IF && (Var=vars(MIK=nm(Mul)))!=[]){
1905: TF=fctr(MIK);
1906: for(FF=0,Q0=1,TP=cdr(TF);TP!=[];TP=cdr(TP)){
1907: if(type(dn(red(PC/(TP0=car(car(TP))))))<2) continue; /* divisible */
1908: Q0*=TP0;
1909: for(Var=vars(TP0);Var!=[];Var=cdr(Var)){
1910: if(mydeg(TP0,X=car(Var))==1 && type(dn(red(PC/mycoef(TP0,1,X))))<2){
1911: /* TP0=A*X+B with non-vanishing A */
1912: T=red(-mycoef(TP0,0,X)/mycoef(TP0,1,X));
1913: M0=mysubst(M,[X,T]);
1914: if(TeX){
1915: Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{If }",
1916: X,"=",T,","] ,Lout);
1917: Lout=append(mtoupper(M0,F|step=St+1,opt=Opt,dviout=-2,tab=Tab),
1918: Lout);
1919: }else{
1920: mycat([str_times(" ",St-1)+"If",X,"=",T,","]);
1921: mtoupper(M0,F|step=St+1,opt=Opt);
1922: }
1923: break;
1924: }
1925: }
1926: if(Var==[] && Opt>6){
1927: for(Var=vars(TP0);Var!=[];Var=cdr(Var)){
1928: if(mydeg(TP0,X=car(Var))==1){
1929: /* TP0=A*X+B, A is a poly of X0 with rational funct */
1930: T=nm(mycoef(TP0,1,X));
1931: for(Var0=vars(T);Var0!=[]; Var0=cdr(Var0)){
1932: X0=car(Var0);
1933: if(type(dn(red(PC/type(mycoef(T,mydeg(T,X0),X0)))))>1) continue;
1934: TR=getroot(T,X0|mult=1);
1935: if(findin(X0,vars(TR))<0) break;
1936: }
1937: if(Var0==[]) continue;
1938: for(;TR!=[0];TR=cdr(TR)){
1939: if(TR==[]){
1940: TR=[0,0];
1941: T0=-mycoef(TP0,0,X)/mycoef(TP0,1,X);
1942: X0=X;
1943: }else T0=car(TR)[1];
1944: M0=mysubst(M,[X0,T0]);
1945: if(TeX){
1946: Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{If }",
1947: X0,"=",T0,","] ,Lout);
1948: Lout=append(mtoupper(M0,F|step=St+1,opt=Opt,dviout=-2,tab=Tab),
1949: Lout);
1950: }else{
1951: mycat([str_times(" ",St-1)+"If",X0,"=",T0,","]);
1952: mtoupper(M0,F|step=St+1,opt=Opt);
1953: }
1954: }
1955:
1956: }
1957: break;
1958: }
1959: }
1960: if(Var==[]){
1961: FF=1;
1962: }
1963: }
1964: if(Q0!=1){
1965: if(FF) FF=1;
1966: if(TeX) Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{"+Assume[FF]+" }",Q0/=fctr(Q0)[0][0],"\\ne0,"],
1967: Lout);
1968: else mycat([str_times(" ",St-1)+Assume[FF],Q0,"!=0,"]);
1969: PC*=Q0;St++;
1970: }
1971: }
1972: IF=M[JJ][K]=1;
1973: if(Mul!=1){
1974: for(L=K+1; L<Size[1]; L++)
1975: M[JJ][L]=red(M[JJ][L]/Mul);
1976: if(St){
1977: if(TeX)
1978: Lout=cons([Top+"\\xrightarrow{",Line,JJ+1,
1979: "\\ \\times=\\ \\left(",red(1/Mul),"\\right)}",
1980: dupmat(M)],Lout);
1981: else
1982: mycat0([Top+"line",JJ+1, " *= (",red(1/Mul), ")\n",M,"\n\n"],0);
1983: }
1984: }
1985:
1986: }
1987: for(J = (Opt>0)?0:(JJ+1); J < Size[0]; J++){
1988: if(J == JJ)
1989: continue;
1990: Mul = -M[J][K];
1991: if(Mul!=0){
1992: if(Opt!=2) Mul=rmul(Mul,1/M[JJ][K]);
1993: for(I = K+1; I < Size[1]; I++)
1994: M[J][I] = radd(M[J][I],rmul(M[JJ][I],Mul));
1995: M[J][K] = 0;
1996: if(St){
1997: if(Mul<0){
1998: Mul=-Mul;Sgn=0;
1999: }else Sgn=1;
2000: if(TeX){
2001: if(Mul==1)
2002: Lout=cons([Top+"\\xrightarrow{", Line,J+1,TeXs[Sgn],Line,JJ+1,
2003: "}",dupmat(M)],Lout);
2004: else Lout=cons([Top+"\\xrightarrow{", Line,J+1,TeXs[Sgn],Line,JJ+1,
2005: "\\times\\left(",Mul,"\\right)}",dupmat(M)],Lout);
2006: }else{
2007: if(Mul==1)
2008: mycat0([Top+"line",J+1, Lins[Sgn],JJ+1,"\n",M,"\n\n"],0);
2009: else
2010: mycat0([Top+"line",J+1, Lins[Sgn],JJ+1," * (",Mul,")\n",M,"\n\n"],0);
2011: }
2012: }
2013: }
2014: }
2015: JJ++;
2016: }
2017: }
2018: }
2019: if(TeX){
2020: if(TeX==-2) return Lout;
2021: Lout=reverse(Lout);
2022: Br="\\allowdisplaybreaks";
2023: Cr="\\\\\n &";
2024: if(getopt(pages)==1) Cr=Br+Cr;
2025: if(type(S=getopt(cr))==7) Cr=S;
2026: if(type(Lim=getopt(lim))==1){
2027: if(Lim>0){
2028: if(Lim<30) Lim=TeXLim;
2029: Lim*=2;
2030: }
2031: }else Lim=0;
2032: Out = ltotex(Lout|opt=["cr","spts0"],str=1,cr=Cr,lim=Lim);
2033: if(TeX<0) return Out;
2034: dviout(Out|eq=(str_str(Cr,Br)>=0)?6:5,keep=(TeX==1)?0:1);
2035: }
2036: return M;
2037: }
2038:
2039: def mydet2(M)
2040: {
2041: S = size(M);
2042: Det = 1;
2043: MM = mtoupper(M,0);
2044: for(I = 0; I < S[0]; I++)
2045: Det = rmul(Det,MM[I][I]);
2046: return Det;
2047: }
2048:
2049: def myrank(MM)
2050: {
2051: S = size(MM);
2052: M = dupmat(MM);
2053: M = mtoupper(M,0);
2054: C = 0;
2055: for(I = K = 0; I < S[0]; I++){
2056: for(J = K; J < S[1]; J++){
2057: if(M[I][J] != 0){
2058: C++; K++;
2059: break;
2060: }
2061: }
2062: }
2063: return C;
2064: }
2065:
2066: def meigen(M)
2067: {
2068: F = getopt(mult);
2069: if(type(M)==4 || type(M)==5){
2070: II=length(M);
2071: for(R=[],I=II-1; I>=0; I--){
2072: if(F==1)
2073: R=cons(meigen(M[I]|mult=1),R);
2074: else
2075: R=cons(meigen(M[I]),R);
2076: }
2077: return R;
2078: }
2079: S = size(M)[0];
2080: P = mydet2(mgen(S,0,[zz],0)-M);
2081: return (F==1)?getroot(P,zz|mult=1):getroot(P,zz);
2082: }
2083:
2084: def transm(M)
2085: {
2086: if(type(M)!=6) M=s2m(M);
2087: if(type(M)!=6){
2088: errno(0);
2089: return 0;
2090: }
2091: L=[M];TeX="";
2092: Line=["\\text{line}","\\text{col}"];
2093: if((DVI=getopt(dviout)) !=1) DVI=0;
2094: else dviout(M);
2095: for(;;){
2096: print(L0=dupmat(car(L)));
2097: Sz=size(L0);
2098: S=keyin("? ");
2099: N=0;
2100: if(str_len(S)<=1){
2101: if(S=="q") return L;
2102: if(S=="t"){
2103: N=mtranspose(L0);
2104: TeX=["\\text{transpose}"];
2105: }
2106: else if(S=="f"){
2107: if(length(L)>1){
2108: if(LF!=0) TeX="";
2109: L=cdr(L);LF=L0;
2110: if(DVI){
2111: dviout0(-1);
2112: dviout(" ");
2113: }
2114: }
2115: }else if(S=="g"){
2116: if(LF!=0) N=LF;
2117: }else if(S=="0"){
2118: N=M;L=[];TeX=[];
2119: }else if(S=="a"||S=="A"){
2120: if(DVI&&S=="A") mtoupper(L0,0|step=1,opt=10,dviout=1);
2121: else mtoupper(L0,0|step=1,opt=10);
2122: }else{
2123: mycat0([
2124: "2,5 : line2 <-> line5",
2125: "2,5,-2 ; line2 += (-2)*line5",
2126: "2,2,-2 : line2 *= -2",
2127: "2,5,0 : line2 += (?)*line5 for reduction",
2128: "r,2,5 : raw2 <-> raw5 (r,2,5,-2 etc.)",
2129: "s,x,2 : subst(*,x,2)",
2130: "t : transpose",
2131: "0 : first matrix",
2132: "f : previous matrix",
2133: "g : next matrix (only after f)",
2134: "A : auto (a : without TeX)",
2135: "q : quit"
2136: ],1|delim="\n");
2137: }
2138: }else{
2139: FR=0;
2140: S=evals(S|del=",");
2141: if(S[0]==r){
2142: FR=1; S=cdr(S);
2143: }
2144: if((LL=length(S))>=2){
2145: S0=S[0]-1;S1=S[1]-1;
2146: if(S[0]==s){
2147: if(length(S)==3) N=subst(L0,S[1],S[2]);
2148: if(DVI) TeX=[S[1],"\\mapsto",S[2]];
2149: }else if(FR==0){
2150: if(S0<0 || S0>=Sz[0] || S1<0 || S1>=Sz[0]) continue;
2151: if(LL==2){
2152: N=rowx(L0,S0,S1);
2153: if(DVI) TeX=[Line[0],S[0],"\\ \\leftrightarrow\\ ",Line[0],S[1]];
2154: }else{
2155: S2=S[2];
2156: if(S0==S1){
2157: N=rowm(L0,S0,S2);
2158: if(DVI) TeX=[Line[0],S[0],"\\ \\times=\\ ",S2];
2159: }else{
2160: if(S2==0){
2161: for(J=0;J<Sz[1] && L0[S1][J]==0;J++);
2162: if(J<Sz[1]) S2=-L0[S0][J]/L0[S1][J];
2163: }
2164: if(S2!=0){
2165: N=rowa(L0,S0,S1,S2);
2166: if(DVI) TeX=[Line[0],S[0],"\\ +=\\ ",Line[0],
2167: S[1],"\\ \\times\\ (",S2,")"];
2168: }
2169: }
2170: }
2171: }else{
2172: if(S0<0 || S0>=Sz[1] || S1<0 && S1>=Sz[1]) continue;
2173: if(LL==2){
2174: N=colx(L0,S0,S1);
2175: if(DVI) TeX=[Line[1],S[0],"\\ \\leftrightarrow\\ ",Line[1],S[1]];
2176: }else{
2177: S2=S[2];
2178: if(S0==S1){
2179: N=colm(L0,S0,S2);
2180: if(DVI) TeX=[Line[1],S[0],"\\ \\times=\\ ",S[2]];
2181: }else{
2182: if(S2!=0){
2183: for(J=0; I1<Sz[0] && L0[I1][J]==0; J++);
2184: if(J<Sz[0]) S2=-L0[J][S0]/L0[J][S1];
2185: }if(S2!=0){
2186: N=cola(L0,S0,S1,S2);
2187: if(DVI) TeX=[Line[1],S[0],"\\ +=\\ ",Line[1],
2188: S[1],"\\ \\times\\ (",S2,")"];
2189: }
2190: }
2191: }
2192: }
2193: }
2194: }
2195: if(N!=0){
2196: LF=0;L=cons(N,L);
2197: if(DVI) dviout("\\xrightarrow{"+ltotex(TeX|opt="spts0",str=1)+"}"+mtotex(N)|eq=8);
2198: }
2199: }
2200: }
2201:
2202: def vgen(V,W,S)
2203: {
2204: IM=length(V);
2205: I=(getopt(opt)==0)?IM:0;
2206: for(SS=0; I<IM && (SS==0 || V[I]<=W[I]); I++)
2207: SS += W[I];
2208: if(I<IM){
2209: W[I]++;
2210: SS--;
2211: }else
2212: SS=S;
2213: for(J=0;J<I;J++){
2214: W[J] = (SS<=V[J])?SS:V[J];
2215: SS -= W[J];
2216: }
2217: if(SS>0)
2218: return -1;
2219: return(I==IM)?0:I;
2220: }
2221:
2222: def mmc(M,X)
2223: {
2224: Mt=getopt(mult);
2225: if(type(M)==7) M=os_md.s2sp(M);
2226: if(type(M)!=4||type(M[0])!=6) return 0;
2227: if(type(M[0])!=6){ /* spectre type -> GRS */
2228: G=s2sp(M|std=1);
2229: L=length(G);
2230: for(V=[],I=L-2;I>=0;I--) V=cons(makev([I+10]),V);
2231: V=cons(makev([L+9]),V);
2232: G=sp2grs(G,V,[1,length(G[0]),-1]|mat=1);
2233: if(getopt(short)!=0){
2234: V=append(cdr(V),[V[0]]);
2235: G=shortv(G,V);
2236: }
2237: R=chkspt(G|mat=1);
2238: if(Mt!=1) Mt=0;
2239: if(R[2]!=2 || R[3]!=0 || !(R=getbygrs(G,1|mat=1))) return 0;
2240: MZ=newmat(1,1);
2241: SS=length(G);
2242: if(Mt==1) SS=SS*(SS-1)/2;
2243: for(M=[],I=0;I<SS;I++) M=cons(MZ,M);
2244: for(RR=R; RR!=[]; RR=cdr(RR)){
2245: RT=car(RR)[0];
2246: if(type(RT)==4){
2247: if(RT[0]!=0) M=mmc(M,[RT[0]]|simplify=Simp);
2248: M=mmc(M,[cdr(RT)]);
2249: }
2250: }
2251: /* for(R=cdr(R);R!=[];R=cdr(R)) M=mmc(M,[car(R)[0]]|mult=Mt); */
2252: }
2253: if(X==0) return M;
2254: L=length(M);
2255: if((L>=6 && Mt!=0)||(L==3&&Mt==1)){
2256: for(SS=2,I=3; I<L; I+=(++SS));
2257: if(I!=L) return -1;
2258: Mt=1;
2259: }else{
2260: SS=L;Mt=0;
2261: }
2262: if(length(X)==SS+1){
2263: if(car(X)!=0&&(M=mmc(M,[car(X)]|mult=Mt))==0) return M;
2264: return mmc(M,cdr(X)|mult=Mt);
2265: }
2266: for(I=X;I!=[];I=cdr(I)) if(I[0]!=0) break;
2267: if(I==[]) return M;
2268: Simp=getopt(simplify);
2269: if(Simp!=0 && type(Simp)!=1) Simp=2;
2270: N=newvect(L);
2271: for(I=0;I<L;I++) N[I]=dupmat(M[I]);
2272: S=size(N[0])[0];
2273: if(type(X)==4&&length(X)>SS){ /* addition */
2274: for(I=0;I<SS;I++,X=cdr(X)) if(X[I] != 0) N[I] = radd(N[I],car(X));
2275: }
2276: if(length(X)!=1) return 0;
2277: X=X[0];
2278: MZ = newmat(S,S);
2279: MM = newvect(L);
2280: for(M1=J=0; J<SS; J++){
2281: for(R=[],I=SS-1; I>=0; I--){
2282: if(I==J){
2283: for(RR=[],K=SS-1; K>=0; K--)
2284: RR=cons((K==I)?N[K]+diagm(S,[X]):N[K],RR);
2285: R=cons(RR,R);
2286: }else R=cons([MZ],R);
2287: }
2288: MM[J]=newbmat(SS,SS,R);
2289: if(J==0) M1=MM[0];
2290: else M1=radd(M1,MM[J]);
2291: }
2292: /* middle convolution */
2293: for(P=0,Q=1;J<L;J++){ /* A_{P,Q} */
2294: for(R=[],I=SS-1; I>=0; I--){
2295: for(RR=[],K=SS-1;K>=0;K--){
2296: MT=MZ;
2297: if(I==K){
2298: MT=N[J];
2299: if(I==P) MT-=N[Q];
2300: else if(I==Q) MT-=N[P];
2301: }else if(I==P && K==Q) MT=N[Q];
2302: else if(I==Q && K==P) MT=N[P];
2303: RR=cons(MT,RR);
2304: }
2305: R=cons(RR,R);
2306: }
2307: MM[J]=newbmat(SS,SS,R);
2308: if(++Q==SS){
2309: P++;Q=P+1;
2310: }
2311: }
2312: for(R=[],I=SS-1; I>=0; I--){
2313: for(RR=[N[I]],J=0; J<I; J++) RR=cons(MZ,RR);
2314: R=cons(RR,R);
2315: }
2316: M0 = newbmat(SS,SS,R);
2317: KE = append(mykernel(M0|opt=1),mykernel(M1|opt=1));
2318: if(length(KE) == 0) return MM;
2319: KK = mtoupper(lv2m(KE),0);
2320: for(I=0;I<L;I++) MM[I] = mmod(MM[I],KK);
2321: if(Simp!=0) MM = mdsimplify(MM|type=Simp);
2322: return MM;
2323: }
2324:
2325: def lpgcd(L)
2326: {
2327: for(F=[]; L!=[]; L=cdr(L)){
2328: if((P=car(L))==0) continue;
2329: if(F==[]){
2330: F=fctr(P);
2331: S=length(F);
2332: S--;
2333: V=newvect(S);
2334: M=newvect(S);
2335: for(I=0; I<S; I++){
2336: M[I] = F[I+1][1];
2337: V[I] = F[I+1][0];
2338: }
2339: N=nm(ptozp(P|factor=1)[1]);
2340: continue;
2341: }
2342: N=igcd(ptozp(P|factor=1)[1],N);
2343: for(I=0; I<S; I++){
2344: for(Q=P,CT=0; CT<M[I]; CT++)
2345: if((Q=tdiv(Q,V[I])) == 0) break;
2346: if(CT<M[I]) M[I]=CT;
2347: }
2348: }
2349: if(F==[]) return 0;
2350: for(Q=N,I=0;I<S; I++){
2351: while(M[I]>0){
2352: Q *= V[I];
2353: M[I]--;
2354: }
2355: }
2356: return Q;
2357: }
2358:
2359: def mdivisor(M,X)
2360: {
2361: S=size(M=dupmat(M));
2362: XX=(type(X)==4||X==0)?X:[0,X];
2363: S0=S[0]; S1=S[1];
2364: if((Tr=getopt(trans))==1||Tr==2){
2365: Tr0=1;
2366: GR=mgen(S0,0,1,0); GC=mgen(S1,0,1,0);
2367: }else Tr=Tr0=0;
2368: /* 0,a,b : (a,b)->(1,1)
2369: 1 : (1,1) invertible
2370: 2,i,M : line 0,i by M
2371: 3,j,M : col 0,j by M
2372: 4,j : col 1 += col j
2373: 5,j,T : line j by T
2374: 6,j,T : col 1 += col j by T (non-com)
2375: 7,j : line 2<->j (non-com)
2376: */
2377: if(type(V=getopt(dviout))==1){
2378: if(type(XX)==4 && type(XX[0])>1) Var=[XX[1],"\\partial"];
2379: else Var=0;
2380: Tr=(abs(V)==3)?0:1;
2381: MM=dupmat(M);
2382: II=((S[0]>S[1])?S[1]:S[0])+1;
2383: if(abs(V)>1){
2384: Is1=Js1=S[0]+S[1];
2385: Is=Js=[0,[Is1]];
2386: }else{
2387: Is=[0,[Is1=S[0]]];Js=[0,[Js1=S[1]]];
2388: }
2389: VV=V;
2390: V=newvect(II);
2391: for(I=0;I<II;I++) V[I]=[];
2392: N=newbmat(2,2,[[M,mgen(S[0],0,[1],0)],[mgen(S[1],0,[1],0)]]);
2393: mdivisor(M,X|step=1,dviout=V);
2394: L=S[0]+S[1];
2395: if(Tr){
2396: NN=mperm(N,Is1,Js1);
2397: for(K=S[0];K<Is1;K++){
2398: for(L=S[1];L<Js1;L++)
2399: NN[K][L]=" ";
2400: }
2401: Out=[[mperm(NN,Is,Js)]];
2402: }
2403: for(I=1;I<II;I++){
2404: I0=I-1;
2405: if(V[I]==[]) continue;
2406: for(T=reverse(V[I]);T!=[];T=cdr(T)){
2407: St=[];
2408: C=car(R=car(T));
2409: if(C==0){
2410: N=mperm(N,(R[1]==0)?0:[[R[1]+I0,I0]],(R[2]==0)?0:[[R[2]+I0,I0]]);
2411:
2412: if(Tr){
2413: if(R[2]!=0) St=append(["C",I,"\\leftrightarrow C",R[2]+I],St);
2414: if(R[1]!=0){
2415: if(R[2]!=0) St=cons(",\\ ",St);
2416: St=append(["L",I,"\\leftrightarrow L",R[1]+I],St);
2417: }
2418: Out=cons(St,Out);
2419: }
2420: }else if(C==1){
2421: P=1/N[I0][I0];N[I0][I0]=1;
2422: if(P!=1){
2423: for(J=I;J<L;J++)
2424: N[I0][J]=muldo(P,N[I0][J],XX);
2425:
2426: if(Tr){
2427: St=append(["L",I,"\\leftarrow(",P,")","\\times L",I],St);
2428: Out=cons(St,Out);
2429: NN=mperm(N,Is1,Js1);
2430: for(K=S[0];K<Is1;K++){
2431: for(L=S[1];L<Js1;L++)
2432: NN[K][L]=" ";
2433: }
2434: Out=cons(["\\to",mperm(NN,Is,Js)],Out);
2435: }
2436: }
2437: for(F=0,J=I;J<S[0];J++){
2438: if((P=N[J][I0])==0) continue;
2439: F++;
2440: N[J][I0]=0;
2441: for(K=I;K<L;K++)
2442: N[J][K]=red(N[J][K]-muldo(P,N[I0][K],XX));
2443:
2444: }
2445: if(F){
2446: if(Tr){
2447: Out=cons(["Li\\ -\\!=\\ \\circ\\times L",I,"\\quad(i>",I,")"],Out);
2448: NN=mperm(N,Is1,Js1);
2449: for(K=S[0];K<Is1;K++){
2450: for(L=S[1];L<Js1;L++)
2451: NN[K][L]=" ";
2452: }
2453: Out=cons(["\\to",mperm(NN,Is,Js)],Out);
2454: }
2455: }
2456: for(F=0,J=I;J<S[1];J++){
2457: if((P=N[I0][J])==0) continue;
2458: F++;
2459: N[I0][J]=0;
2460: for(K=I;K<L;K++)
2461: N[K][J]=red(N[K][J]-muldo(N[K][I0],P,XX));
2462: }
2463: if(F&&Tr) Out=cons(["Cj\\ -\\!=\\ C",I,"\\times\\circ\\quad(j>",I,")"],Out);
2464: else continue;
2465: }else if(C==2){
2466: C=mat(N[I0],N[R[1]+I0]);C=muldo(R[2],C,XX);
2467: for(J=0;J<L;J++){
2468: N[I0][J]=C[0][J];N[R[1]+I0][J]=C[1][J];
2469: }
2470: if(Tr) Out=cons([dupmat(R[2]),"\\begin{pmatrix}L",I,"\\\\L",R[1]+I,
2471: "\\end{pmatrix}"],Out);
2472: }else if(C==3){
2473: C=newmat(L,2);
2474: for(J=0;J<L;J++){
2475: C[J][0]=N[J][I0];C[J][1]=N[J][R[1]+I0];
2476: }
2477: C=muldo(C,R[2],XX);
2478: for(J=0;J<L;J++){
2479: N[J][I0]=C[J][0];N[J][R[1]+I0]=C[J][1];
2480: }
2481: if(Tr) Out=cons(["\\begin{pmatrix}C",I,"&C",R[1]+I,"\\end{pmatrix}",
2482: dupmat(R[2])],Out);
2483: }else if(C==4){
2484: for(J=0;J<L;J++)
2485: N[J][I0]=red(N[J][I0]+N[J][R[1]+I0]);
2486: if(Tr) Out=cons(["C",I,"\\ +\\!=\\ C",R[1]+I],Out);
2487: }else if(C==5){
2488: for(J=0;J<L;J++)
2489: N[I0+R[1]][J]=red(R[2]*N[I0+R[1]][J]);
2490: if(Tr) Out=cons(["L",I+R[1],"\\leftarrow(", R[2],")\\times L",I+R[1]],
2491: Out);
2492: }else if(C==6){
2493: for(J=0;J<L;J++)
2494: N[J][I0]=N[J][I0]+muldo(N[J][I0+R[1]],R[2],XX);
2495: if(Tr) Out=cons(["C",I,"\\ +\\!=\\ C",I+R[1],"\\times(", R[2],")"],
2496: Out);
2497: }else if(C==7){
2498: mycat(["line",I+1,"\\leftrightarrow",R[1]+I]);
2499: for(J=0;J<L;J++){
2500: C=N[I][J];N[I][J]=N[R[1]+I0][J];N[R[1]+I0][J]=C;
2501: }
2502: if(Tr) Out=cons(["L",I+1,"\\leftrightarrow L",R[1]+I],Out);
2503: }
2504: if(Tr){
2505: NN=mperm(N,Is,Js);
2506: for(K=S[0];K<Is1;K++){
2507: for(L=S[1];L<Js1;L++)
2508: NN[K][L]=" ";
2509: }
2510: Out=cons(["\\to",NN],Out);
2511: }
2512: }
2513: }
2514: if(!Tr){
2515: NN=mperm(N,Is,Js);
2516: Out=[];
2517: }
2518: if(S[0]+S[1]==Is1){
2519: N1=mperm(NN,[0,[S[0]]],[S[1],[S[0]]]);
2520: N2=mperm(NN,[S[0],[S[1]]],[0,[S[1]]]);
2521: N3=mperm(NN,[0,[S[0]]],[0,[S[1]]]);
2522: R1=mdivisor(N1,X|trans=1)[1];
2523: R2=mdivisor(N2,X|trans=1)[1];
2524: if(Tr){
2525: Out=cons(["\\text{As a result,}"],Out);
2526: Out=cons([N3,"=",N1,MM,N2],Out);
2527: if(S[0]==S[1] && N3==mgen(S[0],0,1,0)){
2528: Out=cons(["=",muldo(N2,N1,XX),MM,"."],Out);
2529: }else{
2530: Out=cons([N1,"^{-1}=",R1,","],Out);
2531: Out=cons([N2,"^{-1}=",R2,"."],Out);
2532: }
2533: }else{
2534: Out=cons([N3,"=P",MM,"Q,"],Out);
2535: Out=cons(["P=",N1,"=",R1,"^{-1},"],Out);
2536: Out=cons(["Q=",N2,"=",R2,"^{-1}."],Out);
2537: }
2538: }
2539: Out = ltotex(reverse(Out)|opt=["cr","spts0"],str=1,cr=15,var=Var);
2540: if(S[0]+S[1]==Is1)
2541: Out=str_subst(Out,"\\texttt{ }","");
2542: if(VV>0){
2543: dviout(Out|eq=6);
2544: return NN;
2545: }
2546: return Out;
2547: }else if(type(V)!=5) V=0;
2548:
2549: if(type(St=getopt(step))!=1) St=0;
2550: for(FF=": start";;){
2551: if(St && V==0){
2552: if(Tr){
2553: mycat0([St,FF,"\n"],0);
2554: mycat([GR,"\n"]);mycat([M,"\n"]);mycat([GC,"\n"]);
2555: }
2556: else mycat0([St,FF,"\n",M,"\n"],0);
2557: }
2558: if(X==0||X==[0,0]){ /* search minimal non-zero element */
2559: for(K=F=I=0; I<S0; I++){
2560: for(J=0; J<S1; J++){
2561: if((P=abs(M[I][J]))!=0 && (K>P || K==0)){
2562: K=P; R=[I,J];
2563: }
2564: }
2565: }
2566: R=cons(K-1,[R]);
2567: }
2568: else R=mymindeg(M,XX[1]|opt=1);
2569: if(R[0]<0){ /*zero matrix */
2570: if(Tr) return [[],mgen(S0,0,1,0),mgen(S1,0,1,0)];
2571: return [];
2572: }
2573: R0=R[1][0];R1=R[1][1];
2574: if(R0!=0){
2575: M=rowx(M,0,R0);
2576: if(Tr) GR=rowx(GR,0,R0);
2577: }
2578: if(R1!=0){
2579: M=colx(M,0,R1);
2580: if(Tr) GC=colx(GC,0,R1);
2581: }
2582: if(St>0 && (R0!=0 || R1!=0))
2583: if(type(V)==5) V[St]=cons([0,R0,R1],V[St]);
2584: else if(Tr){
2585: mycat0([St,": (",R0+1,",",R1+1,") -> (1,1)\n"],0);
2586: mycat([GR,"\n"]);mycat([M,"\n"]);mycat([GC,"\n"]);
2587: }else mycat0([St,": (",R0+1,",",R1+1,") -> (1,1)\n",M,"\n"],0);
2588: if(R[0]==0){ /* (1,1) : invertible */
2589: if(type(V)==5) V[St]=cons([1],V[St]);
2590: P=M[0][0]; M[0][0]=1;
2591: for(J=0;J<S1;J++){ /* (1,1) -> 1 */
2592: if(J>0) M[0][J]= red(M[0][J]/P);
2593: if(Tr) GR[0][J]=red(GR[0][J]/P);
2594: }
2595: if(S0>1 && S1>1) N=newmat(S0-1,S1-1);
2596: else N=0;
2597: for(I=1;I<S0;I++){
2598: P=M[I][0]; M[I][0]=0;
2599: for(J=1;J<S1;J++)
2600: N[I-1][J-1]=M[I][J]=red(M[I][J] - muldo(P,M[0][J],XX));
2601: if(Tr){
2602: for(J=0;J<S0;J++)
2603: GR[I][J] = red(GR[I][J] -muldo(P,GR[0][J],XX));
2604: }
2605: }
2606: if(Tr){
2607: for(J=1;J<S1; J++){
2608: for(I=0;I<S1;I++) GC[I][J]=red(GC[I][J]-muldo(GC[I][0],M[0][J],XX));
2609: M[0][J]=0;
2610: }
2611: }
2612: if(St>0 && V==0){
2613: if(Tr){
2614: mycat0([St,": unit\n"],0);
2615: mycat([GR,"\n"]);mycat([M,"\n"]);mycat([GC,"\n"]);
2616: }
2617: else mycat0([St,": unit\n",M,"\n"],0);
2618: }
2619: if(N==0){
2620: if(!Tr) return [1];
2621: if(Tr==2){
2622: GR0=mdivisor(GR,X|trans=1)[1];
2623: GC0=mdivisor(GC,X|trans=1)[1];
2624: return [[1],GR,GC,GR0,GC0];
2625: }
2626: return [[1],GR,GC];
2627: }
2628: R=mdivisor(N,XX|dviout=V,trans=Tr0,step=(St>0)?St+1:St);
2629: if(!Tr) return cons(1,R);
2630: GR=muldo(newbmat(2,2,[[1],[0,R[1]]]),GR,XX);
2631: GC=muldo(GC,newbmat(2,2,[[1],[0,R[2]]]),XX);
2632: if(S0==S1 && countin(1,1,R[0])==S0-1){
2633: GR=muldo(GC,GR,XX); GC=mgen(S0,0,1,0);
2634: }
2635: if(Tr==2){
2636: GR0=mdivisor(GR,X|trans=1)[1];
2637: GC0=mdivisor(GC,X|trans=1)[1];
2638: return [cons(1,R[0]),GR,GC,GR0,GC0];
2639: }
2640: return [cons(1,R[0]),GR,GC];
2641: }
2642: for(I=1;I<S0;I++){
2643: if(M[I][0]!=0){
2644: /* Error! when mygcd(A,B,0) with A<=0 or B<=0 */
2645: R=mygcd(M[I][0],M[0][0],XX); /* R[0]=R[1]*M[I][0]+R[2]*M[0][0] */
2646: M[0][0]=R[0]; M[I][0]=0; /* 0=R[3]*M[I][0]+R[4]*M[0][0] */
2647: for(J=1;J<S1;J++){
2648: T=red(muldo(R[1],M[I][J],XX)+muldo(R[2],M[0][J],XX));
2649: M[I][J]=red(muldo(R[3],M[I][J],XX)+muldo(R[4],M[0][J],XX));
2650: M[0][J]=T;
2651: }
2652: if(Tr){
2653: for(J=0;J<S0;J++){
2654: T=red(muldo(R[1],GR[I][J],XX)+muldo(R[2],GR[0][J],XX));
2655: GR[I][J]=red(muldo(R[3],GR[I][J],XX)+muldo(R[4],GR[0][J],XX));
2656: GR[0][J]=T;
2657: }
2658: }
2659: if(St && V==0){
2660: mycat([" [",R[2],R[1],"]*"]);
2661: mycat([" [",R[4],R[3],"]"]);
2662: }
2663: if(type(V)==5) V[St]=cons([2,I,mat([R[2],R[1]],[R[4],R[3]])],V[St]);
2664: FF=": line 1 & "+rtostr(I+1); I=S0;
2665: }
2666: }
2667: if(I>S0) continue;
2668: for(J=1;J<S1;J++){
2669: if(M[0][J]!=0){
2670: R=mygcd(M[0][J],M[0][0],XX|rev=1); /* R[0]=M[0][J]*R[1]+M[0][0]*R[2] */
2671: M[0][0]=R[0]; M[0][J]=0; /* 0=M[0][J]*R[3]+M[0][0]*R[4] */
2672: for(I=1;I<S0;I++){
2673: T=red(muldo(M[I][J],R[1],XX)+muldo(M[I][0],R[2],XX));
2674: M[I][J]=red(muldo(M[I][J],R[3],XX)+muldo(M[I][0],R[4],XX));
2675: M[I][0]=T;
2676: }
2677: if(Tr){
2678: for(I=0;I<S1;I++){
2679: T=red(muldo(GC[I][J],R[1],XX)+muldo(GC[I][0],R[2],XX));
2680: GC[I][J]=red(muldo(GC[I][J],R[3],XX)+muldo(GC[I][0],R[4],XX));
2681: GC[I][0]=T;
2682: }
2683: }
2684: if(type(V)==5) V[St]=cons([3,J,mat([R[2],R[4]],[R[1],R[3]])],V[St]);
2685: FF=": column 1 & "+rtostr(J+1);J=S1;
2686: if(St && V==0){
2687: mycat([" *[",R[2],R[4],"]"]);
2688: mycat([" [",R[1],R[3],"]"]);
2689: }
2690: }
2691: }
2692: if(J>S1) continue;
2693: if(S0==1 || S1==1){
2694: P=M[0][0];
2695: if(X==0){
2696: if(P<0){
2697: P=-P;
2698: if(Tr) for(J=0;J<S0;J++) GR[0][J]=-GR[0][J];
2699: if(type(V)==5) V[St]=cons([5,0,-1],V[St]);
2700: }
2701: }else{
2702: P=nm(P);
2703: if((R=fctr(P)[0][0])!=1){
2704: P/=R;
2705: if(Tr) for(J=0;J<S0;J++) GR[0][J]/=R;
2706: if(type(V)==5) V[St]=cons([5,0,1/R],V[St]);
2707: }
2708: }
2709: if(!Tr) return [P];
2710: if(Tr==2){
2711: GR0=mdivisor(GR,X|trans=1)[1];
2712: GC0=mdivisor(GC,X|trans=1)[1];
2713: return [[P],GR,GC,GR0,GC0];
2714: }
2715: return [[P],GR,GC];
2716: }
2717: if(XX==0 || (type(XX)==4 && XX[0]==0)){ /* commutative case */
2718: P=M[0][0];
2719: for(I=1; I<S0; I++){
2720: for(J=1; J<S1; J++)
2721: if(divdo(M[I][J],P,XX)[1]!=0) break;
2722: if(J<S1){
2723: if(type(V)==5) V[St]=cons([4,J],V[St]);
2724: FF=": column 1 += col"+rtostr(J+1);
2725: for(I=1;I<S0;I++) M[I][0]=M[I][J];
2726: if(Tr) for(I=0;I<S1;I++) GC[I][0]=red(GC[I][0]+GC[I][J]);
2727: break;
2728: }
2729: }
2730: if(J<S1) continue;
2731: N=newmat(S0-1,S1-1);
2732: for(I=1;I<S0;I++)
2733: for(J=1;J<S1;J++) N[I-1][J-1]=red(M[I][J]/P);
2734: if(X==0){
2735: if(P<0) P=-P;
2736: if(Tr) for(J=0;J<S0;J++) GR[0][J]=-GR[0][J];
2737: }else{
2738: P=M[0][0];
2739: P=nm(P);
2740: P/=fctr(P)[0][0];
2741: if(Tr) for(J=0;J<S0;J++) GR[0][J]/=fctr(P)[0][0];
2742: }
2743: R=mdivisor(N,XX|dviout=V,trans=Tr0,step=(St>0)?St+1:St);
2744: RT=(Tr)?R[0]:R;
2745: for(RR=[],L=reverse(RT);L!=[];L=cdr(L))
2746: RR=cons(red(P*car(L)),RR);
2747: RR=cons(P,RR);
2748: if(!Tr) return RR;
2749: GR=muldo(newbmat(2,2,[[1],[0,R[1]]]),GR,XX);
2750: GC=muldo(GC,newbmat(2,2,[[1],[0,R[2]]]),XX);
2751: if(S0==S1 && countin(1,1,RR)==S0){
2752: GR=muldo(GC,GR,XX); GC=mgen(S0,0,1,0);
2753: }
2754: if(Tr==2){
2755: GR0=mdivisor(GR,X|trans=1)[1];
2756: GC0=mdivisor(GC,X|trans=1)[1];
2757: return [RR,GR,GC,GR0,GC0];
2758: }
2759: return [RR,GR,GC];
2760: } /* End of commutative case */
2761: for(I=1; I<S0; I++){
2762: for(J=1; J<S1; J++){
2763: if(M[I][J] != 0){
2764: for(T=1;I<S0;T*=XX[0]){
2765: R=divdo(muldo(M[I][J],T,XX),M[0][0],XX);
2766: if(R[1]!=0){
2767: if(type(V)==5) V[St]=cons([6,J,T],V[St]);
2768: FF=": column 1 += col"+rtostr((J+1)*T);
2769: if(I>1){
2770: M=rowx(M,1,I);
2771: if(Tr) GR=rowx(GR,1,I);
2772: if(type(V)==5) V[St]=cons([7,I],V[St]);
2773: FF+=", line 2<->"+rtostr(I+1);
2774: }
2775: for(I=1;I<S0;I++) M[I][0]=muldo(M[I][J],T,XX);
2776: if(Tr)
2777: for(I=1;I<S1;I++) GC[I][0]=red(GC[I][0]+muldo(GC[I][J],T,XX));
2778: I=S0+1; J=S1;
2779: break;
2780: }
2781: }
2782: }
2783: }
2784: if(I>S0) break;
2785: }
2786: if(I==S0) return []; /* zero matrix : never happen */
2787: }
2788: }
2789:
2790: def mdsimplify(L)
2791: {
2792: T=getopt(type);
2793: SS=0;
2794: if(type(L)==6){
2795: L=[L]; SS=1;
2796: }
2797: if(type(L)==5){
2798: SS=2;
2799: L = vtol(L);
2800: }
2801: M=car(L);
2802: S=size(M)[0];
2803: #if 0
2804: MN=newmat(S,S);
2805: MD=newmat(S,S);
2806: for(I=0;I<S;I++){
2807: for(J=0;J<S;J++){
2808: TN=0;TD=1;
2809: for(PL=L;PL!=[];PL=cdr(PL)){
2810: TM=red(car(PL)[I][J]);
2811: TN=lgcd([TN,nm(TM)]|pol=1);
2812: TD=llcm([TD,dn(TM)]|pol=1);
2813: }
2814: MN[I][J]=TM;
2815: MD[I][J]=TN;
2816: }
2817: }
2818: for(I=0;I<S;I++){
2819: for(J=0;J<S;J++){
2820: if(I==J||type(TD[I][J])<2||type(TN[J][I])<2) continue;
2821: for(FC=cdr(fctr(TD[I][J]));FC!=[];){
2822: TFC=car(FC);
2823: if(type(red(TN[J][I]/TFC[0]))>2) continue;
2824: }
2825: }
2826: }
2827: #endif
2828: DD=newvect(S);
2829: for(I=0; I<S; I++){
2830: LN=RN=[];
2831: LD=RD=1;
2832: for(LL=L; LL!=[]; LL=cdr(LL)){
2833: M = car(LL);
2834: for(J=0; J<S; J++){
2835: if(J==I) continue;
2836: if((MM=M[I][J]) != 0){
2837: LN = cons(nm(MM),LN);
2838: if(type(MM)==3 && tdiv(LD,P=dn(MM))==0)
2839: LD=tdiv(LD*P,gcd(LD,P));
2840: }
2841: if((MM=M[J][I]) != 0){
2842: RN = cons(nm(MM),RN);
2843: if(type(MM)==3 && tdiv(RD,P=dn(MM))==0)
2844: RD=tdiv(RD*P,gcd(RD,P));
2845: }
2846: }
2847: }
2848: if(T==1 || T==3) LQ=RD;
2849: else{
2850: P=lpgcd(LN);
2851: LQ=gcd(P,RD);
2852: if(P!=0) LQ *= nm(fctr(P)[0][0]);
2853: }
2854: if(T==1 || T==2) RQ=LD;
2855: else{
2856: P=lpgcd(RN);
2857: RQ=gcd(P,LD);
2858: if(P!=0) RQ *= nm(fctr(P)[0][0]);
2859: }
2860: if((P=gcdz(LQ,RQ))!=1){
2861: LQ = red(LQ/P); RQ=red(RQ/P);
2862: }
2863: DD[I]=red(LQ/RQ);
2864: if(LQ!=1 || RQ!=1){
2865: for(LA=[],LL=L; LL!=[]; LL=cdr(LL)){
2866: M = car(LL);
2867: for(J=0; J<S; J++){
2868: if(I!=J){
2869: if(LQ!=1){
2870: M[I][J] = red(M[I][J]/LQ);
2871: M[J][I] = red(M[J][I]*LQ);
2872: }
2873: if(RQ!=1){
2874: M[J][I] = red(M[J][I]/RQ);
2875: M[I][J] = red(M[I][J]*RQ);
2876: }
2877: }
2878: }
2879: }
2880: }
2881: }
2882: if(SS==2) L=ltov(L);
2883: if(SS==1) L=L[0];
2884: if(getopt(show)==1) L=[L,DD];
2885: return L;
2886: }
2887:
2888: def m2mc(M,X)
2889: {
2890: if(type(M)<2){
2891: mycat([
2892: "m2mc(m,t) or m2mc(m,[t,s])\t Calculation of Pfaff system of two variables\n",
2893: " m : list of 5 residue mat. or GRS/spc for rigid 4 singular points\n",
2894: " t : [a0,ay,a1,c], swap, GRS, GRSC, sp, irreducible, pair, pairs, Pfaff, All\n",
2895: " s : TeX, dviout, GRSC\n",
2896: " option : swap, small, simplify, operator, int\n",
2897: " Ex: m2mc(\"21,21,21,21\",\"All\")\n"
2898: ]);
2899: return 0;
2900: }
2901: if(type(M)==7) M=s2sp(M);
2902: if(type(X)==7) X=[X];
2903: Simp=getopt(simplify);
2904: if(Simp!=0 && type(Simp)!=1) Simp=2;
2905: Small=(getopt(small)==1)?1:0;
2906: if(type(M[0])==4){
2907: if(type(M[0][0])==1){ /* spectral type */
2908: XX=getopt(dep);
2909: if(type(XX)!=4 || type(XX[0])>1) XX=[1,length(M[0])];
2910: M=sp2grs(M,[d,a,b,c],[XX[0],XX[1],-2]|mat=1);
2911: if(XX[0]>1 && XX[1]<2) XX=[XX[0],2];
2912: if(getopt(int)!=0){
2913: T=M[XX[0]-1][XX[1]-1][1];
2914: for(V=vars(T);V!=[];V=cdr(V)){
2915: F=coef(T,1,car(V));
2916: if(type(F)==1 && dn(F)>1)
2917: M = subst(M,car(V),dn(F)*car(V));
2918: }
2919: }
2920: V=vars(M);
2921: if(findin(d1,V)>=0 && findin(d2,V)<0 && findin(d3,V)<0)
2922: M=subst(M,d1,d);
2923: }
2924: RC=chkspt(M|mat=1);
2925: if(RC[2] != 2 || RC[3] != 0){ /* rigidity idx and Fuchs cond */
2926: erno(0);return 0;
2927: }
2928: R=getbygrs(M,1|mat=1);
2929: if(getopt(anal)==1) return R; /* called by mc2grs() */
2930: Z=newmat(1,1,[[0]]);
2931: N=[Z,Z,Z,Z,Z];
2932: for(RR=R; RR!=[]; RR=cdr(RR)){
2933: RT=car(RR)[0];
2934: if(type(RT)==4){
2935: if(RT[0]!=0) N=m2mc(N,RT[0]|simplify=Simp);
2936: N=m2mc(N,[RT[1],RT[2],RT[3]]|simplify=Simp);
2937: }
2938: }
2939: if(type(X)==4 && type(X[0])==7)
2940: return m2mc(N,X|keep=Keep,small=Small);
2941: return N;
2942: }
2943: if(type(X)==4 && type(X[0])==7){
2944: Keep=(getopt(keep)==1)?1:0;
2945: if(X[0]=="All"){
2946: dviout("Riemann scheme"|keep=1);
2947: m2mc(M,[(findin("GRSC",X)>=0)?"GRSC":"GRS","dviout"]|keep=1);
2948: dviout("Spectral types : "|keep=1);
2949: m2mc(M,["sp","dviout"]|keep=1);
2950: dviout("\\\\\nBy the decompositions"|keep=1);
2951: R=m2mc(M,["pairs","dviout"]|keep=1);
2952: for(R0=R1=[],I=1; R!=[]; I++, R=cdr(R)){
2953: for(S=0,RR=car(R)[1][0];RR!=[]; RR=cdr(RR)) S+=RR[0];
2954: if(S==0) R0=cons(I,R0);
2955: else if(S<0) R1=cons(I,R1);
2956: }
2957: S="irreducibility\\ $"+((length(R0)==0)?"\\Leftrightarrow":"\\Leftarrow")
2958: +"\\ \\emptyset=\\mathbb Z\\cap$";
2959: dviout(S|keep=1);
2960: m2mc(M,["irreducible","dviout"]|keep=1);
2961: if(R0!=[])
2962: dviout(ltotex(reverse(R0))|eq=0,keep=1,
2963: title="The following conditions may not be necessary for the irreducibility.");
2964: if(R1!=[])
2965: dviout(ltotex(reverse(R1))|eq=0,keep=1,title="The following conditions can be omitted.");
2966: if(getopt(operator)!=0){
2967: dviout("The equation in a Pfaff form is"|keep=1);
2968: m2mc(M,["Pfaff","dviout"]|keep=Keep,small=Small);
2969: }
2970: else if(Keep!=1) dviout(" ");
2971: return M;
2972: }
2973: Show=0;
2974: if(length(X)>1){
2975: if(X[1]=="dviout") Show=2;
2976: if(X[1]=="TeX") Show=1;
2977: }
2978: if(X[0]=="GRS"||X[0]=="GRSC"||X[0]=="sp"){
2979: Y=radd(-M[0],-M[1]-M[2]);
2980: if(X[0]!="GRSC"){
2981: L=meigen([M[0],M[1],M[2],M[3],M[4],Y,radd(-M[1],-M[3]-M[4]),radd(Y,-M[3]-M[4])]|mult=1);
2982: if(X[0]=="sp"){
2983: L=chkspt(L|opt="sp");
2984: V=[L[1],L[0],L[2],L[5]]; W=[L[1],L[3],L[4],L[6]];
2985: if(Show==2) dviout(s2sp(V)+" : "+s2sp(W)|keep=Keep);
2986: return [V,W];
2987: }
2988: S="x=0&x=y&x=1&y=0&y=1&x=\\infty&y=\\infty&x=y=\\infty\\\\\n";
2989: }else{
2990: L=meigen([M[0],M[1],M[2],M[3],M[4],Y,radd(-M[1],-M[3]-M[4]),radd(Y,-M[3]-M[4]),
2991: radd(M[0],M[1]+M[3]),radd(M[1],M[2]+M[4])]|mult=1);
2992: S="x=0&x=y&x=1&y=0&y=1&x=\\infty&y=\\infty&x=y=\\infty&x=y=0&x=y=1\\\\\n";
2993: }
2994: T=ltotex(L|opt="GRS",pre=S,small=Small);
2995: if(Show==2) dviout(T|eq=0,keep=Keep);
2996: if(Show==1) L=T;
2997: return L;
2998: }
2999: if(X[0]=="Pfaff"){
3000: S=ltotex(M|opt=["Pfaff",u,x,x-y,x-1,y,y-1],small=Small);
3001: if(Show==2) dviout(S|eq=0,keep=Keep);
3002: return S;
3003: }
3004: if(X[0]=="irreducible"){
3005: L=meigen([M[0],M[1],M[2],radd(-M[0],-M[1]-M[2])]|mult=1);
3006: S=getbygrs(L,10|mat=1);
3007: if(Show==2) dviout(ltotex(S)|eq=0,keep=Keep);
3008: return S;
3009: }
3010: if(X[0]=="pairs"||X[0]=="pair"){
3011: L=meigen([M[0],M[1],M[2],radd(-M[0],-M[1]-M[2])]|mult=1);
3012: S=chkspt(L|opt=0);
3013: V=(Show==2)?1:0;
3014: S=sproot(L,X[0]|dviout=V,keep=Keep);
3015: return S;
3016: }
3017: if(X[0]=="swap"){
3018: Swap=getopt(swap);
3019: if(type(Swap)<1 || Swap==1)
3020: return newvect(5,[M[3],M[1],M[4],M[0],M[2]]);
3021: if(Swap==2)
3022: return newvect(5,[radd(M[0],M[1]+M[3]),M[4],M[2],radd(-M[1],-M[3]-M[4]),M[1]]);
3023: if(type(Swap)==4 && length(Swap)==3){
3024: MX=radd(-M[0],-M[1]-M[2]); MY=radd(-M[3],-M[1]-M[4]);
3025: if(Swap[0]==1){
3026: MX0=M[2];MY0=M[4];
3027: }
3028: else if(Swap[0]==2){
3029: MX0=MX;MY0=MY;
3030: }else{
3031: MX0=M[0];MY0=M[3];
3032: }
3033: if(Swap[1]==1){
3034: MX1=M[2];MY1=M[4];
3035: }
3036: else if(Swap[1]==2){
3037: MX1=MX;MY1=MY;
3038: }else{
3039: MX1=M[0];MY1=M[3];
3040: }
3041: return newvect(5,MX0,M[1],MX1,MY0,MY1);
3042: }
3043: }
3044: return 0;
3045: }
3046: if(getopt(swap)==1)
3047: return m2mc(m2mc(m2mc(M,"swap"),X),"swap");
3048: N=newvect(5);
3049: for(I=0;I<5;I++)
3050: N[I]=M[I];
3051: S=size(N[0])[0];
3052: if(type(X)==4){
3053: for(I=0;I<3;I++){
3054: if(X[I] != 0)
3055: N[I] = radd(N[I],X[I]);
3056: }
3057: if(length(X)==3) return N;
3058: X=X[3];
3059: }
3060: MZ = newmat(S,S);
3061: ME = mgen(S,0,[X],0);
3062: MM = newvect(5);
3063: MM[0] = newbmat(3,3, [[N[0]+ME,N[1],N[2]], [MZ], [MZ]]);
3064: MM[1] = newbmat(3,3, [[MZ], [N[0],N[1]+ME,N[2]], [MZ]]);
3065: MM[2] = newbmat(3,3, [[MZ], [MZ], [N[0],N[1],N[2]+ME]]);
3066: MM[3] = newbmat(3,3, [[N[3]+N[1],-N[1]], [-N[0],radd(N[0],N[3])], [MZ,MZ,N[3]]]);
3067: MM[4] = newbmat(3,3, [[N[4]], [MZ,N[4]+N[2],-N[2]], [MZ,-N[1],radd(N[4],N[1])]]);
3068: M0 = newbmat(3,3, [[N[0]], [MZ,N[1]], [MZ,MZ,N[2]]]);
3069: M1 = radd(MM[0],MM[1]+MM[2]);
3070: KE = append(mykernel(M0|opt=1),mykernel(M1|opt=1));
3071: if(length(KE) == 0) return MM;
3072: KK = mtoupper(lv2m(KE),0);
3073: for(I=0;I<5;I++)
3074: MM[I] = mmod(MM[I],KK);
3075: if(Simp!=0) MM = mdsimplify(MM|type=Simp);
3076: return MM;
3077: }
3078:
3079: def easierpol(P,X)
3080: {
3081: if(type(X) == 4){
3082: for( Y = [] ; X != []; X = cdr(X) )
3083: Y = cons([0,car(X)], Y);
3084: }else
3085: Y = [0,X];
3086: return rede(P,Y);
3087: }
3088:
3089: def l2p(L,V)
3090: {
3091: if(type(L)==4){
3092: for(S=I=0;L!=[];L=cdr(L),I++)
3093: S+=car(L)*V^I;
3094: return S;
3095: }else if(type(L)==5){
3096: for(S=0,I=size(L)-1;I>=0;I--)
3097: S+=L[I]*V^I;
3098: return S;
3099: }else{
3100: if(type(D=getopt(size))==1) D--;
3101: else D=mydeg(L,V);
3102: for(S=[];D>=0;D--)
3103: S=cons(mycoef(L,D,V),S);
3104: return S;
3105: }
3106: }
3107:
3108: def paracmpl(L,V)
3109: {
3110: if(type(L)==4) L=ltov(L);
3111: S=length(L);
3112: Lim=getopt(lim);Low=getopt(low);
3113: if((F=type(L[0]))>3){
3114: SV=length(L[0]);
3115: V0=makenewv(L);
3116: for(LL=[];S>0;S--)
3117: LL=cons(l2p(L[S-1],V0),LL);
3118: G=paracmpl(LL,V|option_list=getopt());
3119: H=(Lim==1)?G:G[0];
3120: for(HH=[];H!=[];H=cdr(H)){
3121: HT=l2p(car(H),V0|size=SV);
3122: if(F==5) HT=ltov(HT);
3123: HH=cons(HT,HH);
3124: }
3125: H=reverse(HH);
3126: return (Lim==1)?H:[H,G[1]];
3127: }
3128: H=newvect(S);D=newvect(S);
3129: for(Dn=1,I=0;I<S;I++){
3130: P=dn(L[I]=red(L[I]));
3131: Dn=red(Dn*P/gcd(Dn,P));
3132: }
3133: if(Dn!=1){
3134: for(I=0;I<S;I++) L[I]=red(Dn*L[I]);
3135: }
3136: G=diagm(S,[1]);
3137: if(type(V)<4) V=[V];
3138: VV=lsort(vars(L),V,1);
3139: V=car(V);
3140: for(I=0;I<S;I++){
3141: P=L[I];
3142: for(J=0,C=P;J<I;J++){
3143: if(D[J]!=[]){
3144: C=mycoef(C,DT,VV);
3145: P-=C*H[J];
3146: G=cola(G,I,J,-C);
3147: }
3148: }
3149: if(P==0){
3150: D[I]=[];continue;
3151: }
3152: P0=nm(red(P));
3153: K=mymindeg(P0,V);
3154: C=mycoef(P0,K,V);
3155: if(K>0){
3156: P=red(P/V^K);
3157: G=colm(G,I,1/V^K);
3158: }
3159: for(DT=[],VT=VV;VT!=[];VT=cdr(VT)){
3160: K=(Low==1)?mymindeg(C,car(VT)):mydeg(C,car(VT));
3161: C=mycoef(C,K,car(VT));
3162: DT=cons(K,DT);
3163: }
3164: D[I]=DT=reverse(DT);
3165: for(C=P,VT=VV;VT!=[];VT=cdr(VT),DT=cdr(DT))
3166: C=mycoef(C,car(DT),car(VT));
3167: H[I]=P=red(P/C);
3168: G=colm(G,I,1/C);
3169: }
3170: if(Dn!=1){
3171: for(I=0;I<S;I++){
3172: TH=red(H[I]/Dn);
3173: F=fctr(dn(TH));F=cdr(F);
3174: if(Lim!=1||subst(Dn,V,0)==0){
3175: for(;F!=[];F=cdr(F)){
3176: if(lsort(vars(car(F)[0]),VV,2)==[]){
3177: C=car(F)[0]^car(F)[1];
3178: TH=red(TH*C);
3179: G=colm(G,I,C);
3180: }
3181: }
3182: }
3183: H[I]=TH;
3184: }
3185: }
3186: H=vtol(H);
3187: if(Lim==1){
3188: H=subst(H,V,0);
3189: return map(red,H);
3190: }
3191: return [H,map(red,G)];
3192: }
3193:
3194: def mykernel(M)
3195: {
3196: if(getopt(opt) == 1)
3197: M = mtranspose(M);
3198: S = size(M);
3199: R = [];
3200: MM = mtoupper(M,-1);
3201: for(I = S[0]-1; I >= 0; I--){
3202: for(J = S[1]-1; J >= 0; J--){
3203: if(MM[I][J] != 0)
3204: return R;
3205: }
3206: P = easierpol(MM[I][S[1]],zz);
3207: RR = newvect(S[0]);
3208: for(J = 0; J < S[0]; J++)
3209: RR[J] = mycoef(P,J,zz);
3210: R = cons(RR,R);
3211: }
3212: return R;
3213: }
3214:
3215: def myimage(M)
3216: {
3217: if(getopt(opt) == 1)
3218: M = mtranspose(M);
3219: S = size(M);
3220: V = [];
3221: M0 = newvect(S[1]);
3222: M = mtoupper(M,0|opt=1);
3223: for(I = S[0]-1; I >= 0; I--)
3224: if(M0 != M[I])
3225: V = cons(vtozv(M[I])[0], V);
3226: return V;
3227: }
3228:
3229: def mymod(V,L)
3230: {
3231: Opt = getopt(opt);
3232: S = length(V);
3233: VP = newvect(S);
3234: if(type(L)==6)
3235: L=m2lv(L);
3236: CT = length(L);
3237: for(LT = L; LT != []; LT = cdr(LT)){
3238: for(VT = car(LT), I = 0; I < S; I++)
3239: if(VT[I] != 0) break;
3240: if(I >= S){
3241: CT--;
3242: continue;
3243: }
3244: VP[I] = 1;
3245: MI = -red(V[I]/VT[I]);
3246: if(MI != 0)
3247: V = radd(V,rmul(MI,VT));
3248: }
3249: if(Opt==1){
3250: for(I = 0; I < S; I++)
3251: if(V[I] != 0)
3252: return 1;
3253: return 0;
3254: }
3255: if(Opt==2){
3256: W=newvect(S-CT);
3257: for(CC = I = 0; I < S; I++){
3258: if(VP[I]==0) W[CC++] =V[I];
3259: }
3260: return W;
3261: }
3262: return V;
3263: }
3264:
3265: def mmod(M,L)
3266: {
3267: S=size(M)[1];
3268: MM=mtranspose(M);
3269: VP = newvect(S);
3270: if(type(L)==6)
3271: L=m2lv(L);
3272: for(CT = 0, LT = L; LT != []; LT = cdr(LT)){
3273: for(VT = car(LT), I = 0; I < S; I++){
3274: if(VT[I] != 0){
3275: VP[I] = 1;
3276: break;
3277: }
3278: }
3279: }
3280: if(getopt(opt)==1)
3281: NE=1;
3282: for(D=I=0; I<S; I++){
3283: if(NE != 1 && VP[I] == 1) continue;
3284: T = mymod(MM[I],L|opt=2);
3285: if(D==0){
3286: K=length(T);
3287: MN=newmat((NE==1)?S:K,K);
3288: }
3289: for(J=0;J<K;J++)
3290: MN[J][D]=T[J];
3291: D++;
3292: }
3293: return MN;
3294: }
3295:
3296: def llsize(V)
3297: {
3298: for(I=J=0;V!=[];V=cdr(V),I++)
3299: if(length(car(V))>J) J=length(car(V));
3300: return [I,J];
3301: }
3302:
3303: def llbase(VV,L)
3304: {
3305: S = length(VV);
3306: V = dupmat(VV);
3307: if(type(V) == 4)
3308: V = ltov(V);
3309: T = length(L);
3310: for(I = 0; I < S; I++)
3311: V[I] = nm(red(V[I]));
3312: LV = 0;
3313: for(J = 0; J < T; J++){
3314: X = var(L[J]); N = deg(L[J],X);
3315: for(I = LV; I < S; I++){
3316: if((C2=coef(V[I],N,X)) != 0){
3317: if(I > LV){
3318: Temp = V[I];
3319: V[I] = V[LV];
3320: V[LV] = Temp;
3321: }
3322: for(I = 0; I < S; I++){
3323: if(I == LV || (C1 = coef(V[I],N,X)) == 0)
3324: continue;
3325: Gcd = gcd(C1,C2);
3326: V[I] = V[I]*tdiv(C2,Gcd)-V[LV]*tdiv(C1,Gcd);
3327: }
3328: LV++;
3329: }
3330: }
3331: }
3332: return V;
3333: }
3334:
3335: def lsort(L1,L2,T)
3336: {
1.10 takayama 3337: C1=getopt(c1);C2=getopt(c2);
1.8 takayama 3338: if(type(T)==4){
3339: K=T;
1.10 takayama 3340: if(length(T)>0){
3341: T=K[0];
3342: K=cdr(K);
1.12 takayama 3343: }else T=0;
1.8 takayama 3344: }else K=0;
1.10 takayama 3345: if(type(TT=T)==7)
3346: T = findin(T,["cup","setminus","cap","reduce","sum","subst"]);
3347: if(type(L2)==7&&T<0)
3348: T=findin(TT,["put","get","sub"]);
3349: if(K){ /* [[..],..] */
3350: if(K!=[]) KN=K[0];
3351: if(L2==[]||L2=="sort"){ /* sort or deduce duplication */
3352: if((T!=0&&T!=3)||length(K)!=1) return L1;
1.8 takayama 3353: if(KN<0){
3354: KN=-KN-1;
3355: F=-1;
3356: }else F=1;
3357: L1=msort(L1,[F,0,KN]);
1.10 takayama 3358: if(T==3){
1.8 takayama 3359: R=[car(L1)];L1=cdr(L1);
3360: for(;L1!=[];L1=cdr(L1)){
3361: if(car(L1)[KN]!=car(R)[KN]) R=cons(car(L1),R);
3362: }
3363: L1=reverse(R);
3364: }
3365: return L1;
1.10 takayama 3366: }else if((L2==0||L2=="col")&&type(C1)==4){
1.8 takayama 3367: if(T==0||T==1){ /* extract or delete columns */
3368: for(R=[];L1!=[];L1=cdr(L1)){
1.10 takayama 3369: if(T==1&&C1==[0]){ /* delete top column */
1.8 takayama 3370: R=cons(cdr(car(L1)),R);
3371: continue;
3372: }
1.10 takayama 3373: LT=car(L1);RT=[];
1.8 takayama 3374: if(T==0){
1.10 takayama 3375: for(CT=C1;CT!=[];CT=cdr(CT)) RT=cons(LT[car(CT)],RT);
1.8 takayama 3376: }else{
1.10 takayama 3377: for(I=0;LT!=[];I++,LT=cdr(LT))
1.8 takayama 3378: if(findin(I,C1)<0) RT=cons(car(LT),RT);
3379: RT=reverse(RT);
3380: }
3381: R=cons(RT,R);
3382: }
3383: return reverse(R);
3384: }
1.10 takayama 3385: }else if(type(L2)==1||type(L2)==7){
3386: if(L2==1||L2=="num"){
3387: if(T==4) T=3;
3388: I=(length(K)<2)?(-1):K[1];
3389: if(T==0||T==1||T==2||T==3){
3390: S=F=CT=0;R=[];
3391: if(K==[] || type((S=K[0]))==1 || S==0){
3392: if(T==0||T==1||T==2){
3393: for(J;L1!=[];L1=cdr(L1),J++){
3394: if(T==0) R=cons(cons(J+S,car(L1)),R);
3395: else if(T==1){
3396: for( ;C1!=[]; C1=cdr(C1))
3397: R=cons(L1[car(C1)],R);
3398: }else{
3399: if(findin(J,C1)<0) R=cons(car(L1),R);
3400: }
3401: }
3402: return reverse(R);
3403: }else if(T==3) return length(L1);
3404: }else{
3405: if(type(S)==2&&vtype(S)>2) F=1;
3406: else if(type(S)==4) F=2;
3407: else if(S=="+") F=3;
3408: else return L1;
3409: }
3410: for(R=[];L1!=[];L1=cdr(L1)){
3411: L1T=car(L1);
3412: if(F==1) V=call(S,(I<0)?L1T:L1T[I]);
3413: else if(F==2) V=calc((I<0)?L1T:L1T[I],S);
3414: else if(F==3){
3415: for(C=C1,V=0;C!=[];C=cdr(C))
3416: if(type(X=L1T[car(C)])==1) V+=X;
3417: }
3418: if(T==0) R=cons(cons(V,L1T),R);
3419: else if(T==1){
3420: if(V) R=cons(L1T,R);
3421: }else if(T==2){
3422: if(!V) R=cons(L1T,R);
3423: }else if(T==3){
3424: if(F==3) CT+=V;
3425: else if(V) CT++;
3426: }
3427: }
3428: return (T==3)?CT:reverse(R);
3429: }else if(TT=="col"){
3430: J=(length(K)>0)?car(K):0;
3431: I=length(car(L1))+J;
3432: for(V=[];I>J;)
3433: V=cons(--I,V);
3434: return cons(V,L1);
3435: }
3436: }else if(L2=="transpose") return mtranspose(L1);
1.12 takayama 3437: else if(L2=="subst"||L2=="adjust"){
3438: Null=(!K)?"":car(K);
1.17 takayama 3439: if(L2=="adjust") C1=[];
1.12 takayama 3440: R=lv2m(L1|null="");
1.10 takayama 3441: for(;C1!=[];C1=cdr(C1)) R[car(C1)[0]][car(C1)[1]]=car(C1)[2];
3442: return m2ll(R);
3443: }
3444: return L1;
3445: }else{ /* [[..],..], [[..],..] */
3446: if(type(L2[0])<4){
3447: for(R=[];L2!=[];L2=cdr(L2)) R=cons([car(L2)],R);
3448: L2=reverse(R);
3449: }
3450: if(TT=="sum") T=3;
3451: if(TT=="over") T=4;
3452: if(findin(T,[0,1,2,3,4,5])<0) return L1;
3453: if(T==4||T==5){
3454: if(type(C1)<2) C1=[C1];
3455: if(type(C2)<2) C2=[C2];
3456: }
1.8 takayama 3457: if(type(car(L2))!=4){
3458: for(R=[];L2!=[];L2=cdr(L2)) R=cons([car(L2)],R);
3459: R=reverse(R);
3460: if(length(K)==1) K=[K[0],0];
3461: C2=0;
3462: }
1.10 takayama 3463: L1=lsort(L1,"num",["put",0]); /* insert number */
3464: K0=(length(K)>0)?K[0]+1:1;
3465: K1=(length(K)>1)?K1=K[1]:0;
3466: L1=lsort(L1,"sort",[0,K0]);
3467: if(T<4&&type(C2)==4&&length(L2[0])>1){
3468: L2=lsort(L2,"col",["put"]|c1=cons(K1,C2)); /* add key and extract columns */
3469: C2=0;K1=0;
3470: }
3471: L2=lsort(L2,"sort",[0,K1]);
3472: for(R0=[],S=S1=length(L1[0]);S>0;S--) R0=cons("",R0);
3473: for(R1=[],S=length(L2[0]);S>0;S--) R1=cons("",R1);
3474: if(!K1&&T!=3) R1=cdr(R1);
3475: for(R=[];L1!=[];L1=cdr(L1)){
3476: while(L2!=[]&&car(L1)[K0]>car(L2)[K1]){
3477: if(T==3) R=cons(append(R0,car(L2)),R);
3478: L2=cdr(L2);
3479: }
3480: if(L2==[]||car(L1)[K0]<car(L2)[K1]){
3481: if(T!=2) R=cons((T==1||T>3||R1==[])?car(L1):append(car(L1),R1),R);
3482: }else if(T==0||T==2||T==3){
3483: if(R0==[]) R=append(car(L1),R);
3484: else R=cons(append(car(L1),(!K1&&T!=3)?cdr(car(L2)):car(L2)),R);
3485: L2=cdr(L2);
3486: }else if(T==4||T==5){
3487: V1=ltov(car(L1));V2=ltov(car(L2));
3488: for(D1=C1,D2=C2;D1!=[];D1=cdr(D1),D2=cdr(D2))
3489: if((I=V2[car(D2)])!=""||T==4) V1[car(D1)+1]=I;
3490: R=cons(vtol(V1),R);
3491: }
3492: }
3493: if(T==3){
3494: while(L2!=[]){
3495: R=cons(append(R0,car(L2)),R);
3496: L2=cdr(L2);
3497: }
3498: }
3499: R=lsort(R,"sort",["put",0]); /* original order */
3500: D=(((T==0||T==2)&&!K1)||T==3)?[0]:[0,S1+K1];
3501: R=lsort(R,0,[1]|c1=D); /* delete */
3502: if(type(C1)!=4||T==1||T==4||T==5) return R;
3503: C=[];S0=size(L1[0]);
3504: for(;C1!=[];C1=cdr(C1)) C=cons(car(C1),C);
3505: for(I=0;I<S0-S1;I++) C=cons(I+S1,C);
1.8 takayama 3506: C=reverse(C);
1.10 takayama 3507: return lsort(R,"col",[1]|c1=C);
1.8 takayama 3508: }
3509: }
1.10 takayama 3510: if(L2 == []){ /* [...] */
3511: if(T==8||TT=="count") return [length(L1),length(lsort(L1,[],1))];
3512: if(T==7||TT=="cut"){
3513: K=length(L1);
3514: if(C1<0) C1=K+C1;
3515: for(R=[],I=0;I<C1&&L1!=[];I++,L1=cdr(L1))
3516: R=cons(car(L1),R);
3517: for(S=[];L1!=[];L1=cdr(L1))
3518: S=cons(car(L1),S);
3519: return [reverse(R),reverse(S)];
3520: }
3521: if(T==2) return L2;
3522: if(T==3) return [L1,L2];
1.6 takayama 3523: L1 = ltov(L1); qsort(L1);
3524: if(T != 1)
3525: return vtol(L1);
3526: L3 = [];
3527: for(I = length(L1)-1; I >= 0; I--){
3528: if(I > 0 && L1[I] == L1[I-1])
3529: continue;
3530: L3 = cons(L1[I], L3);
3531: }
3532: return L3;
3533: }
1.10 takayama 3534: if(T==8||TT=="count"){
3535: K=length(lsort(L1,L2,3)[0]);
3536: R=[length(L2),length(L1)];
3537: L1 = lsort(L1,[],1);
3538: L2 = lsort(L2,[],1);
3539: R=append([length(L2),length(L1)],R);
3540: R=cons(length(lsort(L1,L2,2)),R);
3541: return reverse(cons(K,R));
3542: }
1.12 takayama 3543: if((T==9||TT=="cons")&&type(car(L1))==4){
3544: if(type(L2)!=4) L2=[L2];
3545: for(R=[];L1!=[];L1=cdr(L1)){
3546: R=cons(cons(car(L2),car(L1)),R);
3547: if(length(L2)>1) L2=cdr(L2);
3548: }
3549: return reverse(R);
3550: }
1.13 takayama 3551: if(T==10||TT=="cmp"){
3552: if(length(L1)!=length(L2)){
3553: mycat("Different length!");
3554: return 1;
3555: }
3556: R=[];
3557: if(type(car(L1))==4){
3558: for(U=[],I=0;L1!=[];I++,L1=cdr(L1),L2=cdr(L2)){
3559: if(length(S=car(L1))!=length(T=car(L2))){
3560: mycat(["Different size : line ",I]);
3561: return 0;
3562: }
3563: for(J=0;S!=[];S=cdr(S),T=cdr(T),J++)
3564: if(car(S)!=car(T)) U=cons([[I,J],car(S),car(T)],U);
3565: }
3566: if(U!=[]) R=cons(reverse(U),R);
3567: }else{
3568: for(I=0;L1!=[];L1=cdr(L1),L2=cdr(L2),I++)
3569: if(car(L1)!=car(L2)) R=cons([I,car(L1),car(L2)],R);
3570: }
3571: return reverse(R);
3572: }
3573: if(T==11||TT=="append"){
3574: if(type(car(L1))!=4) return append(L1,L2);
3575: for(R=[];L1!=[];L1=cdr(L1),L2=cdr(L2))
3576: R=cons(append(car(L1),car(L2)),R);
3577: return reverse(R);
3578: }
1.6 takayama 3579: if(T == 1 || T == 2){
3580: L1 = lsort(L1,[],1);
3581: L2 = lsort(L2,[],1);
3582: L3 = [];
3583: if(T == 1){
3584: while(L1 != []){
3585: if(L2 == [] || car(L1) < car(L2)){
3586: L3 = cons(car(L1), L3);
3587: L1 = cdr(L1);
3588: continue;
3589: }
3590: if(car(L1) > car(L2)){
3591: L2 = cdr(L2);
3592: continue;
3593: }
3594: L1 = cdr(L1); L2 = cdr(L2);
3595: }
3596: return reverse(L3);
3597: }
3598: if(T==2){
3599: while(L1 != [] && L2 != []){
3600: if(car(L1) != car(L2)){
3601: if(car(L1) <= car(L2))
3602: L1 = cdr(L1);
3603: else L2 = cdr(L2);
3604: continue;
3605: }
3606: while(car(L1) == car(L2))
3607: L1 = cdr(L1);
3608: L3 = cons(car(L2), L3);
3609: }
3610: return reverse(L3);
3611: }
3612: }
3613: if(T==3){
3614: L1 = qsort(L1); L2 = qsort(L2);
3615: L3 = L4 = [];
3616: while(L1 != [] && L2 != []){
3617: if(car(L1) == car(L2)){
3618: L1 = cdr(L1); L2 = cdr(L2);
3619: }else if(car(L1) < car(L2)){
3620: L3 = cons(car(L1),L3);
3621: L1 = cdr(L1);
3622: }else{
3623: L4 = cons(car(L2), L4);
3624: L2 = cdr(L2);
3625: }
3626: }
3627: L4 = append(reverse(L4),L2);
3628: L3 = append(reverse(L3),L1);
3629: return [L3,L4];
3630: }
3631: L1 = append(L1,L2);
3632: return lsort(L1,[],1);
3633: }
3634:
3635: def mqsub(X,Y)
3636: {
3637: for(L=LQS;L!=[];L=cdr(L)){
3638: F=(T=car(L))[0];M=(T=cdr(T))[0];
3639: X0=X;Y0=Y;
3640: for(T=cdr(T);T!=[];T=cdr(T)){
3641: X0=X0[car(T)];Y0=Y0[car(T)];
3642: }
3643: if(type(M)==1){
3644: if(M==3){
3645: X0=type(X0);Y0=type(Y0);
3646: }else if(M==4&&type(X0)<2&&type(Y0)<2){
3647: X0=abs(X0);Y0=abs(Y0);
3648: }else if(M==5){
3649: X0=str_len(rtostr(X0));Y0=str_len(rtostr(Y0));
3650: }else if(type(X0)==type(Y0)&&type(X0)>3&&type(X0)<7){
3651: if(M==1){
3652: X0=length(X0);Y0=length(Y0);
3653: }else if(M==2){
3654: LX=length(X0);LY=length(Y0);
3655: L0=(LX<LY)?LX:LY;
3656: for(I=0;;I++){
3657: if(I==L0){
3658: X0=LX;Y0=LY;break;
3659: }
3660: if(X0[I]==Y0[I]) continue;
3661: X0=X0[I];Y0=Y0[I];break;
3662: }
3663: }
3664: }
3665: }else if(type(M)==2){
3666: X0=(*M)(X0,Y0);Y0=0;
3667: }else if(type(M)==4&&length(M)==1){
3668: X0=(*car(M))(X0);Y0=(*car(M))(Y0);
3669: }
3670: if(X0==Y0) continue;
3671: return (X0<Y0)?-F:F;
3672: }
3673: return 0;
3674: }
3675:
3676: def msort(L,S)
3677: {
3678: if(type(S)!=4) return qsort(L);
3679: if(type(S[0])!=4) S=[S];
3680: LQS=S;
3681: return qsort(L,os_md.mqsub);
3682: }
3683:
1.22 takayama 3684: def lpair(A,B)
3685: {
3686: if(B==0){
3687: for(S=T=[];A!=[];A=cdr(A)){
3688: S=cons(car(A)[0],S);T=cons(car(A)[1],T);
3689: }
3690: return [reverse(S),reverse(T)];
3691: }else{
3692: for(R=[];A!=[];A=cdr(A),B=cdr(B))
3693: R=cons([car(A),car(B)],R);
3694: return reverse(R);
3695: }
3696: }
3697:
1.6 takayama 3698: def lmax(L)
3699: {
3700: if(type(L)==4){
3701: V=car(L);
3702: while((L=cdr(L))!=[])
3703: if(V < car(L)) V=car(L);
3704: return V;
3705: }else if(type(L)==5||type(L)==6)
3706: return lmax(m2l(L));
3707: return [];
3708: }
3709:
3710: def lmin(L)
3711: {
3712: if(type(L)==4){
3713: V=car(L);
3714: while((L=cdr(L))!=[])
3715: if(V > car(L)) V=car(L);
3716: return V;
3717: }else if(type(L)==5||type(L)==6)
3718: return lmin(m2l(L));
3719: return [];
3720: }
3721:
3722: def lgcd(L)
3723: {
3724: if(type(L)==4){
3725: F=getopt(poly);
3726: V=car(L);
3727: while((L=cdr(L))!=[]&&V!=1){
3728: if(V!=0)
3729: V=(F==1)?gcd(V,car(L)):igcd(V,car(L));
3730: }
3731: return V;
3732: }else if(type(L)==5||type(L)==6)
3733: return lgcd(m2l(L)|option_list=getopt());
3734: return [];
3735: }
3736:
3737: def llcm(L)
3738: {
3739: if(type(L)==4){
3740: F=getopt(poly);
3741: V=car(L);
3742: while((L=cdr(L))!=[]){
3743: if(V!=0){
3744: if((V0=car(L))!=0)
3745: V=(F==1)?red(V*V0/gcd(V,V0)):ilcm(V,V0);
3746: }
3747: else V=car(L);
3748: }
3749: if(F!=1&&V<0) V=-V;
3750: return V;
3751: }
3752: else if(type(L)==5||type(L)==6)
3753: return llcm(m2l(L)|option_list=getopt());
3754: return [];
3755: }
3756:
3757: def ldev(L,S)
3758: {
3759: M=abs(lmax(L));N=abs(lmin(L));
3760: if(M<N) M=N;
3761: for(C=0,LT=L;;C++){
3762: LT=ladd(LT,S,1);
3763: MT=abs(lmax(LT));NT=abs(lmin(LT));
3764: if(MT<NT) MT=NT;
3765: if(MT>=M) break;
3766: M=MT;
3767: }
3768: if(!C){
3769: for(C=0,LT=L;;C--){
3770: LT=ladd(LT,S,-1);
3771: MT=abs(lmax(LT));NT=abs(lmin(LT));
3772: if(MT<NT) MT=NT;
3773: if(MT>=M) break;
3774: M=MT;
3775: }
3776: }
3777: return [C,ladd(L,S,C)];
3778: }
3779:
3780: def lchange(L,P,V)
3781: {
3782: if(getopt(flat)==1&&type(P)==4){
3783: for(L=ltov(L);P!=[];P=cdr(P),V=cdr(V))
3784: L[car(P)]=car(V);
3785: return vtol(L);
3786: }
3787: if(type(P)==4){
3788: IP=car(P); P=cdr(P);
3789: }else{
3790: IP=P; P=[];
3791: }
3792: for(I=0, LL=[], LT=L; LT!=[]; I++,LT=cdr(LT)){
3793: if(I==IP){
3794: LL=cons((P==[])?V:lchange(car(LT),P,V),LL);
3795: }else
3796: LL=cons(car(LT),LL);
3797: }
3798: return reverse(LL);
3799: }
3800:
3801: def lsol(VV,L)
3802: {
3803: if(type(VV)<4 && type(L)==2)
3804: return red(L-VV/mycoef(VV,1,L));
3805: S = length(VV);
3806: T = length(L);
3807: V = llbase(VV,L);
3808: for(J = K = 0; J < T; J++){
3809: X = var(L[J]); N = deg(L[J],X);
3810: for(I = K; I < S; I++){
3811: if((C=mycoef(V[I], N, X)) != 0){
3812: V[I] = [L[J],red(X^N-V[I]/C)];
3813: K++;
3814: break;
3815: }
3816: }
3817: }
3818: return V;
3819: }
3820:
3821: def lnsol(VV,L)
3822: {
3823: LL=lsort(vars(VV),L,1);
3824: VV=ptol(VV,LL|opt=0);
3825: return lsol(VV,L);
3826: }
3827:
3828:
3829: def ladd(X,Y,M)
3830: {
1.22 takayama 3831: if(type(Y)==4) Y=ltov(Y);
1.6 takayama 3832: if(type(X)==4) X=ltov(X);
3833: return vtol(X+M*Y);
3834: }
3835:
3836: def mrot(X)
3837: {
1.22 takayama 3838: if(type(X)==4){
3839: if(getopt(deg)==1)
3840: X=[deval(@pi*X[0]/180),deval(@pi*X[1]/180),deval(@pi*X[2]/180)];
3841: if(getopt(conj)==1)
3842: return mrot([-X[2],-X[1],0])*mrot([X[0],X[1],X[2]]);
3843: if(X[1]==0){
3844: X=[X[0]+X[2],0,0];
3845: if(X[0]==0) return diagm(3,[1]);
3846: }
3847: if(X[0]!=0){
3848: M=mat([dcos(X[0]),-dsin(X[0]),0],[dsin(X[0]),dcos(X[0]),0],[0,0,1]);
3849: if(X[1]==0) return M;
3850: }
3851: N=mat([dcos(X[1]),0,-dsin(X[1])],[0,1,0],[dsin(X[1]),0,dcos(X[1])]);
3852: if(X[0]!=0) N=M*N;
3853: if(X[2]==0) return N;
3854: return N*mrot([X[2],0,0]);
3855: }
1.6 takayama 3856: if(getopt(deg)==1) X=@pi*X/180;
3857: X=deval(X);
1.22 takayama 3858: return mat([dcos(X),-dsin(X)],[dsin(X),dcos(X)]);
1.6 takayama 3859: }
3860:
3861: def m2v(M)
3862: {
3863: S = size(M);
3864: V = newvect(S[0]*S[1]);
3865: for(I = C = 0; I < S[0]; I++){
3866: MI = M[I];
3867: for(J = 0; J < S[1]; J++)
3868: V[C++] = MI[J];
3869: }
3870: return V;
3871: }
3872:
3873: def lv2m(L)
3874: {
3875: if(type(L)==5) L=vtol(L);
3876: II=length(L);
3877: for(J=1,T=L; T!=[]; T=cdr(T))
3878: if(length(car(T))>JJ) JJ=length(car(T));
3879: M = newmat(II,JJ);
3880: N = getopt(null);
3881: if(type(N)<0) N=0;
3882: for(I=0; I<II; I++){
3883: V=car(L); L=cdr(L);
3884: for(J=length(V);--J>=0;)
3885: M[I][J] = V[J];
3886: if(N!=0){
3887: for(J=length(V); J<JJ; J++)
3888: M[I][J]=N;
3889: }
3890: }
3891: return M;
3892: }
3893:
3894: def m2lv(M)
3895: {
3896: I=size(M)[0];
3897: for(N=[],I=size(M)[0];I-->0;)
3898: N=cons(M[I],N);
3899: return N;
3900: }
3901:
3902: def s2m(S)
3903: {
3904: if(type(S)==6) return S;
3905: if(type(S)==7){
3906: if(str_chr(S,0,"[")!=0) S=s2sp(S);
3907: else if(str_chr(S,0,",")>=0) return eval_str(S);
3908: else{
3909: for(L=LL=[],I=0; ; ){
3910: II=str_chr(S,I+2,"]");
3911: if(II<0) return 0;
3912: J=str_chr(S,I+2," ");
3913: while(str_chr(S,J+1," ")==J+1) J++;
3914: if(J>II-2 || J<0) J=II;
3915: V=eval_str(sub_str(S,I+1,J-1));
3916: L=cons(V,L);
3917: I=J;
3918: if(J==II){
3919: LL=cons(ltov(reverse(L)),LL);
3920: L=[];
3921: if((I=str_chr(S,II+1,"["))<0)
3922: return lv2m(reverse(LL));
3923: }
3924: }
3925: }
3926: }
3927: if(type(S)==5) S=vtol(S);
3928: if(type(S[0])==5) return lv2m(S);
3929: I=length(S);
3930: for(J=1,T=S; T!=[]; T=cdr(T))
3931: if(length(car(T))>J) J=length(car(T));
3932: return newmat(I,J,S);
3933: }
3934:
3935: def c2m(L,V)
3936: {
3937: if(type(Pow=getopt(pow))!=1){
3938: if(isvar(V)==1){
3939: for(Pow=0,LT=L;LT!=[];LT=cdr(LT)){
3940: if(mydeg(car(LT),V)>JJ) Pow=mydeg(car(LT),V);
3941: }
3942: JJ=Pow+1;
3943: }else{
3944: Pow=-1;
3945: JJ=length(V);
3946: }
3947: }else JJ=Pow+1;
3948: M=newmat(length(L),JJ);
3949: for(I=0;L!=[];L=cdr(L),I++){
3950: for(J=0;J<JJ;J++){
3951: LT=car(L);
3952: M[I][J]=(Pow>=0)?mycoef(LT,J,V):mycoef(LT,1,V[J]);
3953: }
3954: }
3955: return M;
3956: }
3957:
3958: #if 0
3959: def m2diag(M,N)
3960: {
3961: S = size(M);
3962: MM = mtoupper(M,N);
3963: for(I = S[0]-1; I >= 0; I--){
3964: for(J = 0; I < S[1]-N; I++){
3965: if(MM[I][J] != 0){
3966: P = MM[I][J];
3967: for(K = 0; K < I; K++){
3968: Q = -rmul(MM[K][J],1/P);
3969: MM[K][J] = 0;
3970: if(Q != 0){
3971: for(L = J+1; L < S[1]; L++){
3972: if(MM[I][L] != 0)
3973: MM[K][L] = radd(MM[K][L], rmul(MM[I][L],Q));
3974: }
3975: }
3976: }
3977: }
3978: }
3979: }
3980: return MM;
3981: }
3982: #endif
3983:
3984: def myinv(M)
3985: {
3986: S = size(M);
3987: if((T=S[0]) != S[1])
3988: return 0;
3989: MM = mtoupper(M,-T|opt=2);
3990: if(MM[T-1][T-1] != 1) return 0;
3991: return mperm(MM,0,[T,[T]]);
3992: }
3993:
3994: def madj(G,M)
3995: {
3996: H=myinv(G);
3997: if(type(M)==6)
3998: return rmul(rmul(G,M),H);
3999: if(type(M)==4||type(M)==5){
4000: L=length(M);
4001: N=newvect(L);
4002: for(I=0;I<L;I++){
4003: N[I]=rmul(rmul(G,M[I]),H);
4004: }
4005: if(type(N)==4) N=vtol(N);
4006: return N;
4007: }
4008: return -1;
4009: }
4010:
4011: def mpower(M,N)
4012: {
4013: if(type(M)<=3) return (red(M))^N;
4014: S = size(M);
4015: if(S[0] != S[1])
4016: return 0;
4017: if(N == 0) return mgen(S[0],0,[1],0);
4018: if(N < 0)
4019: return(mpower(myinv(M), -N));
4020: R = dupmat(M);
4021: V=1;
4022: for(V=1;;){
4023: if(iand(N,1)){
4024: V=map(red,R*V);
4025: N--;
4026: }
4027: if((N/=2)==0) break;
4028: R=map(red,R*R);
4029: }
4030: return V;
4031: }
4032:
4033: def texlen(S)
4034: {
4035: if(type(S)!=7) return 0;
4036: LF=I=J=0;
4037: LM=str_len(S);
4038: while((I=str_str(S,"\\frac{"|top=J))>=0){
4039: if(I>J) LF+=texlen(str_cut(S,J,I-1));
4040: I+=6;
4041: for(F=L=0,J=I;F<2 && J<LM-1;F++){
4042: for(C=1;C>0 && J<LM;){
4043: if((K0=str_char(S,J,"}"))<0) K0=LM;
4044: if((K1=str_char(S,J,"{"))<0) K1=LM;
4045: if(K0<0 && K1<0){
4046: J = str_len(S)-1;
4047: break;
4048: }
4049: if(K0<K1){
4050: J=K0+1; C--;
4051: }else{
4052: J=K1+1; C++;
4053: }
4054: }
4055: T=str_cut(S,I,J-1);
4056: if(F==0){
4057: I=J=K1+1;C=1;
4058: }else J=K0+1;
4059: if(type(T)==7 && (LL=texlen(T))>L) L=LL;
4060: }
4061: LF+=L;
4062: }
4063: if(J>0) S=str_cut(S,J,str_len(S)-1);
4064: if(S==0) return LF;
4065: S=ltov(strtoascii(S));
4066: L=LL=length(S);
4067: for(I=F=0; I<L; I++){
4068: if(S[I]==92) F=1;
4069: else if(F==1){
4070: if((S[I]>96 && S[I]<123)||(S[I]>64 && S[I]<91)) LL--;
4071: else F=0;
4072: }
4073: if(S[I]<=32||S[I]==123||S[I]==125||S[I]==94||S[I]==38) LL--; /* {}^& */
4074: else if(S[I]==95){
4075: LL--;
4076: if(I+2<L && S[I+2]==94) LL--; /* x_2^3 */
4077: else if(I+6<L && S[I+1]==123 && S[I+4]==125){ /* x_{11}^2 */
4078: if(S[I+5]==94 || (S[I+5]==125 && S[I+6]==94)) LL-- ; /* x_{11}}^2 */
4079: }
4080: }
4081: }
4082: return LL+LF;
4083: }
4084:
4085: def isdif(P)
4086: {
4087: if(type(P)<1 || type(P)>3) return 0;
4088: for(Var=[],R=vars(P);R!=[];R=cdr(R)){
4089: V0=rtostr(car(R));
4090: if(V0>"d" && V0<"e"){
4091: V=sub_str(V0,1,str_len(V0)-1);
4092: if(V>="a" && V<"{") Var=cons([strtov(V),strtov(V0)],Var);
4093: }
4094: }
4095: if(Var==[]) return 0;
4096: for(V=Var; V!=[]; V=cdr(V))
4097: if(ptype(P,car(V)[1])==3) return 0;
4098: return Var;
4099: }
4100:
4101: def texsp(P)
4102: {
4103: Q=strtoascii(P);
4104: if((J=str_char(Q,0,92))<0 || (C=Q[L=str_len(P)-1])==32||C==41||C==125)
4105: return P;
4106: for(;;){
4107: if((I=str_char(Q,J+1,92))<0) break;
4108: J=I;
4109: };
4110: for(I=J+1;I<L&&isalpha(Q[I]);I++);
4111: return(I==L)?P+" ":P;
4112: }
4113:
4114: def fctrtos(P)
4115: {
4116: /* extern TeXLim; */
4117:
4118: if(!chkfun("write_to_tb", "names.rr"))
4119: return 0;
4120:
4121: TeX = getopt(TeX);
4122: if(TeX != 1 && TeX != 2 && TeX != 3)
4123: TeX = 0;
4124: if((Dvi=getopt(dviout)==1) && TeX<2) TeX=3;
4125: if(TeX>0){
4126: Lim=getopt(lim);
4127: if(Lim!=0 && TeX>1 && (type(Lim)!=1||Lim<30)) Lim=TeXLim;
4128: else if(type(Lim)!=1) Lim=0;
4129: CR=(TeX==2)?"\\\\\n":"\\\\\n&";
4130: if(TeX==1 || Lim==0) CR="";
4131: else if((Pages=getopt(pages))==1) CR="\\allowdisplaybreaks"+CR;
4132: if(!chkfun("print_tex_form", "names.rr"))
4133: return 0;
4134: Small=getopt(small);
4135: }
4136: Dif=getopt(dif);
4137: Var=getopt(var);
4138: if(Lim>0 && type(Var)<2 && TeX!=1) Var=[strtov("0"),""];
4139: Dif=0;
4140: if(Var=="dif"){
4141: Dif=DV=1;
4142: }else if (Var=="dif0") Dif=1;
4143: else if(Var=="dif1") Dif=2;
4144: else if(Var=="dif2") Dif=3;
4145: if(Dif>0){
4146: for(Var=[],R=vars(P);R!=[];R=cdr(R)){
4147: V=rtostr(car(R));
4148: if(V>"d" && V<"e"){
4149: V=sub_str(V,1,str_len(V)-1);
4150: if(V>="a" && V<"{"){
4151: if(TeX>0){
4152: V=my_tex_form(strtov(V));
4153: if(Dif>=1){
4154: if(Dif==1){
4155: if(str_len(V)==1) V="\\partial_"+V;
4156: else V="\\partial_{"+V+"}";
4157: }
4158: Var=cons([car(R),V],Var);
4159: }
4160: else Var=cons([car(R)],Var);
4161: }else Var=cons([car(R)],Var);
4162: }
4163: }
4164: }
4165: if(TeX>0){
4166: if(length(Var)==1){
4167: if(DV==1 && str_len(Var[0][1])==10) Var=[[Var[0][0],"\\partial"]];
4168: }else if(DV==1){
4169: for(V=Var;V!=[];V=cdr(V)){
4170: VV=rtostr(car(V)[0]);
4171: if(VV<"dx0" || VV>= "dx:" || str_len(VV)>4) break;
4172: }
4173: if(V==[]){
4174: for(VT=[],V=Var;V!=[];V=cdr(V)){
4175: VV=str_cut(rtostr(car(V)[0]),2,3);
4176: if(str_len(VV)==1) VT=cons([car(V)[0],"\\partial_"+VV],VT);
4177: else VT=cons([car(V)[0],"\\partial_{"+VV+"}"],VT);
4178: }
4179: Var=reverse(VT);
4180: }
4181: }else
4182: if(Dif==2 && length(Var)>1) Dif=3;
4183: }
4184: if(Dif>0) Dif--;
4185: }
4186: if(type(Var)>1 && Var!=[]){ /* as a polynomial of Var */
4187: Add=getopt(add);
4188: if(type(Add)>0){
4189: if(type(Add)!=7){
4190: Add=my_tex_form(Add);
4191: if(str_char(Add,0,"-")>=0 || str_char(Add,0,"+")>=0) Add="("+Add+")";
4192: }
4193: if(str_char(Add,0,"(")!=0) Add = " "+Add;
4194: }else Add=0;
4195: if(type(Var)!=4) Var=[Var];
4196: if(length(Var)==2 && type(Var[1]) == 7)
4197: Var = [Var];
4198: for(VV=VD=[]; Var!=[];Var=cdr(Var)){
4199: VT=(type(car(Var))==4)?car(Var):[car(Var)];
4200: VT0=var(car(VT));
4201: VV=cons(VT0,VV);
4202: if(length(VT)==1){
4203: VD=cons((TeX>=1)?my_tex_form(VT0):rtostr(VT0),VD);
4204: }else VD=cons(VT[1],VD);
4205: }
4206: VV=reverse(VV);VD=reverse(VD);
4207: Rev=(getopt(rev)==1)?1:0;
4208: Dic=(getopt(dic)==1)?1:0;
4209: TT=terms(P,VV|rev=Rev,dic=Dic);
4210: if(TeX==0){
4211: Pre="("; Post=")";
4212: }else{
4213: Pre="{"; Post="}";
4214: }
4215: Out = string_to_tb("");
4216: for(L=C=0,Tm=TT;Tm!=[];C++,Tm=cdr(Tm)){
4217: for(I=0,PC=P,T=cdr(car(Tm)),PW="";T!=[];T=cdr(T),I++){
4218: PC=mycoef(PC,D=car(T),VV[I]);
4219: if(PC==0) continue;
4220: PT="";
4221: if(D!=0 && VD[I]!=""){
4222: if(TeX==0 && PW!="") PW+="*";
4223: if(D>1){
4224: if(D>9) PT="^"+Pre+rtostr(D)+Post;
4225: else PT="^"+rtostr(D);
4226: }
4227: if(Dif>0) PW+=(Dif==1)?"d":"\\partial ";
4228: PW+=VD[I]+PT;
4229: }
4230: }
4231: D=car(Tm)[0];
4232: if(Dif>0 && D>0){
4233: Op=(Dif==1)?"\\frac{d":"\\frac{\\partial";
4234: if(D>1) Op+="^"+((D>9)?(Pre+rtostr(D)+Post):rtostr(D));
4235: PW=Op+Add+"}{"+PW+"}";
4236: }else if(Add!=0) PW=PW+Add;
4237: if(TeX>=1){
4238: if(type(PC)==1 && ntype(PC)==0 && PC<0)
4239: OC="-"+my_tex_form(-PC);
4240: else OC=fctrtos(PC|TeX=1,br=1);
4241: }else OC=fctrtos(PC|br=1);
4242: if(PW!=""){
4243: if(OC == "1") OC = "";
4244: else if(OC == "-1") OC = "-";
4245: }
4246: if(TeX==0 && D!=0 && OC!="" && OC!="-") PW= "*"+PW;
4247: if((TOC=type(OC)) == 4){ /* rational coef. */
4248: if(Lim>0 && (texlen(OC[0])>Lim || texlen(OC[0])>Lim)){
4249: OC = (Small==1)?"("+OC[0]+")/("+OC[1]+")"
4250: :"\\Bigl("+OC[0]+"\\Bigr)\\Bigm/\\Bigl("+OC[1]+"\\Bigr)";
4251: TOC = 7;
4252: }else{
4253: if(str_char(OC[0],0,"-")==0){
4254: OC = fctrtos(-PC|TeX=1,br=1);
4255: OC = "-\\frac{"+OC[0]+"}{"+OC[1]+"}";
4256: }
4257: else
4258: OC = "\\frac{"+OC[0]+"}{"+OC[1]+"}";
4259: }
4260: }
4261: if(Lim>0){
4262: LL=texlen(OC)+texlen(PW);
4263: if(LL+L>=Lim){
4264: if(L>0) str_tb(CR,Out);
4265: if(LL>Lim){
4266: if(TOC==7) OC=texlim(OC,Lim|cut=CR);
4267: PW+=CR; L=0;
4268: }else L=LL;
4269: }else L+=LL;
4270: }else if(length(Tm)!=1) PW += CR; /* not final term */
4271: if(TeX) OC=texsp(OC);
4272: if(str_chr(OC,0,"-") == 0 || C==0) str_tb([OC,PW], Out);
4273: else{
4274: str_tb(["+",OC,PW],Out);
4275: if(LL<=Lim) L++;
4276: }
4277: }
4278: S=str_tb(0,Out);
4279: if(S=="") S="0";
4280: }else{ /* Var is not specified */
4281: if((TP=type(P)) == 3){ /* rational function */
4282: P = red(P); Nm=nm(P); Dn=dn(P);
4283: Q=dn(ptozp(Nm|factor=1)[1]);
4284: if(Q>1){
4285: Nm*=Q;Dn*=Q;
4286: }
4287: if(TeX>0){
4288: return (TeX==2)?
4289: "\\frac\{"+fctrtos(Nm|TeX=1)+"\}\{"+fctrtos(Dn|TeX=1)+"\}"
4290: :[fctrtos(Nm|TeX=1),fctrtos(Dn|TeX=1)];
4291: }
4292: else{
4293: S=fctrtos(Nm);
4294: if(nmono(Nm)>1) S="("+S+")";
4295: return S+"/("+fctrtos(Dn)+")";
4296: }
4297: }
4298: if(imag(P)==0) P = fctr(P); /* usual polynomial */
4299: else P=[[P,1]];
4300: S = str_tb(0,0);
4301: for(J = N = 0; J < length(P); J++){
4302: if(type(P[J][0]) <= 1){
4303: if(P[J][0] == -1){
4304: write_to_tb("-",S);
4305: if(length(P) == 1)
4306: str_tb("1", S);
4307: }else if(P[J][0] != 1){
4308: str_tb((TeX>=1)?my_tex_form(P[J][0]):rtostr(P[J][0]), S);
4309: N++;
4310: }else if(length(P) == 1)
4311: str_tb("1", S);
4312: else if(getopt(br)!=1 && length(P) == 2 && P[1][1] == 1){
4313: str_tb((TeX>=1)?my_tex_form(P[1][0]):rtostr(P[1][0]), S);
4314: J++;
4315: }
4316: continue;
4317: }
4318: if(N > 0 && TeX != 1 && TeX != 2 && TeX != 3)
4319: write_to_tb("*", S);
4320: SS=(TeX>=1)?my_tex_form(P[J][0]):rtostr(P[J][0]);
4321: N++;
4322: if(P[J][1] != 1){ /* (log(x))^2 */
4323: if(nmono(P[J][0])>1||
4324: (!isvar(P[J][0])||vtype(P[J][0]))&&str_len(SS)>1) SS="("+SS+")";
4325: write_to_tb(SS,S);
4326: str_tb(["^", (TeX>1)?rtotex(P[J][1]):monotos(P[J][1])],S);
4327: }else{
4328: if(nmono(P[J][0])>1) SS="("+SS+")";
4329: write_to_tb(SS,S);
4330: }
4331: }
4332: S = str_tb(0,S);
4333: if((Lim>0 || TP!=2) && CR!="") S=texlim(S,Lim|cut=CR);
4334: }
4335: if(TeX>0){
4336: if(Small==1) S=str_subst(S,"\\frac{","\\tfrac{");
4337: if(Dvi==1){
4338: dviout(strip(S,"(",")")|eq=(Pages==1)?6:0); S=1;
4339: }
4340: }
4341: return S;
4342: }
4343:
4344: def strip(S,S0,S1)
4345: {
4346: SS=strtoascii(S);
4347: if(length(SS)>1){
4348: if(SS[0]==40&&SS[length(SS)-1]==41&&str_pair(SS,1,S0,S1)==length(SS)-1)
4349: S=str_cut(SS,1,length(SS)-2);
4350: }
4351: return S;
4352: }
4353:
4354: def texlim(S,Lim)
4355: {
4356: /* extern TeXLim; */
4357: if(S==1 && Lim>10){
4358: TeXLim=Lim;
4359: mycat(["Set TeXLim =",Lim]);
4360: return 1;
4361: }
4362: if(type(Out=getopt(cut))!=7) Out="\\\\\n&";
4363: if(type(Del=getopt(del))!=7) Del=Out;
4364: if(Lim<30) Lim=TeXLim;
4365: S=ltov(strtoascii(S));
4366: for(L=[0],I=F=0;F==0; ){
4367: II=str_str(S,Del|top=I)+2;
4368: if(II<2){
4369: F++;II=/* str_len(S) */ length(S)-1;
4370: }
4371: for(J=JJ=I+1;;JJ=K+1){
4372: K=str_char(S,JJ,43); /* + */
4373: if((K1=str_char(S,JJ,45))>2 && K1<K){ /* - */
4374: if(S[K1-1]!=123 && S[K1-1]!=40) K=K1; /* {, ( */
4375: }
4376: if((K1=str_char(S,JJ,40))>0 && K1-JJ>6 && K1<K && S[K1-1]!=43 && S[K1-1]!=45){ /* ( */
4377: T=str_char(S,K1-6,"\\"); /* \Big*(, \big*( */
4378: if((T==K1-6 || T==K1-5)
4379: && (str_str(S,"big"|top=T+1,end=T+1)>0 || str_str(S,"Big"|top=T+1,end=T+1)>0))
4380: K=T;
4381: else if(K1>0 && K1<K) K=K1;
4382: }
4383: if(K<0 || K>II) break;
4384: if(K-J>Lim && texlen(str_cut(S,J,K-1))>=Lim){
4385: J=K+1; L=cons(JJ-1,L); SL=0;
4386: }
4387: }
4388: I=II;
4389: }
4390: SS=str_tb(0,0);
4391: L=cons(length(S),L);
4392: L=reverse(L);
4393: for(I=0; L!=[]; I=J,L=cdr(L)){
4394: str_tb((I==0)?"":Out,SS);
4395: J=car(L);
4396: str_tb(str_cut(S,I,J-1),SS);
4397: }
4398: return str_tb(0,SS);
4399: }
4400:
4401: def fmult(FN,M,L,N)
4402: {
4403: Opt=getopt();
4404: for(I = 0; I < length(M); I++)
4405: M = call(FN, cons(M,cons(L[I],N))|option_list=Opt);
4406: return M;
4407: }
4408:
4409: def radd(P,Q)
4410: {
4411: if(type(P) <= 3 || type(Q) <= 3){
4412: if(type(P) >= 5)
4413: return radd(Q,P);
4414: if(type(Q) >= 5){
4415: R = dupmat(Q);
4416: if(P == 0)
4417: return R;
4418: if(type(Q) == 6){
4419: S = size(Q);
4420: if(S[0] != S[1])
4421: return 0;
4422: for(I = 0; I < S[0]; I++)
4423: R[I][I] = radd(R[I][I], P);
4424: }else{
4425: for(I = length(R)-1; I >= 0; I--)
4426: R[I] = radd(R[I],P);
4427: }
4428: return R;
4429: }
4430: /* P=red(P);Q=red(Q); */
4431: if((P1=dn(P)) == (Q1=dn(Q))){
4432: if(P1==1) return P+Q;
4433: return red((nm(P)+nm(Q))/P1);
4434: }
4435: R=gcd(P1,Q1);S=tdiv(P1,R);
4436: return red((nm(P)*tdiv(Q1,R)+nm(Q)*S)/(S*Q1));
4437: }
4438: if(type(P) == 5){
4439: S = length(P);
4440: R = newvect(S);
4441: for(I = 0; I < S; I++)
4442: R[I] = radd(P[I],Q[I]);
4443: return R;
4444: }
4445: if(type(P) == 6){
4446: S = size(P);
4447: R = newmat(S[0],S[1]);
4448: for(I = 0; I < S[0]; I++){
4449: for(J = 0; J < S[1]; J++)
4450: R[I][J] = radd(P[I][J],Q[I][J]);
4451: }
4452: return R;
4453: }
4454: erno(0);
4455: }
4456:
4457: def getel(M,I)
4458: {
4459: if(type(M) >= 4 && type(M) <= 6 && type(I) <= 1)
4460: return M[I];
4461: if(type(M) == 6 && type(I) == 5)
4462: return M[I][J];
4463: return M;
4464: }
4465:
4466: def ptol(P,X)
4467: {
4468: F=(getopt(opt)==0)?0:1;
4469: if(type(P) <= 3)
4470: P = [P];
4471: if(type(X) == 4){
4472: for( ; X != []; X = cdr(X))
4473: P=ptol(P,car(X)|opt=F);
4474: return P;
4475: }
4476: P = reverse(P);
4477: for(R=[]; P != []; P = cdr(P)){
4478: Q = car(P);
4479: for(I = mydeg(Q,X); I >= 0; I--){
4480: S=mycoef(Q,I,X);
4481: if(F==1 || S!=0) R = cons(S,R);
4482: }
4483: }
4484: return R;
4485: }
4486:
4487: def rmul(P,Q)
4488: {
4489: if(type(P) <= 3 && type(Q) <= 3){
4490: P=red(P);Q=red(Q);
4491: P1=dn(P);P2=nm(P);Q1=dn(Q);Q2=nm(Q);
4492: if(P1==1 && Q1==1)
4493: return P*Q;
4494: if((R=gcd(P1,Q2)) != 1){
4495: P1=tdiv(P1,R);Q2=tdiv(Q2,R);
4496: }
4497: if((R=gcd(Q1,P2)) != 1){
4498: Q1=tdiv(Q1,R);P2=tdiv(P2,R);
4499: }
4500: return P2*Q2/(P1*Q1);
4501: }
4502: #ifdef USEMODULE
4503: return mmulbys(os_md.rmul,P,Q,[]);
4504: #else
4505: return mmulbys(rmul,P,Q,[]);
4506: #endif
4507: }
4508:
4509: def mtransbys(FN,F,LL)
4510: {
4511: Opt=getopt();
4512: if(type(F) == 4){
4513: F = ltov(F);
4514: S = length(F);
4515: R = newvect(S);
4516: for(I = 0; I < S; I++)
4517: R[I] = mtransbys(FN,F[I],LL|option_list=Opt);
4518: return vtol(R);
4519: }
4520: if(type(F) == 5){
4521: S = length(F);
4522: R = newvect(S);
4523: for(I = 0; I < S; I++)
4524: R[I] = mtransbys(FN,F[I],LL|option_list=Opt);
4525: return R;
4526: }
4527: if(type(F) == 6){
4528: S = size(F);
4529: R = newmat(S[0],S[1]);
4530: for(I = 0; I < S[0]; I++){
4531: for(J = 0; J < S[1]; J++)
4532: R[I][J] = mtransbys(FN,F[I][J],LL|option_list=Opt);
4533: }
4534: return R;
4535: }
4536: if(type(F) == 7) return F;
4537: return call(FN, cons(F,LL)|option_list=Opt);
4538: }
4539:
4540: def drawopt(S,T)
4541: {
4542: if(type(S)!=7) return -1;
4543: if(T==0||T==1){
4544: for(I=0,R=LCOPT;I<7;I++,R=cdr(R))
4545: if(str_str(S,car(R))>=0) return(T==0)?COLOPT[I]:car(R);
4546: return -1;
4547: }
4548: if(T==2){
4549: V0=V1=0;
4550: for(I=0,R=LPOPT;R!=[];I++,R=cdr(R)){
4551: if(str_str(S,car(R))>=0){
4552: if(I==0) V1++;
4553: else if(I==1) V1--;
4554: else if(I==2) V0--;
4555: else V0++;
4556: }
4557: }
4558: if(V0==0&&V1==0) return -1;
4559: return [V0,V1];
4560: }
4561: if(T==3){
4562: V=0;
4563: for(I=1,R=LFOPT;R!=[];R=cdr(R),I*=2){
4564: if(str_str(S,car(R))>=0) V+=I;
4565: }
4566: return (V==0)?-1:V;
4567: }
4568: return -1;
4569: }
4570:
4571: def execdraw(L,P)
4572: {
4573: if((Proc=getopt(proc))!=1) Proc=0;
4574: if(type(P)<2) P=[P];
4575: if(L!=[]&&type(L[0])!=4) L=[L];
4576: /* special command */
4577: if(P[0]<0){
4578: if(length(P)==1&&(P[0]==-1||P[0]==-2||P[0]==-3)){ /* Bounding Box */
4579: W=WS=N=LS=0;
4580: for(LL=L;LL!=[];LL=cdr(LL)){
4581: T=car(LL);
4582: if(P[0]!=-3 && T[0]==0){
4583: if(length(T)>3) S=" by "+rtostr(T[3])+" cm";
4584: else S="";
4585: if(P[0]==-1){
4586: mycat(["Windows : ",T[1][0],"< x <",T[1][1],", ",
4587: T[2][0],"< y <",T[2][1],S]);
4588: if(length(T)>4 && type(T[4])==4) mycat(["ext :",T[4]]);
4589: if(length(T)>5) mycat(["shift :",T[5]]);
4590: }
4591: return cdr(T);
4592: }
4593: if(type(T[0])==1){
4594: if(T[0]==1){
4595: for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){
4596: D=car(TT);
4597: if(type(D[0][0])==4){
4598: for(DT=D;DT!=[];DT=cdr(DT)){
4599: if(N++==0) W=ptbbox(car(DT));
4600: else W=ptbbox(car(DT)|box=W);
4601: }
4602: }else{
4603: if(N++==0) W=ptbbox(D);
4604: else W=ptbbox(D|box=W);
4605: }
4606: }
4607: }else if(T[0]==2){
4608: V=T[2];
4609: if(type(V[0])>1||type(V[1])>1) continue; /* not supported */
4610: if((Sc=delopt(T[1],"scale"|inv=1))!=[]){
4611: Sc=car(Sc)[1];
4612: if(type(Sc)==1) V=[Sc*V[0],Sc*V[1]];
4613: else V=[Sc[0]*V[0],Sc[1]*V[1]];
4614: }
4615: if(LS==0) WS=ptbbox([V]);
4616: else WS=ptbbox([V]|box=WS);
4617: if(length(T)>4) S=T[4];
4618: else if(type(S=T[3])==4){
4619: S=S[0];
4620: if(type(S)==4) S=S[length(S)-1];
4621: S=rtostr(S);
4622: }
4623: if(str_len(S)>LS) LS=str_len(S);
4624: }else if(T[0]==3||T[0]==4){
4625: if(N++==0) W=ptbbox(cdr(cdr(T)));
4626: else W=ptbbox(cdr(cdr(T))|box=W);
4627: }
4628: }
4629: }
4630: if(W!=0&&WS!=0) W=ptbbox([W,WS]|box=1);
4631: return (P[0]==-3)?[W,LS,WS]:W;
4632: }else if(length(P)>1&&P[0]==-1){ /* set Bounding Box */
4633: P=cons(0,cdr(P));
4634: Ex=Sft=[0,0];
4635: if(type(X=getopt(ext))==4) Ex=X;
4636: if(type(X=getopt(shift))==4) Sft=X;
4637: if(Ex!=Sft||Ex!=[0,0]){
4638: if(Sft==[0,0]) Sft=[Ex];
4639: else Sft=[Ex,Sft];
4640: if(length(P)==3) Sft=cons(1,Sft);
4641: if(length(P)==3||length(P)==4) P=append(P,Sft);
4642: }
4643: return cons(P,delopt(L,0));
4644: }
4645: if(P[0]==-4){
4646: for(N=0,LT=L;LT!=[];LT=cdr(LT)){ /* count coord. */
4647: T=car(LT);
4648: if(T[0]==1){
4649: for(T=cdr(cdr(T));T!=[];T=cdr(T)){
4650: if(type((S=car(T))[0][0])==4) N+=length(S);
4651: else for(;S!=[];S=cdr(S)) if(type(car(S))==4) N++;
4652: }
4653: }else if(T[0]==2) N++;
4654: else if(T[0]==3||T[0]==4) N+=2;
4655: }
4656: return N;
4657: }
4658: if(P[0]==-5){ /* functions */
4659: for(N=0,R=[],LT=L;LT!=[];LT=cdr(LT)){
4660: T=car(LT);
4661: if(T[0]==0) N=ior(N,1);
4662: else if(type(T[0])==1){
4663: if(T[0]>0) N=ior(N,2^T[0]);
4664: }
4665: else if(Type(T[0])==2){
4666: if(findin(T[0],R)<0) R=cons(T[0],R);
4667: }
4668: }
4669: for(I=5;I>=0;I--) if(iand(N,2^I)) R=cons(I,R);
4670: return R;
4671: }
4672: return 0;
4673: }
4674:
4675: if(length(P)>1){
4676: if(type(P[1])==6||(type(P[1])<2&&P[1]>0)) M=P[1];
4677: else if(type(P[1])==4&&length(P[1])==2) M=diagm(2,P[1]);
4678: }
4679: if(length(P)>2&&type(P[2])==4){
4680: Org=[["shift",P[2]]];
4681: if(M==0) M=1;
4682: }else Org=[];
4683: if(P[0]==0||(type(P[0])==4&&P[0][0]==0)){ /* Risa/Asir */
4684: PP=car(P);PPP=0;
4685: if(type(PP)!=4) PP=[PP];
4686: if(length(PP)<3){
4687: if(length(PP)==1 || type(PP[1])==4){
4688: if(ID_PLOT<0) ID_PLOT=ox_launch_nox(0,"ox_plot");
4689: Id=ID_PLOT;
4690: if(length(PP)==1&&type(Canvas)==4&&length(Canvas)==2)
4691: PP=cons(PP[0],[Canvas]);
4692: if(length(PP)>1){
4693: PPP=PP[1][0];
4694: PPQ=(length(PP[1])==2)?PP[1][1]:PPP;
4695: open_canvas(Id,[PPP,PPQ]);
4696: }else open_canvas(Id);
4697: Ind=ox_pop_cmo(Id);
4698: }else{
4699: Ind=PP[1];
4700: if(getopt(cl)==1) clear_canvas(Id,Ind);
4701: }
4702: }else{
4703: Id=PP[1];Ind=PP[2];
4704: if(length(PP)>3 && type(PP[3])==1) PPP=PP[3];
4705: if(length(PP)>4 && type(PP[4])==1) PPQ=PP[4];
4706: if(getopt(cl)==1) clear_canvas(Id,Ind);
4707: }
4708: if(L==[]) return (PPP>0)? [0,Id,Ind,PPP,PPQ]:[0,Id,Ind];
4709: Ex0=Ex0;Sft=[0,0];
4710: if(length(P)>1&&P[1]==0&&length(P)<4){
4711: R=execdraw(L,-3);
4712: Ex0=Ex1=Ex2=10;
4713: if((U=R[1])>0){ /* string */
4714: if(U>20) U=16; /* adj 16,8,2,7,15 */
4715: if(R[0][0][0]>R[2][0][0]-(R[0][0][1]-R[0][0][0])/256) Ex0+=8*U; /* adj 256 */
4716: else Ex0+=2*U;
4717: if(R[0][0][1]<R[2][0][1]+(R[0][0][1]-R[0][0][0])/256) Ex1+=7*U;
4718: else Ex1+=2*U;
4719: if(R[0][1][1]<R[2][1][1]+(R[0][1][1]-R[0][1][0])/256) Ex2+=15;
4720: }
4721: R=[R[0][0],R[0][1],0,[Ex0,Ex1],[0,-Ex2]];
4722: if(length(P)>2 && P[2]==1)
4723: mycat0(["Box:",[R[0],R[1]], ", ext=",R[3],", shift=",R[4]],1);
4724: }else R=execdraw((length(P)>3)?P[3]:L,-2); /* Windows */
4725: XW=R[0];YW=R[1];
4726: if(length(R)>3){
4727: if(R[3]!=0 && R[3]!=[0,0]) Ex=R[3];
4728: if(length(R)>4) Sft=R[4];
4729: }
4730: if(type(X=getopt(ext))==4)
4731: Ex=(Ex0)?[X[0]+Ex[0],X[1]+Ex[1]]:X;
4732: if(type(M)<2){
4733: if(length(P)>1&&type(P[1])==1) M=P[1];
4734: else if((length(P)==1||P[1]==0||P[1]==1)&& PPP>0) M=PPP;
4735: if(M<2) M=400;
4736: if(Ex!=0 && type(Ex)==4){
4737: M-=Ex[0]+Ex[1];
4738: }
4739: M=(M/(XW[1]-XW[0]))*diagm(2,[1,-1]);
4740: }
4741: if(type(X=getopt(shift))==4) Sft=(Ex0)?[Sft[0]+X[0],Sft[1]+X[1]]:X;
4742: if(type(Sft)==4) Sft=[Sft[0],-Sft[1]];
4743: if(Ex!=0) Sft=[Sft[0]+Ex[0],Sft[1]];
4744: Org=[["shift",ptaffine(M,[-XW[0],-YW[1]]|shift=Sft)]];
4745: for(CT=0;CT<2;CT++){
4746: for(LT=L;LT!=[];LT=cdr(LT)){
4747: T=car(LT);
4748: if(!CT && T[0]!=2) continue;
4749: if(CT && T[0]==2) continue;
4750: if(T[0]==1){
4751: for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){
4752: D=car(TT);
4753: if(type(D[0][0])==4){
4754: for(DT=D;DT!=[];DT=cdr(DT)){
4755: V=car(DT);
4756: if(M) V=ptaffine(M,V|option_list=Org);
4757: draw_bezier(Id,Ind,V|option_list=T[1]);
4758: }
4759: }else{
4760: if(M) D=ptaffine(M,D|option_list=Org);
4761: draw_bezier(Id,Ind,D|option_list=T[1]);
4762: }
4763: }
4764: }else if(T[0]==2){ /* put */
4765: if(length(T)<4) continue;
4766: V=T[2];
4767: if(type(VLB)==4&&V[0]=="_") V=VLB;
4768: else if(type(V[0])>1||type(V[1])>1) continue; /* not supported */
4769: if(length(T)>3&&type(T[3])==4&&length(T[3])>1&&T[3][1]==1) VLB=V;
4770: F++;MM=M;
4771: if((Sc=delopt(T[1],"scale"|inv=1))!=[]){
4772: if(!MM) MM=1;
4773: Sc=car(Sc)[1];
4774: if(type(Sc)==1) MM=MM*Sc;
4775: else if(type(Sc)==6) MM=MM*diagm(2,Sc);
4776: }
4777: if(MM) V=ptaffine(MM,V|option_list=Org);
4778: if(type(S=S0=T[3])==4) S=S0[0];
4779: if(length(T)>4) S=T[4]; /* subst. string */
4780: if(type(S0)==4&&type(S0[0])==4){
4781: if((Col=drawopt(S0[0][0],0))<0) Col=0; /* attrib. */
4782: if(type(S)!=7) S=rtostr(S0[0][1]);
4783: S=str_subst(S,[["$\\bullet$","*"],["$\\times$","x"],["$",""]],0);
4784: if(type(Pos=drawopt(S0[0][0],2))==4)
4785: V=[V[0]+4*str_len(S)*Pos[0],V[1]-10*Pos[1]]; /* adjustable */
4786: }else S=str_subst(rtostr(S),[["$\\bullet$","*"],["$\\times$","x"],["$",""]],0);
4787: V=[V[0]-str_len(S)*4,V[1]-8]; /* adjustable */
4788: draw_string(Id,Ind,V,S,Col);
4789: }else if(T[0]==3){ /* arrow */
4790: F++;
4791: T1=T[2];T2=T[3];
4792: if(M){
4793: T1=ptaffine(M,T1|option_list=Org);
4794: T2=ptaffine(M,T2|option_list=Org);
4795: }
4796: draw_bezier(Id,Ind,[T1,T2]|option_list=T[1]);
4797: }else if(T[0]==4){ /* line */
4798: F++;
4799: T1=T[2];T2=T[3];
4800: if(M){
4801: T1=ptaffine(M,T1|option_list=Org);
4802: T2=ptaffine(M,T2|option_list=Org);
4803: }
4804: V=delopt(T1=T[1],"opt"|inv=1);
4805: if(V!=[]&&str_str(V[1],".")>=0)
4806: T1=cons(["opt",cons("dotted,",V[1])],delopt(T1,"opt"));
4807: draw_bezier(Id,Ind,[T1,T2]|option_list=T1);
4808: }else if(T[0]==5){ /* TeX */
4809: mycat(rtostr(T[2]));
4810: if(F){
4811: S=str_tb(0,Out);
4812: Out=str_tb(0,0);
4813: F=0;
4814: if(S!=""){
4815: if(P[0]==2) dviout(xyproc(S)|keep=1);
4816: else LOut=cons(xyproc(S),LOut);
4817: }
4818: if(P[0]==2) dviout(T[2]|option_list=T[1]);
4819: else{
4820: LOut=cons(T[2],Out);
4821: }
4822: }
4823: }else if(Proc==1&&type(T[0])==2){
4824: if(length(T)<3) call(T[0],T[1]);
4825: else call(T[0],T[1]|option_list=T[2]);
4826: }
4827: }
4828: }
4829: S=(PPP>0)? [0,Id,Ind,PPP,PPQ]:[0,Id,Ind];
4830: if(Ex==0&&Sft!=[0,0]) Ex=[0,0];
4831: return (Ex!=0&&length(P)>2&&P[2]==-1)?
4832: [S,0,0,[0,R[0],R[1],0,Ex,[Sft[0]-Ex[0],-Sft[1]]]]:S;
4833: }
4834: if(P[0]==1||P[0]==2){ /* TeX */
4835: Out=str_tb(0,0);LOut=[];F=0;
4836: if(getopt(cl)==1) dviout0(0);
4837: for(;L!=[];L=cdr(L)){
4838: T=car(L);Opt=T[1];
4839: if(type(T[0])>=2) continue;
4840: if(T[0]==0){
4841: XW=T[1];YW=T[2];
4842: if(length(P)>1&&type(P[1])==1&&P[1]<0)
4843: M=-P[1]/(XW[0]-XW[1]);
4844: }else if(T[0]==1){
4845: F++;
4846: for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){
4847: D=car(TT);
4848: if(type(D[0][0])==4){
4849: for(DT=D;DT!=[];DT=cdr(DT)){
4850: V=car(DT);
4851: if(M) V=ptaffine(M,V|option_list=Org);
4852: str_tb(xybezier(V|option_list=Opt),Out);
4853: }
4854: }else{
4855: if(M) D=ptaffine(M,D|option_list=Org);
4856: str_tb(xybezier(D|option_list=Opt),Out);
4857: }
4858: }
4859: }else if(T[0]==2){
4860: F++;V=T[2];
4861: Opt=delopt(Opt,"scale"|inv=1);
4862: MM=M;
4863: if(Opt!=[]){
4864: Opt=car(Opt)[1];
4865: if(type(Opt)==1) Opt=[Opt,Opt];
4866: if(Opt!=[1,1]){
4867: if(!MM) MM=1;
4868: MM=MM*diagm(2,[Opt[0],Opt[1]]);
4869: }
4870: }
4871: if(MM) V=ptaffine(MM,V|option_list=Org);
4872: if(length(T)>3) V=append(V,T[3]);
4873: str_tb(xyput(V),Out);
4874: }else if(T[0]==3){
4875: F++;
4876: T1=T[2];T2=T[3];
4877: if(M){
4878: T1=ptaffine(M,T1|option_list=Org);
4879: T2=ptaffine(M,T2|option_list=Org);
4880: }
4881: str_tb(xyarrow(T1,T2|option_list=Opt),Out);
4882: }else if(T[0]==4){
4883: F++;
4884: T1=T[2];T2=T[3];
4885: if(M){
4886: T1=ptaffine(M,T1|option_list=Org);
4887: T2=ptaffine(M,T2|option_list=Org);
4888: }
4889: str_tb(xyline(T1,T2|option_list=Opt),Out);
4890: }else if(T[0]==5){
4891: if(F){
4892: S=str_tb(0,Out);
4893: Out=str_tb(0,0);
4894: F=0;
4895: if(S!=""){
4896: if(P[0]==2) dviout(xyproc(S)|keep=1);
4897: else LOut=cons(xyproc(S),LOut);
4898: }
4899: if(P[0]==2) dviout(T[2]|option_list=T[1]);
4900: else LOut=cons(T[2],Out);
4901: }
4902: }else if(T[0]==-2)
4903: str_tb(["%",T[1],"\n"],Out);
4904: else if(Proc==1&&type(T[0])==2){
4905: if(length(T)<3) call(T[0],T[1]);
4906: else call(T[0],T[1]|option_list=T[2]);
4907: }
4908: }
4909: S=str_tb(0,Out);
4910: if(P[0]==1){
4911: if(F) LOut=cons(xyproc(S),LOut);
4912: Out=str_tb(0,0);
4913: for(L=reverse(LOut);L!=[];L=cdr(L))
4914: str_tb(car(L),Out);
4915: return str_tb(0,Out);
4916: }
4917: if(F) dviout(xyproc(S));
4918: else dviout(" ");
4919: }
4920: }
4921:
4922: def execproc(L)
4923: {
4924: if(type(N=getopt(var))!=1&&N!=0) N=2;
4925: for(R=[];L!=[];L=cdr(L)){
4926: P=car(L);
4927: if(type(P[0])==2&&vtype(P[0])==3){
4928: if((VS=vars(cdr(P)))!=[]){
4929: for(I=0;I<N;I++){
4930: V=makev(["v",I+1]);
4931: if(findin(V,VS)>=0) P=mysubst(P,[V,R[I]]);
4932: }
4933: }
4934: if(length(P)<3) R=cons(call(P[0],P[1]),R);
4935: else R=cons(call(P[0],P[1]|option_list=P[2]),R);
4936: }
4937: }
4938: return (getopt(all)==1)?R:car(R);
4939: }
4940:
4941: def myswap(P,L)
4942: {
4943: X=makenewv(P);
4944: for(L=reverse(L);length(L)>1;L=cdr(L))
4945: P=subst(P,L[0],X,L[1],L[0],X,L[1]);
4946: return P;
4947: }
4948:
4949: def mysubst(P,L)
4950: {
4951: if(P==0) return 0;
1.29 takayama 4952: if(getopt(lpair)==1||(type(L[0])==4&&length(L[0])>2)) L=lpair(L[0],L[1]);
1.6 takayama 4953: Inv=getopt(inv);
4954: if(type(L[0]) == 4){
4955: while((L0 = car(L))!=[]){
4956: P = mysubst(P,(Inv==1)?[L0[1],L0[0]]:L0);
4957: L = cdr(L);
4958: }
4959: return P;
4960: }
4961: if(Inv==1) L=[L[1],L[0]];
4962: if(type(P) > 3){
4963: if(type(P)==7) return P;
4964: if(type(P)>7)
4965: return subst(P,L[0],L[1]);
4966: #ifdef USEMODULE
4967: return mtransbys(os_md.mysubst,P,[L]);
4968: #else
4969: return mtransbys(mysubst,P,[L]);
4970: #endif
4971: }
4972: P = red(P);
4973: if(type(P) == 3){
4974: A=mysubst(nm(P),L);B=mysubst(dn(P),L);
4975: return red(nm(A)/nm(B))*red(dn(B)/dn(A));
4976: }
4977: L1=(type(L[1])==3)?red(L[1]):L[1];X=L[0];
4978: if(ptype(L1,X)==3){
4979: LN=nm(L1);LD=dn(L1);
4980: Deg=mydeg(P,X);
4981: if(Deg <= 0) return P;
4982: V = newvect(Deg+1);
4983: for(V[I=Deg]=1;I >= 1;I--)
4984: V[I-1]=V[I]*LD;
4985: for(R = 0, I = Deg; I >= 0; I--)
4986: R = R*LN + mycoef(P,I,X)*V[I];
4987: return red(R/V[0]);
4988: }
4989: return subst(P,X,L1);
4990: }
4991:
4992: def mmulbys(FN,P,F,L)
4993: {
4994: Opt=getopt();
4995: if(type(F) <= 3){
4996: if(type(P) <= 3)
4997: return call(FN, cons(P,cons(F,L))|option_list=Opt);
4998: if(type(P) == 5){
4999: S = length(P);
5000: R = newvect(S);
5001: for(I = 0; I < S; I++)
5002: R[I] = call(FN, cons(P[I],cons(F,L))|option_list=Opt);
5003: return R;
5004: }else if(type(P) == 6){
5005: S = size(P);
5006: R = newmat(S[0],S[1]);
5007: for(I = 0; I < S[0]; I++){
5008: for(J = 0; J < S[1]; J++)
5009: R[I][J] = call(FN, cons(P[I][J],cons(F,L))|option_list=Opt);
5010: }
5011: return R;
5012: }
5013: }
5014: if(type(F) == 5){
5015: S = length(F);
5016: if(type(P) <= 3){
5017: R = newvect(S);
5018: for(I = 0; I < S; I++)
5019: R[I] = call(FN, cons(P,cons(F[I],L))|option_list=Opt);
5020: return R;
5021: }
5022: if(type(P) == 5){
5023: for(J=R=0; J<S; J++)
5024: R = radd(R, call(FN, cons(P[J],cons(F[J],L)))|option_list=Opt);
5025: return R;
5026: }
5027: T = size(P);
5028: R = newvect(T[0]);
5029: for(I = 0; I < T[0]; I++){
5030: for(J = 0; J < S; J++)
5031: R[I] = radd(R[I], call(FN, cons(P[I][J],cons(F[J],L))|option_list=Opt));
5032: }
5033: return R;
5034: }
5035: if(type(F) == 6){
5036: S = size(F);
5037: if(type(P) <= 3){
5038: R = newmat(S[0],S[1]);
5039: for(I = 0; I < S[0]; I++){
5040: for(J = 0; J < S[1]; J++)
5041: R[I][J] = call(FN, cons(P,cons(F[I][J],L))|option_list=Opt);
5042: }
5043: return R;
5044: }
5045: if(type(P) == 5){
5046: R = newvect(S[1]);
5047: for(J = 0; J < S[1]; J++){
5048: for(K = U = 0; K < S[0]; K++)
5049: U = radd(U, call(FN, cons(P[K],cons(F[K][J],L))|option_list=Opt));
5050: R[J] = U;
5051: }
5052: return R;
5053: }
5054: T = size(P);
5055: R = newmat(T[0],S[1]);
5056: for(I = 0; I < T[0]; I++){
5057: for(J = 0; J < S[1]; J++){
5058: for(K = U = 0; K < S[0]; K++)
5059: U = radd(U, call(FN, cons(P[I][K],cons(F[K][J],L)|option_list=Opt)));
5060: R[I][J] = U;
5061: }
5062: }
5063: return R;
5064: }
5065: erno(0);
5066: return 0;
5067: }
5068:
5069: def appldo(P,F,L)
5070: {
5071: if(type(F) <= 3){
5072: if(type(L) == 4 && type(L[0]) == 4)
5073: return applpdo(P,F,L);
5074: L = vweyl(L);
5075: X = L[0]; DX = L[1];
5076: J = mydeg(P,DX);
5077: for(I = R = 0; I <= J; I++){
5078: if(I > 0)
5079: F = mydiff(F,X);
5080: R = radd(R,mycoef(P,I,DX)*F);
5081: }
5082: return R;
5083: }
5084: #ifdef USEMODULE
5085: return mmulbys(os_md.appldo,P,F,[L]);
5086: #else
5087: return mmulbys(appldo,P,F,[L]);
5088: #endif
5089: }
5090:
5091: def appledo(P,F,L)
5092: {
5093: if(type(F) <= 3){
5094: L = vweyl(L);
5095: X = L[0]; DX = L[1];
5096: J = mydeg(P,DX);
5097: for(I = R = 0; I <= J; I++){
5098: if(I > 0)
5099: F = myediff(F,X);
5100: R = radd(R,mycoef(P,I,DX)*F);
5101: }
5102: return R;
5103: }
5104: #ifdef USEMODULE
5105: mmulbys(os_md.appledo,P,F,[L]);
5106: #else
5107: mmulbys(appledo,P,F,[L]);
5108: #endif
5109: }
5110:
5111: def muldo(P,Q,L)
5112: {
5113: if(type(Lim=getopt(lim))!=1) Lim=100;
5114: if(type(Q) <= 3){
5115: if(type(L) == 4 && type(L[0]) == 4)
5116: return mulpdo(P,Q,L|lim=Lim); /* several variables */
5117: R = rmul(P,Q);
5118: L = vweyl(L);
5119: X = L[0]; DX = L[1];
5120: if(X != 0){
5121: for(I = F = 1; ; I++){
5122: P = mydiff(P,DX);
5123: if(I>Lim){
5124: mycat(["Over", Lim,"derivations!"]);
5125: break;
5126: }
5127: if(P == 0)
5128: break;
5129: Q = mydiff(Q,X);
5130: if(Q == 0)
5131: break;
5132: F *= I;
5133: R = radd(R,P*Q/F);
5134: }
5135: }
5136: return R;
5137: }
5138: #ifdef USEMODULE
5139: return mmulbys(os_md.muldo,P,Q,[L]);
5140: #else
5141: return mmulbys(muldo,P,Q,[L]);
5142: #endif
5143: }
5144:
5145: def jacobian(F,X)
5146: {
5147: F=ltov(F);X=ltov(X);
1.30 takayama 5148: N=length(F);L=length(X);
5149: M=newmat(N,L);
1.6 takayama 5150: for(I=0;I<N;I++)
1.30 takayama 5151: for(J=0;J<L;J++) M[I][J]=red(diff(F[I],X[J]));
5152: if(N!=L||getopt(mat)==1) return M;
1.6 takayama 5153: return mydet(M);
5154: }
5155:
5156: def hessian(F,X)
5157: {
5158: X=ltov(X);
5159: N=length(X);
5160: M=newmat(N,N);
5161: for(I=0;I<N;I++){
5162: G=red(diff(F,X[I]));
5163: for(J=0;J<N;J++) M[I][J]=red(diff(G,X[J]));
5164: }
5165: if(getopt(mat)==1) return M;
5166: return mydet(M);
5167: }
5168:
5169: def wronskian(F,X)
5170: {
5171: N=length(F);
5172: M=newmat(N,N);
5173: for(I=0;F!=[];F=cdr(F),I++){
5174: M[I][0]=car(F);
5175: for(J=1;J<N;J++) M[I][J]=red(diff(M[I][J-1],X));
5176: }
5177: if(getopt(mat)==1) return M;
5178: return mydet(M);
5179: }
5180:
5181: def adj(P,L)
5182: {
5183: if(type(P) == 4)
5184: #ifdef USEMODULE
5185: return map(os_md.adj,mtranspose(P),L);
5186: #else
5187: return map(adj,mtranspose(P),L);
5188: #endif
5189: if(type(L) == 4 && type(L[0]) == 4)
5190: #ifdef USEMODULE
5191: return fmult(os_md.adj,P,L,[]);
5192: #else
5193: return fmult(adj,P,L,[]);
5194: #endif
5195: L = vweyl(L);
5196: X = L[0]; DX = L[1];
5197: P = R = subst(P, DX, -DX);
5198: for(I = 1; (R = mydiff(mydiff(R, X), DX)/I) != 0 && I < 100; I++)
5199: P = radd(P,R);
5200: return P;
5201: }
5202:
5203: def laplace1(P,L)
5204: {
5205: if(type(L) == 4 && type(L[0]) == 4)
5206: #ifdef USEMODULE
5207: return fmult(os_md.laplace,P,L,[]);
5208: #else
5209: return fmult(laplace,P,L,[]);
5210: #endif
5211: L = vweyl(L);
5212: X = L[0]; DX = L[1];
5213: P = adj(P, L);
5214: return subst(P,X,o_1,DX,X,o_1,DX);
5215: }
5216:
5217: def laplace(P,L)
5218: {
5219: if(type(L) == 4 && type(L[0]) == 4)
5220: #ifdef USEMODULE
5221: return fmult(os_md.laplace1,P,L,[]);
5222: #else
5223: return fmult(laplace1,P,L,[]);
5224: #endif
5225: L = vweyl(L);
5226: X = L[0]; DX = L[1];
5227: P = adj(P, L);
5228: return subst(P,X,o_1,DX,-X,o_1,-DX);
5229: }
5230:
5231: def mce(P,L,V,R)
5232: {
5233: L = vweyl(L);
5234: X = L[0]; DX = L[1];
5235: P = sftexp(laplace1(P,L),L,V,R);
5236: return laplace(P,L);
5237: }
5238:
5239: def mc(P,L,R)
5240: {
5241: return mce(P,L,0,R);
5242: }
5243:
5244: def rede(P,L)
5245: {
5246: Q = ltov(fctr(nm(red(P))));
5247: P = 1;
5248: if(type(L) < 4)
5249: L = [L];
5250: if(type(L[0]) < 4)
5251: L = [L];
5252: for( ; L != []; L = cdr(L)){
5253: DX = vweyl(car(L))[1];
5254: for(I = 1; I < length(Q); I++){
5255: if(mydeg(Q[I][0],DX) > 0){
5256: P *= (Q[I][0])^(Q[I][1]);
5257: Q[I]=[1,0];
5258: }
5259: }
5260: }
5261: return P;
5262: }
5263:
5264: def ad(P,L,R)
5265: {
5266: L = vweyl(L);
5267: DX = L[1];
5268: K = mydeg(P,DX);
5269: S = mycoef(P,0,DX);
5270: Q = 1;
5271: for(I=1; I <= K;I++){
5272: Q = muldo(Q,DX-R,L);
5273: S = radd(S,mycoef(P,I,DX)*Q);
5274: }
5275: return S;
5276: }
5277:
5278: def add(P,L,R)
5279: {
5280: return rede(ad(P,L,R),L);
5281: }
5282:
5283:
5284: def vadd(P,L,R)
5285: {
5286: L = vweyl(L);
5287: if(type(R) != 4)
5288: return 0;
5289: N = length(R);
5290: DN = 1; Ad = PW = 0;
5291: for( ; R != []; R = cdr(R), PW++){
5292: DN *= (T=1-car(R)[0]*L[0]);
5293: Ad = Ad*T-car(R)[1]*x^PW;
5294: }
5295: Ad /= DN;
5296: return add(P,L,Ad);
5297: }
5298:
5299: def addl(P,L,R)
5300: {
5301: return laplace1(add(laplace(P,L),L,R),L);
5302: }
5303:
5304: def cotr(P,L,R)
5305: {
5306: L = vweyl(L);
5307: X = L[0]; DX = L[1];
5308: T = 1/mydiff(P,DX);
5309: K = mydeg(P,DX);
5310: S = mysubst(mycoef(P,0,DX), [X, R]);
5311: Q = 1;
5312: for(I = 1; I <= K; I++){
5313: Q = muldo(Q, K*DX, L);
5314: S = radd(S,mysubst(mycoef(P,I,DX), [X, R])*Q);
5315: }
5316: }
5317:
5318: def rcotr(P,L,R)
5319: {
5320: return rede(cotr(P,L,R), L);
5321: }
5322:
5323: def muledo(P,Q,L)
5324: {
5325: if(type(Q)>3)
5326: #ifdef USEMODULE
5327: return mmulbys(os_md.muledo,P,Q,[L]);
5328: #else
5329: return mmulbys(muledo,P,Q,[L]);
5330: #endif
5331: R = P*Q;
5332: L = vweyl(L);
5333: X = L[0]; DX = L[1];
5334: for(I = F = 1; I < 100; I++){
5335: P = mydiff(P,DX);
5336: if(P == 0)
5337: break;
5338: Q = myediff(Q,X);
5339: if(Q == 0)
5340: break;
5341: F = rmul(F,I);
5342: R = radd(R,P*Q/F);
5343: }
5344: return R;
5345: }
5346:
5347:
5348: #if 1
5349: def mulpdo(P,Q,L)
5350: {
5351: if(type(Q)>3)
5352: #ifdef USEMODULE
5353: return mmulbys(os_md.mulpdo,P,Q,[L]);
5354: #else
5355: return mmulbys(mulpdo,P,Q,[L]);
5356: #endif
5357: if(type(Lim=getopt(lim))!=1) Lim=100;
5358: M = vweyl(car(L)); X= M[0]; DX = M[1];
5359: L = cdr(L);
5360: R = 0;
5361: for(I = 0; Q != 0 && I <= Lim; I++){
5362: if(I>Lim){
5363: mycat(["Over", Lim,"derivations!"]);
5364: break;
5365: }
5366: if(I > 0)
5367: P /= I;
5368: if(length(L)==0)
5369: R = radd(R,P*Q);
5370: else
5371: R = radd(R,mulpdo(P,Q,L));
5372: if(X==0) break;
5373: P = mydiff(P,DX);
5374: if(P == 0)
5375: break;
5376: Q = mydiff(Q,X);
5377: }
5378: if(I>Lim) mycat(["Over", Lim,"derivations!"]);
5379: return R;
5380: }
5381:
5382: #else
5383: def mulpdo(P,Q,L);
5384: {
5385: if(type(Q)>3)
5386: #ifdef USEMODULE
5387: return mmulbys(os_md.mulpdo,P,Q,[L]);
5388: #else
5389: return mmulbys(mulpdo,P,Q,[L]);
5390: #endif
5391: if(type(Lim=getopt(lim))!=1) Lim=100;
5392: N = length(L);
5393: VO = newvect(2*N);
5394: VN = newvect(2*N);
5395: for(I = J = 0; I < N; J += 2, I++){
5396: M = vweyl(L[I]);
5397: P = subst(P, VO[J]=M[0], VN[J]=strtov("o_"+rtostr(V[J])),
5398: VO[J+1]=M[1], VN[J+1] = strtov("o_"+rtostr(V[J+1])));
5399: }
5400: for(PQ = P*Q, I = 0; I < 2*N; I += 2){
5401: for(R = PQ, J = 1; J < Lim; J++){
5402: R = mydiff(R, VN[I+1])/J;
5403: if(R == 0)
5404: break;
5405: R = mydiff(R, VO[I]);
5406: if(R == 0)
5407: break;
5408: PQ = radd(PQ,R);
5409: }
5410: if(I==Lim) mycat(["Over", Lim,"derivations!"]);
5411: PQ = red(subst(PQ,VN[I],VO[I],VN[I+1],VO[I+1]));
5412: }
5413: }
5414: #endif
5415:
5416: def transpdosub(P,LL,K)
5417: {
5418: Len = length(K)-1;
5419: if(Len < 0 || P == 0)
5420: return P;
5421: KK=K[Len];
5422: if(type(KK)==4){
5423: KK0=KK[0]; KK1=KK[1];
5424: }else{
5425: L = vweyl(LL[Len]);
5426: KK0=L[1]; KK1=K[Len];
5427: }
5428: Deg = mydeg(P,KK0);
5429: K1 = reverse(cdr(reverse(K)));
5430: R = transpdosub(mycoef(P,0,KK0),LL,K1);
5431: for(I = M = 1; I <= Deg ; I++){
5432: M = mulpdo(M,KK1,LL);
5433: S = mycoef(P,I,KK0);
5434: if(Len > 0)
5435: S = transpdosub(S,LL,K1);
5436: R = radd(R,mulpdo(S,M,LL));
5437: }
5438: return R;
5439: }
5440:
5441: def transpdo(P,LL,K)
5442: {
5443: if(type(K[0]) < 4)
5444: K = [K];
5445: Len = length(K)-1;
5446: K1=K2=[];
5447: if(type(LL)!=4) LL=[LL];
5448: if(type(LL[0])!=4) LL=[LL];
5449: if(getopt(ex)==1){
5450: for(LT=LL, KT=K; KT!=[]; LT=cdr(LT), KT=cdr(KT)){
5451: L = vweyl(LL[J]);
5452: K1=cons([L[0],car(KT)[0]],K1);
5453: K2=cons([L[1],car(KT)[1]],K2);
5454: }
5455: K2=append(K1,K2);
5456: }else{
5457: for(J = length(K)-1; J >= 0; J--){
5458: L = vweyl(LL[J]);
5459: if(L[0] != K[J][0])
5460: K1 = cons([L[0],K[J][0]],K1);
5461: K2 = cons(K[J][1],K2);
5462: }
5463: P = mulsubst(P, K1);
5464: }
5465: return transpdosub(P,LL,K2);
5466: }
5467:
5468: def translpdo(P,LL,M)
5469: {
5470: S=length(LL);
5471: L0=newvect(S);L1=newvect(S);
5472: K=newvect(S);
5473: for(J=0;J<S;J++){
5474: L = vweyl(LL[J]);
5475: L0[J]=L[0];
5476: L1[J]=L[1];
5477: }
5478: K=rmul(M,L0);
5479: for(T=[],J=0;J<S;J++)
5480: T=cons([L0[J],K[J]],T);
5481: P=mulsubst(P,T);
5482: K=rmul(myinv(M),L1);
5483: for(T=[],J=0;J<S;J++)
5484: T=cons([L1[J],K[J]],T);
5485: return mulsubst(P,T);
5486: }
5487:
5488: /*
5489: return [R, M, S] : R = M*P - S*Q
5490: deg(R,X) < deg(Q,X)
5491: */
5492: def rpdiv(P,Q,X)
5493: {
5494: if(P == 0)
5495: return [0,1,0];
5496: DQ = mydeg(Q,X);
5497: CO = mycoef(Q,DQ,X);
5498: S = 0;
5499: while((DP = mydeg(P,X)) >= DQ){
5500: R = mycoef(P,DP,X)/CO;
5501: S = radd(S,R*X^(DP-DQ));
5502: P = radd(P, -R*Q*X^(DP-DQ));
5503: }
5504: Lcm = lcm(dn(S),dn(P));
5505: Gcd = gcd(nm(S),nm(P));
5506: return [red(P*Lcm/Gcd), red(Lcm/Gcd),red(S*Lcm/Gcd)];
5507: }
5508:
5509: def texbegin(T,S)
5510: {
5511: if(type(Opt=getopt(opt))==7) Opt="["+Opt+"]\n";
5512: else Opt="\n";
5513: return "\\begin{"+T+"}"+Opt+S+"%\n\\end{"+T+"}\n";
5514: }
5515:
5516: def mygcd(P,Q,L)
5517: {
5518: if((Dvi=getopt(dviout))==3 || Dvi==-3){ /* dviout=3 */
5519: if((Rev=getopt(rev))!=1) Rev=0;
5520: R=mygcd(P,Q,L|rev=Rev);
5521: if(type(L)<2) Var=0;
5522: else if(type(L)==2){
5523: Val=L;L=[0,L];
5524: }else if(type(L)==4){
5525: L=vweyl(L);
5526: Var=[[L[1],"\\partial"]];
5527: }
5528: S=mat([P],[Q]);T=mat([R[0]],[0]);
5529: M=mat([R[1],R[2]],[R[3],R[4]]);
5530: if(type(Val)==4)
5531: N=mdivisor(M,L|trans=1)[1];
5532: else N=myinv(M);
5533: Tb=str_tb(mtotex(S|var=Var),0);
5534: str_tb("&="+mtotex(N|var=Var)+mtotex(T|var=Var)+",\\\\\n",Tb);
5535: str_tb(mtotex(T|var=Var),Tb);
5536: str_tb("&="+mtotex(M|var=Var)+mtotex(S|var=Var)+".",Tb);
5537: Out=str_tb(0,Tb);
5538: if(Dvi<0) return Out;
5539: dviout(Out|eq="align*");
5540: return 1;
5541: }
5542: if((type(Dvi)==1||Dvi==0) && getopt(rev)!=1) V=[[P,Q]];
5543: else V=0;
5544: if(L==0){ /* integer case */
5545: if(type(P) > 1 || type(Q) > 1 || Q==0 /* P <= 0 || Q <= 0 */
5546: || dn(P) > 1 || dn(Q) > 1)
5547: return 0;
5548: CPP = CQQ = 1; CQP = CPQ = 0;
5549: P1 = P; Q1 = Q;
5550: /* P1 = CPP*P + CPQ*Q
5551: Q1 = CQP*P + CQQ*Q */
5552: while(Q1 != 0){
5553: Div1 = idiv(P1,Q1); Div2 = irem(P1,Q1);
5554: if(type(V)==4) V=cons([Div1,Div2],V);
5555: P1 = Q1 ; Q1 = Div2;
5556: TP = CQP; TQ = CQQ;
5557: CQP = CPP-Div1*CQP;
5558: CQQ = CPQ-Div1*CQQ;
5559: CPP = TP; CPQ = TQ;
5560: }
5561: if(V!=0){
5562: V=reverse(V);
5563: if((DVI=abs(Dvi))==0) return V;
5564: PT=P;QT=Q;
5565: if(DVI==1 || DVI==2){
5566: Tb=str_tb(0,0);
5567: for(C=0,V=cdr(V);V!=[];V=cdr(V)){
5568: T=car(V);
5569: if(C++) str_tb(texcr(11),Tb);
5570: if(DVI==1){
5571: Qs=rtostr(QT);
5572: if(QT<0) Qs="("+Qs+")";
5573: if(T[1]>0) Qs=Qs+"+";
5574: if(T[1]!=0) Qs=Qs+rtostr(T[1]);
5575: str_tb(rtostr(PT)+"&="
5576: +rtostr(T[0])+"\\times"+Qs,Tb);
5577: }else{
5578: N=mat([T[0],1],[1,0]);
5579: if(C==1){
5580: str_tb(S0=mtotex(mat([PT],[QT])),Tb);
5581: M=N;
5582: }
5583: str_tb("&=",Tb);
5584: if(C>1) str_tb(mtotex(M),Tb);
5585: str_tb(mtotex(N),Tb);
5586: str_tb(S=mtotex(mat([QT],[T[1]])),Tb);
5587: if(C>1){
5588: str_tb("=",Tb);
5589: str_tb(mtotex(M=M*N),Tb);
5590: str_tb(S,Tb);
5591: }
5592: }
5593: PT=QT;QT=T[1];
5594: }
5595: if(DVI==2){
5596: str_tb(texcr(43)+S+"&=",Tb);
5597: str_tb(mtotex(myinv(M)),Tb);
5598: str_tb(S0,Tb);
5599: }
5600: Out=str_tb(0,Tb);
5601: if(Dvi>0){
5602: dviout(Out|eq="align*");
5603: return 1;
5604: }
5605: return Out;
5606: }
5607: }
5608: if(P1<0) return [-P1,-CPP,-CPQ,CQP,CQQ];
5609: return [P1, CPP, CPQ, CQP, CQQ];
5610: }
5611: if(type(L) == 2) /* polynomical case */
5612: L = [0,L];
5613: if(getopt(rev)==1 && L[0]!=0){
5614: R=mygcd(adj(P,L),adj(Q,L),L);
5615: return [adj(R[0],L),adj(R[1],L),adj(R[2],L),adj(R[3],L),adj(R[4],L)];
5616: }
5617: if(type(P) == 3)
5618: P = red(P);
5619: if(type(Q) == 3)
5620: Q = red(Q);
5621: CP=newvect(2,[1/dn(P),0]); CQ=newvect(2,[0,1/dn(Q)]);
5622: P=PT=nm(P); Q =QT=nm(Q);
5623: L = vweyl(L);
5624: while(Q != 0){
5625: R = divdo(P,Q,L);
5626: if(type(V)==4) V=cons(R,V);
5627: /* R[1] = R[2]*P - R[0]*Q
5628: = R[2]*(CP[0]*P0+CP[1]*Q0) - R[0]*(CQ[0]*P0+CQ[1]*Q0) */
5629: /*
5630: P(n) |0 1 | P(n-1)
5631: = | |
5632: R[1] |R[2] -R[0]| P(n)
5633: P(n+1) = R[1], P(n) = P, P(n-1) = Q
5634: */
5635: P = Q;
5636: Q = R[1];
5637: {
5638: CT = dupmat(CQ);
5639: CQ = [R[2]*CP[0]-muldo(R[0],CQ[0],L),
5640: R[2]*CP[1]-muldo(R[0],CQ[1],L)];
5641: CP = CT;
5642: }
5643: }
5644: if(V!=0){
5645: V=reverse(V);
5646: if((DVI=abs(Dvi))==0) return V;
5647: if(type(L[0])<1) Var=L[1];
5648: else Var=[L[1],"\\partial"];
5649: if(DVI==1 || DVI==2){
5650: Tb=str_tb(0,0);
5651: PT=car(V)[0];QT=car(V)[1];
5652: for(C=0,V=cdr(V);V!=[];V=cdr(V)){
5653: T=car(V);
5654: if(C++) str_tb(texcr(11),Tb);
5655: if(DVI==1){
5656: if(T[2]!=1){
5657: str_tb(monototex(T[2]),Tb);
5658: str_tb("(",Tb);
5659: str_tb(fctrtos(PT|var=Var,TeX=2),Tb);
5660: str_tb(")&=",Tb);
5661: }else{
5662: str_tb(fctrtos(PT|var=Var,TeX=2),Tb);
5663: str_tb("&=",Tb);
5664: }
5665: str_tb("(",Tb);
5666: str_tb(fctrtos(T[0]|var=Var,TeX=2),Tb);
5667: str_tb(")(",Tb);
5668: str_tb(fctrtos(QT|var=Var,TeX=2),Tb);
5669: if(T[1]!=0){
5670: str_tb(")+(",Tb);
5671: str_tb(fctrtos(T[1]|var=Var,TeX=2),Tb);
5672: }
5673: str_tb(")",Tb);
5674: }else{
5675: N=mat([red(T[0]/T[2]),1],[1,0]);
5676: if(C==1){
5677: str_tb(S0=mtotex(mat([PT],[QT])|var=Var),Tb);
5678: M=N;
5679: }
5680: str_tb("&=",Tb);
5681: if(C>1) str_tb(mtotex(M),Tb);
5682: str_tb(mtotex(N|var=Var),Tb);
5683: str_tb(S=mtotex(mat([QT],[T[1]])|var=Var),Tb);
5684: if(C>1){
5685: str_tb("=",Tb);
5686: str_tb(mtotex(M=muldo(M,N,L)|var=Var),Tb);
5687: str_tb(S,Tb);
5688: }
5689: }
5690: PT=QT;QT=T[1];
5691: }
5692: if(DVI==2){
5693: FT=fctr(PT);
5694: for(R=1;FT!=[];FT=cdr(FT)){
5695: if(mydeg(car(FT)[0],L[1])<1)
5696: for(J=car(FT)[1];J>0;J--) R*=car(FT)[0];
5697: }
5698: if(R!=1){
5699: str_tb(texcr(79),Tb);
5700: M=muldo(M,mat([R,0],[0,1]),L);
5701: str_tb(mtotex(M|var=Var),Tb);
5702: str_tb(S=mtotex(mat([PT/R],[QT])|var=Var),Tb);
5703: }
5704: str_tb(texcr(43)+S+"&=",Tb);
5705: if(type(Var)==4){
5706: N=mdivisor(M,L|trans=1);
5707: N=N[1];
5708: }else
5709: N=myinv(M);
5710: str_tb(mtotex(N|var=Var),Tb);
5711: str_tb(S0,Tb);
5712: }
5713: Out=str_tb(0,Tb);
5714: if(Dvi>0){
5715: dviout(Out|eq="align*");
5716: return 1;
5717: }
5718: return Out;
5719: }
5720: }
5721: Q = rede(P,L);
5722: R = red(P/Q);
5723: return [Q,red(CP[0]/R),red(CP[1]/R),red(CQ[0]/R),red(CQ[1]/R)];
5724: }
5725:
5726: def mylcm(P,Q,L)
5727: {
5728: Rev=(getopt(rev)==1)?1:0;
5729: if(Rev==1){
5730: P=adj(P); Q=adj(Q);
5731: }
5732: R = mygcd(P,Q,L);
5733: S=(type(L)<=2)?R[3]*P:muldo(R[3],P,L);
5734: S = nm(S);
5735: if(type(S) <= 1 && type(L) <= 1){
5736: if(S<0) S = -S;
5737: return S;
5738: }
5739: if(type(L) == 2)
5740: return easierpol(S,L);
5741: S=rede(easierpol(S,L[1]),L);
5742: return (Rev==1)?adj(S):S;
5743: }
5744:
5745: def sftpexp(P,LL,F,Q)
5746: {
5747: if(type(LL[0]) < 4)
5748: LL = [LL];
5749: for(L0=L1=[],LT=LL;LT!=[];LT=cdr(LT)){
5750: W=vweyl(car(LT));
5751: L0=cons(W,L0);
5752: D=mydiff(F,W[0]);
5753: if(D!=0) L1=cons(W[1]+Q*D/F,L1);
5754: else L1=cons(W[1],L1);
5755: }
5756: return rede(transpdosub(P,L0,L1),L0);
5757: }
5758:
5759: def applpdo(P,F,LL)
5760: {
5761: if(type(F)>3)
5762: #ifdef USEMODULE
5763: return mmulbys(os_md.applpdo,P,F,[LL]);
5764: #else
5765: return mmulbys(applpdo,P,F,[LL]);
5766: #endif
5767: L = vweyl(LL[0]);
5768: LL = cdr(LL);
5769: Deg = deg(P,L[1]);
5770: S = F;
5771: for(I = R = 0; I <= Deg ; I++){
5772: if(I > 0)
5773: S = mydiff(S,L[0]);
5774: if(LL == [])
5775: R = radd(R,mycoef(P,I,L[1])*S);
5776: else
5777: R = radd(R,applpdo(mycoef(P,I,L[1]), S, LL));
5778: }
5779: return R;
5780: }
5781:
5782: def tranlpdo(P,L,M)
5783: {
5784: N = length(L);
5785: R = size(M);
5786: if(R[0] != N || R[1] != N){
5787: print("Strange size");
5788: return;
5789: }
5790: InvM = M;
5791: if(InvM[1] == 0){
5792: print("Not invertible");
5793: return;
5794: }
5795: XL = newvector(N);
5796: DL = newvector(N);
5797: for(I = 0; I < 0; I++){
5798: R = vweyl(L[I]);
5799: XL[I] = R[0];
5800: DL[I] = R[1];
5801: }
5802: for(I = 0; I < N; I++){
5803: for(J = XX = D0 = 0; J < N; J++){
5804: XX = radd(XX,M[I][J]*XL[J]);
5805: DD = radd(DD, red(InvM[0][I][J]/InvM[1])*DL[J]);
5806: P = mysubst(P,[[XL[I],XX],[DL[I],DD]]);
5807: }
5808: }
5809: return P;
5810: }
5811:
5812: def divdo(P,Q,L)
5813: {
5814: if(L==0){
5815: R=P-idiv(P,Q)*Q;
5816: if(R<0){
5817: if(Q>0) R+=Q;
5818: else R-=Q;
5819: }
5820: return [(P-R)/Q,R,1];
5821: }
5822: L = vweyl(L);
5823: if(getopt(rev)==1){
5824: R=divdo(adj(P,L),adj(Q,L),L);
5825: return [adj(R[0],L),adj(R[1],L),R[2]];
5826: }
5827: X = L[0]; DX = L[1];
5828: S = 0;
5829: M = 1;
5830: I = mydeg(Q,DX);
5831: CQ = mycoef(Q,I,DX);
5832: while((J=mydeg(P,DX)) >= I){
5833: C = mycoef(P,J,DX);
5834: SR = red(C/CQ);
5835: if(dn(SR) != 1){
5836: M *= dn(SR);
5837: P *= dn(SR);
5838: S *= dn(SR);
5839: SR = nm(SR);
5840: }
5841: P -= muldo(SR*(DX)^(J-I),Q,L);
5842: S += SR*(DX)^(J-I);
5843: }
5844: return [S,P,M];
5845: }
5846:
5847: def qdo(P,Q,L)
5848: {
5849: L = vweyl(L); DX = L[1]; OD = deg(P,DX);
5850: V = newvect(OD+1);
5851: for(I = 0; I <= OD; I++){
5852: if(I)
5853: Q = muldo(DX,Q,L);
5854: S = divdo(Q,P,L);
5855: V[I] = S[1]*DX-S[2]*zz^I;
5856: }
5857: for(K = [], I = OD; I >= 0; I--)
5858: K = cons(DX^(I+1), K);
5859: R = lsol(V,K);
5860: S = length(R);
5861: for(I = P1 = 0; I < S; I++){
5862: if(type(R[I]) < 4 && mydeg(R[I],DX) == 0 && R[I] != 0
5863: && (mydeg(R[I],zz) <= mydeg(P,DX)))
5864: P1 = R[I];
5865: else if(type(R[I]) == 4 && R[I][0] == DX)
5866: P2 = R[I][1];
5867: }
5868: T=fctr(P1);
5869: for(I=0, S=length(T), P1=1; I<S; I++){
5870: if(mydeg(T[I][0],zz) > 0)
5871: P1 *= T[I][0]^(T[I][1]);
5872: }
5873: return subst([P1,P2],zz,DX);
5874: }
5875:
5876: def sqrtdo(P,L)
5877: {
5878: L = vweyl(L);
5879: P = toeul(P,L,0);
5880: V = -1;
5881: for(R = 0, Ord = mydeg(P,L[1]); Ord >= 0; Ord--){
5882: Q = coef(P,Ord,L[1]);
5883: M = mydeg(Q,L[0]);
5884: N = mymindeg(Q,L[0]);
5885: if(V < 0)
5886: V = M+N;
5887: else if(V != M+N){
5888: print("Cannot be transformed!");
5889: return;
5890: }
5891: Q = tohomog(red(Q/L[0]^N), [L[0]], z_z);
5892: if(irem(Ord,2))
5893: B = x-z_z;
5894: else
5895: B = x+z_z;
5896: Q = substblock(Q,x,B,z_zz);
5897: if(mydeg(Q,x) > 0){
5898: print("Cannot be transformed!");
5899: return;
5900: }
5901: R += mysubst(Q,[z_zz,x])*L[1]^Ord;
5902: }
5903: return fromeul(R,L,0);
5904: }
5905:
5906: def ghg(A,B)
5907: {
5908: R = dx;
5909: while(length(B)>0){
5910: R = muldo(x*dx+car(B),R,[x,dx]);
5911: B = cdr(B);
5912: }
5913: T = 1;
5914: while(length(A)>0){
5915: T = muldo(x*dx+car(A),T,[x,dx]);
5916: A = cdr(A);
5917: }
5918: return R-T;
5919: }
5920:
5921: def ev4s(A,B,C,S,T)
5922: {
5923: R4 = x^2*(x-1)^2;
5924: R3 = x*(x-1)*((2*A-2*B-8)*x-2*A+5);
5925: R2 = (-3/2*(A^2+B^2)+3*A*B+9*A-9*B-29/2+1/4*(S^2+T^2))*x^2
5926: +(5*A^2/2-13*A-3*A*B+B^2/2+7*B-C^2+C+35/2 - 1/4*(S^2+T^2))*x
5927: - (2*A+2*C-5)*(2*A-2*C-3)/4;
5928: R1 = 1/4*(A-B-2)*(2*A^2-4*A*B-8*A+2*B^2+8*B+10-S^2-T^2)*x
5929: +15/4+3*B^2/4-C^2/2+11*A^2/4 - 11*A/2+3*B+B*C-7*A*B/2+C/2-A*B^2/2
5930: #if 1
5931: + A^2*B
5932: #endif
5933: - B*C^2 - A^3/2+(2*A-3)*(S^2+T^2)/8;
5934: /* OK? for the above term added */
5935: R0 = -(A-B-1-S)*(A-B-1+S)*(A-B-1-T)*(A-B-1+T)/16;
5936: return (R4*dx^4-R3*dx^3-R2*dx^2-R1*dx-R0);
5937: }
5938:
5939: def b2e(A,B,C,S,T)
5940: {
5941: R4 = x^2*(x-1)^2;
5942: R3 = x*(x-1)*(2*x-1)*(2*c-5);
5943: R2 = (-6*C^2+24*C-25+1/2*S^2+1/2*T^2)*x^2
5944: +(6*C^2-24*C+25-1/2*S^2-1/2*T^2-A^2+B^2+A-B)*x
5945: +A^2-C^2-A+4*C-15/4;
5946: R1 = (2*C-3)*(2*C^2-6*C+5-1/2*S^2-1/2*T^2)*x
5947: +(2*C-3)*(-C^2+3*C+1/2*A^2-1/2*B^2+1/2*B-1/2*A-5/2+1/4*S^2+1/4*T^2);
5948: R0 = -(2-2*C+S+T)*(2-2*C-S-T)*(2-2*C+S-T)*(2-2*C-S+T)/16;
5949: return (R4*dx^4-R3*dx^3-R2*dx^2-R1*dx-R0);
5950: }
5951:
5952:
5953: /*
5954: T^m = T(T-1)....(T-m+1)
5955: f(t) -> g(t)
5956:
5957: f(t) = a_mt^m + ... + a_1t+a_0
5958: g(x*dx) = a_m*x^m*dx^m + ... + a_1*x*dx+a_0
5959:
5960: ret: x(x-1)...(x-i+1)
5961: */
5962: def sftpow(X,I)
5963: {
5964: R = 1;
5965: for(J=0;J<I;J++)
5966: R *= X-J;
5967: return(R);
5968: }
5969:
5970: /*
5971: ret: x(x+K)(x+2*k)...(x+(i-1)*k)
5972: */
5973: def sftpowext(X,I,K)
5974: {
5975: R = 1;
5976: for(J=0;J<I;J++)
5977: R *= X+K*J;
5978: return(R);
5979: }
5980:
5981: def polinsft(F,A)
5982: {
5983: R = 0;
5984: while(F != 0){
5985: D = mydeg(F,A);
5986: C = mycoef(F,D,A);
5987: R += C*A^D;
5988: F -= C*sftpow(A,D);
5989: }
5990: return R;
5991: }
5992:
5993: def pol2sft(F,A)
5994: {
5995: S=getopt(sft);
5996: if(type(S)<0 || type(S)>2) S=1;
5997: R = 0;
5998: for(I = mydeg(F,A); I >= 0; I--)
5999: R = R*(A-I*S) + mycoef(F,I,A);
6000: return R;
6001: }
6002:
6003: def binom(P,N)
6004: {
1.20 takayama 6005: if(type(N)!=1 || N<=0) return 1;
1.6 takayama 6006: for(S=1;N>0;N--,P-=1) S*=P/N;
6007: return red(S);
6008: }
6009:
6010: def expower(P,R,N)
6011: {
6012: if(type(N)!=1 || N<0) return 0;
6013: for(S=S0=K=1;K<=N;K++,R-=1){
6014: S0*=P*R/K;S+=S0;
6015: }
6016: return red(S);
6017: }
6018:
6019: def seriesHG(A,B,X,N)
6020: {
1.20 takayama 6021: if(N==0) return 1;
1.6 takayama 6022: if(type(N)!=1 || N<0) return 0;
6023: if(type(X)<4){
6024: for(K=0,S=S0=1;K<N;K++){
6025: for(T=A; T!=[]; T=cdr(T)) S0*=car(T)+K;
6026: for(T=B; T!=[]; T=cdr(T)) S0/=car(T)+K;
6027: S0=red(S0*X/(K+1));
6028: DN=dn(S0);
6029: S=red((red(S*DN)+nm(S0))/DN);
6030: }
6031: return S;
6032: }
6033: S=0;
6034: for(K=0;K<=N;K++){
6035: for(I=0;I<=N-K;I++){
6036: C=1/sftpowext(1,I,1)/sftpowext(1,J,1);
6037: for(T=A[0];T!=[];T=cdr(T)) C*=sftpowext(car(T),I+K,1);
6038: for(T=A[1];T!=[];T=cdr(T)) C*=sftpowext(car(T),I,1);
6039: for(T=A[2];T!=[];T=cdr(T)) C*=sftpowext(car(T),K,1);
6040: for(T=B[0];T!=[];T=cdr(T)) C/=sftpowext(car(T),I+K,1);
6041: for(T=B[1];T!=[];T=cdr(T)) C/=sftpowext(car(T),I,1);
6042: for(T=B[2];T!=[];T=cdr(T)) C/=sftpowext(car(T),K,1);
6043: S+=red(C*X[0]^I*X[1]^K);
6044: }
6045: }
6046: return S;
6047: }
6048:
6049: def evalred(F)
6050: {
6051: Opt=getopt(opt);
6052: if(type(Opt)!=4){
6053: Opt=[];
6054: }else if(length(Opt)==2 && type(Opt[0])!=4) Opt=[Opt];
6055: for(;;){
1.17 takayama 6056: G=mysubst(F,[[tan(0),0],[asin(0),0],[atan(0),0],[sinh(0),0],[tanh(0),0],
6057: [log(1),0],[cosh(0),1],[exp(0),1]]);
1.6 takayama 6058: for(Rep=Opt; Rep!=[]; Rep=cdr(Rep))
6059: G=subst(G,car(Rep)[0],car(Rep)[1]);
6060: Var=vars(G);
6061: for(V=Var; V!=[]; V=cdr(V)){
1.17 takayama 6062: if(!(VV=args(CV=car(V)))) continue;
6063: if((functor(CV)==sin||functor(CV)==cos)){
6064: P=2*red(VV[0]/@pi);
6065: if(functor(CV)==sin) P=1-P;
6066: if(isint(P)){
6067: if(iand(P,1)) G=subst(G,CV,0);
6068: else if(!iand(P,3)) G=subst(G,CV,1);
6069: else G=subst(G,CV,-1);
6070: continue;
6071: }
6072: if(isint(P*=3/2)){
6073: if(iand(P,3)==1) G=subst(G,CV,1/2);
6074: else G=subst(G,CV,-1/2);
6075: }
6076: }
6077: for(;VV!=[];VV=cdr(VV))
6078: if(car(VV)!=(TV=evalred(car(VV)))) G=subst(G,car(VV),TV);
6079: if(functor(CV)!=pow || (args(CV)[0])!=1) continue;
6080: G=subst(G,CV,1);
1.6 takayama 6081: }
6082: if(G==F) return F;
6083: F=G;
6084: }
6085: }
6086:
6087: def seriesMc(F,N,V)
6088: {
6089: if(type(V)<4) V=[V];
6090: V=reverse(V);
6091: L=length(V);
6092: if(type(Opt=getopt(evalopt))!=4) Opt=[];
6093: P=newvect(L);
6094: G=newvect(L+1);
6095: G[0]=F;
6096: for(I=0;I<L;I++)
6097: G[I+1]=eval(evalred(subst(G[I],V[I],0)|opt=Opt));
6098: R=G[L];
6099: for(;;){
6100: for(M=0,I=0;I<L;I++){
6101: M+=P[I];
6102: if(M==N) break;
6103: }
6104: if(M<N){
6105: P[L-1]++;
6106: G[L-1]=mydiff(G[L-1],V[L-1]);
6107: G[L]=eval(evalred(mysubst(G[L-1],[V[L-1],0])|opt=Opt));
6108: }else{
6109: if(I--==0) break;
6110: P[I]++;
6111: G[I]=mydiff(G[I],V[I]);
6112: while(I++<L){
6113: G[I]=eval(evalred(mysubst(G[I-1],[V[I-1],0])|opt=Opt));
6114: if(I<L) P[I]=0;
6115: }
6116: }
6117: K=1;
6118: for(I=0;I<L;I++) K*=V[I]^P[I]/fac(P[I]);
6119: R+=G[L]*K;
6120: }
6121: return R;
6122: }
6123:
6124: def seriesTaylor(F,N,V)
6125: {
6126: G=F;
6127: if(isvar(V)) V=[V];
6128: if(length(V)==2 && type(car(V))!=4 && !isvar(V[1])) V=[V];
6129: for(V0=V1=[];V!=[];V=cdr(V)){
6130: if(type(T=car(V))!=4) T=[T];
6131: V0=cons(X=car(T),V0);
6132: if(length(T)==1 || T[1]==0){
6133: V1=cons(X,V1);continue;
6134: }
6135: S=my_tex_form(-T[1]);
6136: if(str_char(S,0,"-")!=0) S="+"+S;
6137: S="("+my_tex_form(X)+S+")";
6138: V1=cons([X,S],V1);
6139: F=red(subst(F,T[0],T[0]+T[1]));
6140: }
6141: V0=reverse(V0);V1=reverse(V1);
6142: F=seriesMc(F,N,V0|option_list=getopt());
6143: if(getopt(frac)==0) F=frac2n(F);
6144: T=getopt(dviout);
6145: if(type(T)!=1) T=0;
6146: F=fctrtos(F|var=V1,rev=1,TeX=(T==0||T==2)?2:3);
6147: if(getopt(small)==1) F=str_subst(F,"\\frac{","\\tfrac{");
6148: if(T<0 || T==1) F="\\begin{align}\\begin{split}\n"+
6149: my_tex_form(G)+"&="+F+"+\\cdots\n\\end{split}\\end{align}\n";
6150: if(T==1) dviout(F);
6151: else if(T==1) dviout(F|eq=4);
6152: return F;
6153: }
6154:
1.27 takayama 6155: def mulpolyMod(P,Q,X,N)
6156: {
6157: Red=(type(P)>2||type(Q)>2)?1:0;
6158: for(I=R=0;I<=N;I++){
6159: P0=mycoef(P,I,X);
6160: for(J=0;J<=N-I;J++){
6161: R+=P0*mycoef(Q,J,X)*X^(I+J);
6162: if(Red) R=red(R);
6163: }
6164: }
6165: return R;
6166: }
6167:
1.26 takayama 6168: def taylorODE(D){
6169: Dif=(getopt(dif)==1)?1:0;
6170: if(D==0) return Dif?f:f_00;
1.27 takayama 6171: if(type(T=getopt(runge))!=1||ntype(T)!=0) T=0;
1.26 takayama 6172: if(type(F=getopt(f))!=7&&type(F)<2) F="f_";
6173: if(type(D)!=1||ntype(D)!=0||D<0||D>30) return 0;
6174: if(type(H=getopt(taylor))==4&&length(H)==2){
1.27 takayama 6175: if(type(Lim=getopt(lim))==2) DD=D;
6176: else if(type(Lim)==4){
6177: DD=Lim[1];Lim=Lim[0];
6178: }else Lim=0;
6179: for(R=I=0;I<=D;I++){
6180: #if 0
6181: if(I) H0*=H[0];
6182: else H0=1;
6183: if(Lim) H0=os_md.polcut(H0,DD,Lim);
6184: if(type(F)!=7) G=I?mydiff(G,x):F;
6185: for(J=0;J<=D-I;J++){
6186: if(J) H1*=H[1];
6187: else H1=H0;
6188: if(Lim) H1=os_md.polcut(H1,DD,Lim);
6189: if(type(F)==7) G=makev([F,I,J]);
6190: else if(J) G=mydiff(G,y);
6191: if(Lim) H1=os_md.polcut(H1,DD,Lim);
6192: R+=G*H1/fac(I)/fac(J);
6193: #else
6194: if(I){
6195: if(Lim) H0=mulpolyMod(H0,H[0],Lim,DD);
6196: else H0*=H[0];
6197: }else H0=1;
6198: if(type(F)!=7) G=I?mydiff(G,x):F;
6199: for(J=0;J<=D-I;J++){
6200: if(J){
6201: if(Lim) H1=mulpolyMod(H1,H[1],Lim,DD);
6202: else H1*=H[1];
6203: }else H1=H0;
6204: if(type(F)==7) G=makev([F,I,J]);
6205: else if(J) G=mydiff(G,y);
6206: R+=G*H1/fac(I)/fac(J);
6207: #endif
1.26 takayama 6208: }
6209: }
1.27 takayama 6210: if(Lim) R=os_md.polcut(R,DD,Lim);
6211: return R;
1.26 takayama 6212: }else{
6213: if(type(H=getopt(series))>=0||getopt(list)==1){
6214: if(type(F)!=7){
6215: for(PP=[F],I=1;I<D;I++)
6216: PP=cons(mydiff(car(PP),x)+mydiff(car(PP),y)*F,PP);
6217: if(type(H)<0) return PP;
6218: for(R=0,DD=D;DD>=1;DD--,PP=cdr(PP)) R+=car(PP)*H^DD/fac(DD);
6219: return red(R);
6220: }
6221: if(type(H)>=0) D--;
6222: PP=taylorODE(D-1|list=1);
6223: if(type(PP)!=4) PP=[PP];
6224: P=car(PP);
6225: }else P=taylorODE(D-1);
6226: for(R=I=0;I<D;I++){
6227: for(J=0;J<D-I;J++){
6228: Q=diff(P,makev([F,I,J]));
6229: if(Q!=0) R+=Q*(f_00*makev([F,I,J+1])+makev([F,I+1,J]));
6230: }
6231: }
6232: if(getopt(list)==1){
6233: R=cons(R,PP);
6234: if(Dif!=1) return R;
6235: }else if(type(H)>=0){
6236: R=y+R*H^(D+1)/fac(D+1);
6237: for(DD=D;DD>0;PP=cdr(PP),DD--) R+=car(PP)*H^(DD)/fac(DD);
6238: if(T){
6239: TT=(T<0)?-T:T;
6240: K=newvect(TT);K[0]=Dif?f:f_00;
6241: for(I=1;I<TT;I++){
6242: for(S=J=0;J<I;J++) S+=makev(["a_",I+1,J+1])*K[J];
1.27 takayama 6243: K[I]=taylorODE(D|taylor=[makev(["c_",I+1])*H,S*H],lim=[H,TT-1]);
1.26 takayama 6244: }
6245: for(S=I=0;I<TT;I++) S+=makev(["b_",I+1])*K[I];
6246: S=S*H+y;
6247: R=S-R;
6248: if(T<0){
6249: for(V=[H],I=0;I<=D;I++)
6250: for(J=0;J<=D-I;J++) V=cons(makev([F,I,J]),V);
6251: return os_md.ptol(R,reverse(V)|opt=0);
6252: }
6253: }else T=0;
6254: }
6255: }
6256: if(Dif){
6257: for(I=0;I<=D;I++){
6258: for(J=0;J<=D;J++){
6259: if(I==0&&J==0){
6260: R=subst(R,f_00,f);
6261: continue;
6262: }
6263: V=makev([F,str_times("x",I),str_times("y",J)]);
6264: R=subst(R,makev([F,I,J]),V);
6265: }
6266: }
6267: }
6268: return R;
6269: }
6270:
1.6 takayama 6271: def toeul(F,L,V)
6272: {
6273: L = vweyl(L);
6274: X = L[0]; DX = L[1];
6275: I = mydeg(F,DX);
6276: if(V == "infty"){
6277: for(II=I; II>=0; II--){
6278: J = mydeg(P=mycoef(F,I,DX),X);
6279: if(II==I) S=II-J;
6280: else if(P!=0 && II-J>S) S=II-J;
6281: }
6282: F *= X^S;
6283: R = 0;
6284: for( ; I >= 0; I--)
6285: R += red((mysubst(mycoef(F,I,DX),[X,1/X])*(x*DX)^I));
6286: return(subst(pol2sft(R,DX),DX,-DX));
6287: }
6288: F = subst(F,X,X+V);
6289: for(II=I; II>=0; II--){
6290: J = mymindeg(P=mycoef(F,II,DX),X);
6291: if(II==I) S=II-J;
6292: else if(P!=0 && II-J>S) S=II-J;
6293: }
6294: F *= X^S;
6295: R = 0;
6296: for( ; I >= 0; I--)
6297: R += (red(mycoef(F,I,DX)/X^I))*DX^I;
6298: return pol2sft(R,DX);
6299: }
6300:
6301: /*
6302: def topoldif(P,F,L)
6303: {
6304: L = vweyl(L);
6305: P = nm(red(P));
6306: while(deg(P,L[1]) > 0){
6307: R = coef(P,0,L[0]);
6308: Q = red((P-R)/(F*L[0]);
6309: P = nm(Q)*zz+F*R*dn(Q);
6310: }
6311: }
6312: */
6313:
6314: def fromeul(P,L,V)
6315: {
6316: if(P == 0)
6317: return 0;
6318: L = vweyl(L);
6319: X = L[0]; DX = L[1];
6320: I = mydeg(P,DX);
6321: if(V == "infty"){
6322: P = subst(P,DX,-DX);
6323: J = mydeg(P,X);
6324: P = red(mysubst(P,[X,1/X])*X^J);
6325: }
6326: R = mycoef(P,0,DX);
6327: S = 1;
6328: for(S = J = 1; J <= I; J++){
6329: S = DX*(S*X + mydiff(S,DX));
6330: R += mycoef(P,J,DX)*S;
6331: }
6332: while(mycoef(R,0,X) == 0)
6333: R = tdiv(R,X);
6334: if(V != "infty" && V != 0)
6335: R = mysubst(R,[X,X-V]);
6336: return R;
6337: }
6338:
6339: def sftexp(P,L,V,N)
6340: {
6341: L = vweyl(L); DX = L[1];
6342: P = mysubst(toeul(P,L,V),[DX,DX+N]);
6343: return fromeul(P,L,V);
6344: }
6345:
6346:
6347: def fractrans(P,L,N0,N1,N2)
6348: {
6349: L = vweyl(L);
6350: if(N2 != "infty"){
6351: if(N0 == "infty")
6352: N0 = 0;
6353: else
6354: N0 = red(1/(N0-N2));
6355: if(N1 == "infty")
6356: N1 = 0;
6357: else
6358: N1 = red(1/(N1-N2));
6359: P = mysubst(P,[L[0],L[0]+N2]);
6360: P = fromeul(toeul(P,L,"infty"),L,0);
6361: }
6362: if(N0 != 0){
6363: P = mysubst(P,[L[0],L[0]+N0]);
6364: N1 -= N0;
6365: }
6366: if(N1 != 1)
6367: P = mysubst(P,[[L[0],L[0]/N1],[L[1],L[1]*N1]]);
6368: return P;
6369: }
6370:
6371: def soldif(P,L,V,Q,N)
6372: {
6373: L = vweyl(L); X = L[0]; DX = L[1];
6374: P = mysubst(toeul(P,L,V),[DX,DX+Q]);
6375: DEG = mydeg(P,X);
6376: P0 = newvect(DEG+1);
6377: for(I = 0; I <= DEG; I++)
6378: P0[I] = coef(P,I,X);
6379: if(P0[0] == 0)
6380: return 0;
6381: if(subst(P0[0],DX,0) != 0){
6382: mycat([Q,"is not the exponent at", V])$
6383: return 0;
6384: }
6385: R = newvect(N+1);
6386: R[0] = 1;
6387: for(I = 1; I <= N; I++){
6388: for(S = 0, K = 1; K <= DEG && K <= I; K++)
6389: S += mysubst(P0[K],[DX,I-K])*R[I-K];
6390: S = red(S);
6391: M = mysubst(P0[0],[DX,I]);
6392: if(M != 0){
6393: R[I] = -red(S/M);
6394: if(R1 != 0){
6395: for(S = 0, K = 1; K <= DEG && K <= I; K++)
6396: S += mysubst(P0[K],[DX,I-K])*R1[I-K] +
6397: mysubst(P1[K],[DX,I-K])*R[I-K];
6398: R1[I] = -red(S/M);
6399: }
6400: }else{
6401: if(S == 0){
6402: if(R1 != 0){
6403: for(S = 0, K = 1; K <= DEG && K <= I; K++)
6404: S += mysubst(P0[K],[DX,I-K])*R1[I-K] +
6405: mysubst(P1[K],[DX,I-K])*R[I-K];
6406: }
6407: if(S == 0)
6408: continue;
6409: }
6410: R1 = newvect(N+1);
6411: for(K = 0; K < I; K++){
6412: R1[K] = R[K];
6413: R[K] = 0;
6414: }
6415: R1[I] = 0;
6416: P1 = newvect(DEG);
6417: for(K = 0; K <= DEG; K++)
6418: P1[K] = mydiff(P0[K], DX);
6419: M = mysubst(P1[0],[DX,I]);
6420: if(M == 0){
6421: cat(["multiple log at ", I])$
6422: return 0;
6423: }
6424: R[I] = -red(S/M);
6425: }
6426: }
6427: if(R1 != 0)
6428: return [R1, R];
6429: else
6430: return R;
6431: }
6432:
6433: def chkexp(P,L,V,Q,N)
6434: {
6435: L = vweyl(L); X = L[0]; DX = L[1];
6436: P = mysubst(toeul(P,L,V),[DX,DX+Q]);
6437: P = fromeul(P,L,0);
6438: D = mydeg(P,DX);
6439: Z = mindeg(mycoef(P,D,DX), X) - (D-N);
6440: R = [];
6441: for(I = 0; I < Z; I++){
6442: S = mycoef(P,I,X);
6443: if(S != 0){
6444: for(J = mydeg(S,DX); J >= 0; J--){
6445: T = mycoef(S,J,DX);
6446: if(T != 0)
6447: R = cons(T,R);
6448: }
6449: }
6450: }
6451: return R;
6452: }
6453:
6454:
6455: def sqrtrat(P)
6456: {
6457: if(P==0) return 0;
6458: if(type(P)==3||type(P)==2){
6459: P=red(P);
6460: if(imag(dn(P))!=0||imag(nm(P))!=0){
6461: if(imag(dn(P))==0&&real(P)!=0){
6462: F=red(imag(P)/real(P));
6463: if(F==3^(1/2)||F==-3^(1/2)){
6464: if(eval(real(P))<0)
6465: return -real(P)+imag(P)*@i;
6466: else{
6467: if(eval(imag(P))>0) return imag(P)+real(P)*@i;
6468: else return -imag(P)-real(P)*@i;
6469: }
6470: }
6471: }
6472: return [];
6473: }
6474: F=fctr(dn(P));
6475: R=sqrtrat(car(F)[0]);
6476: for(F=cdr(F);F!=[];F=cdr(F)){
6477: if(!iand(car(F)[1],1)) R*=car(F)[0]^(car(F)[1]/2);
6478: else return [];
6479: }
6480: F=fctr(nm(P));
6481: R=sqrtrat(car(F)[0])/R;
6482: for(F=cdr(F);F!=[];F=cdr(F)){
6483: if(!iand(car(F)[1],1)) R*=car(F)[0]^(car(F)[1]/2);
6484: else return [];
6485: }
6486: return R;
6487: }
6488: if(ntype(P)==4){
6489: P0=real(P);P1=imag(P)/2;
6490: X=makenewv(P);
6491: for(R=fctr(X^4-P0*X^2-P1^2);R!=[];R=cdr(R)){
6492: RT=car(R)[0];
6493: if(deg(RT,X)==1){
6494: X=-mycoef(RT,0,X)/mycoef(RT,1,X);
6495: return X+P1/X*@i;
6496: }
6497: if(deg(RT,X)==2){
6498: if((D=mycoef(RT,1,X)^2-4*mycoef(RT,2,X)*mycoef(RT,0,X))<0) continue;
6499: X=(-mycoef(RT,1,X)+sqrtrat(D))/(2*mycoef(RT,2,X));
6500: return X+P1*sqrt2rat(1/X)*@i;
6501: }
6502: }
6503: D=P0^2+4*P1^2;
6504: if(P1>0) return ((sqrtrat(D)+P0)/2)^(1/2)+((sqrtrat(D)-P0)/2)^(1/2)*@i;
6505: return ((sqrtrat(D)+P0)/2)^(1/2)-((sqrtrat(D)-P0)/2)^(1/2)*@i;
6506: }else if(ntype(P)!=0) return [];
6507: if(P==1) return P;
6508: Dn=dn(P);Nm=nm(P);C=R=1;
6509: N=pari(factor,Dn);
6510: if(N){
6511: for(II=car(size(N))-1;II>=0;II--){
6512: if(iand(K=N[II][1],1)){
6513: R*=N[II][0];
6514: K++;
6515: }
6516: C/=N[II][0]^(K/2);
6517: }
6518: }
6519: N=pari(factor,Nm);
6520: if(N){
6521: for(II=car(size(N))-1;II>=0;II--){
6522: if(N[II][0]==-1){
6523: C*=@i;
6524: continue;
6525: }
6526: K=N[II][1];
6527: if(iand(K,1)){
6528: R*=N[II][0];
6529: K--;
6530: }
6531: if(K!=0) C*=N[II][0]^(K/2);
6532: }
6533: }
6534: if(R!=1) C*=R^(1/2);
6535: return C;
6536: }
6537:
6538: def fctri(F)
6539: {
6540: R=(iscoef(F,os_md.israt))?fctr(F):[[1,1],[F,1]];
6541: if(!iscoef(F,os_md.iscrat)||chkfun("af_noalg",0)==0) return R;
6542: X=makenewv(vars(F));
6543: for(S=[];R!=[];R=cdr(R)){
6544: if(length(Var=vars(R0=car(R)[0])) == 1 && (D=mydeg(R0,Var=car(Var))) > 0){
6545: if(imag(T=mycoef(R0,D,Var))!=0) R0/=T;
6546: T=af_noalg(real(R0)+imag(R0)*X,[[X,X^2+1]]);
6547: if(length(T)>1||T[0][1]>1){
6548: T=subst(T,X,@i);
6549: for(; T!=[];T=cdr(T)){
6550: if(vars(T[0])!=[])
6551: S=cons([car(T)[0],car(T)[1]*car(R)[1]],S);
6552: }
6553: continue;
6554: }
6555: }
6556: S=cons(R[0],S);
6557: }
6558: return reverse(S);
6559: }
6560:
6561: def getroot(F,X)
6562: {
6563: S=[];
6564: if(type(Cpx=getopt(cpx))!=1) Cpx=0;
6565: M=getopt(mult);
6566: if(type(F) == 3)
6567: F = nm(red(F));
6568: for(R=fctri(F); length(R)>0; R = cdr(R)){
6569: T=car(R);
6570: P=car(T);
6571: I=car(cdr(T));
6572: if(mydeg(P,X)>0){
6573: if(mydeg(P,X)==1){
6574: C = mycoef(P,1,X);
6575: P = X - red(P/C);
6576: }else if(mydeg(P,X)==2 && Cpx>0){
6577: C2=mycoef(P,2,X);C1=mycoef(P,1,X);C0=mycoef(P,0,X);
6578: C=sqrt2rat(C1^2-4*C0*C2);
6579: C0=[];
6580: if(type(C)==0&&ntype(C)==0&&pari(issquare,-C)) C0=sqrt(C);
6581: else if(Cpx>1) C0=sqrtrat(C);
6582: if(C0==[]&&Cpx>2) C0=C^(1/2);
6583: if(C0!=[]){
6584: if(M==1)
6585: S=cons([I,sqrt2rat((-C1+C0)/(2*C2))],S);
6586: else{
6587: for(II=I; II>0; II--)
6588: S=cons(sqrt2rat((-C1+C0)/(2*C2)),S);
6589: }
6590: P=sqrt2rat((-C1-C0)/(2*C2));
6591: }
6592: }else if(mydeg(P,X)==3 && Cpx>1){
6593: Omg=(-1+3^(1/2)*@i)/2;
6594: PP=P/mycoef(P,3,X);
6595: C2=mycoef(PP,2,X)/3;
6596: PP=subst(PP,X,X-C2);
6597: if((C1=mycoef(PP,1,X))==0){
6598: C0=mycoef(PP,0,X);
6599: if(real(C0)==0||imag(C0)==0){
6600: if(real(C0)==0){
6601: PP=getroot(X^3+imag(C0),X);
6602: if(length(PP)==3){
6603: for(;PP!=[];PP=cdr(PP)){
6604: if(imag(PP[0])==0){
6605: C0=PP[0]*@i;
6606: break;
6607: }
6608: }
6609: if(PP==[]) C0=0;
6610: }
6611: }else{
6612: if(C0>0) C0=C0^(1/3);
6613: else C0=-(-C0)^(1/3);
6614: }
6615: if(C0!=0){
6616: if(M==1){
6617: S=cons([I,C0-C2],S);
6618: S=cons([I,C0*Omg-C2],S);
6619: S=cons([I,C0*(-1-Omg)-C2],S);
6620: }else{
6621: for(II=I; II>0; II--){
6622: S=cons(C0-C2,S);
6623: S=cons(C0*Omg-C2,S);
6624: S=cons(C0*(-1-Omg)-C2,S);
6625: }
6626: }
6627: continue;
6628: }
6629: }
6630: }
6631: if(Cpx>2){
6632: Q=X^2+(mycoef(PP,1,X)/3)*X+mycoef(PP,0,X)^3;
6633: SQ=getroot(Q,X|cpx=2);
6634: SQ=SQ[0]^(1/3);SQ2=mycoef(PP,0,X)/SQ;
6635: if(M==1){
6636: S=cons([I,SQ+SQ2-C2],S);
6637: S=cons([I,SQ*Omg+SQ2*(-1-Omg)-C2],S);
6638: S=cons([I,SQ*(-1-Omg)+SQ2*Omg-C2],S);
6639: }else{
6640: for(II=I; II>0; II--){
6641: S=cons(SQ+SQ2-C2,S);
6642: S=cons(SQ*Omg+SQ2*(-1-Omg)-C2,S);
6643: S=cons(SQ*(-1-Omg)+SQ2*Omg-C2,S);
6644: }
6645: }
6646: continue;
6647: }
6648: }else if(mydeg(P,X)==4 && Cpx>0){
6649: C2=mycoef(P,3,X)/(4*mycoef(P,4,X));
6650: PP=subst(P,X,X-C2);
6651: if(mycoef(PP,1,X)==0){
6652: PP=mycoef(PP,4,X)*X^2+mycoef(PP,2,X)*X+(SQ2=mycoef(PP,0,X));
6653: SQ=getroot(PP,X|cpx=2);
6654: if(length(SQ)==2){
6655: if((C0=sqrtrat(SQ[0]))==[]){
6656: if(mycoef(PP,1,X)==0){
6657: if(SQ2<0) C0=(-SQ2)^(1/4);
6658: else C0=SQ2^(1/4)*(1+@i)/2;
6659: }
6660: else if(Cpx>2) C0=SQ[0]^(1/2);
6661: else C0=0;
6662: }
6663: if((C1=sqrtrat(SQ[1]))==[]){
6664: if(mycoef(PP,1,X)==0) C1=-C0;
6665: else C1=SQ[1]^(1/2);
6666: }
6667: if(C0!=0){
6668: if(M==1)
6669: S=append([[I,C0-C2],[I,-C0-C2],[I,C1-C2],[I,-C1-C2]],S);
6670: else{
6671: for(II=I; II>0; II--)
6672: S=append([C0-C2,-C0-C2,C1-C2,-C1-C2],S);
6673: }
6674: continue;
6675: }
6676: }
6677: }else{
6678: PP/=mycoef(PP,4,X);
6679: CC=mycoef(PP,2,X);C1=mycoef(PP,1,X);C0=mycoef(PP,0,X);
6680: SQ=getroot(X*(CC+X)^2-4*C0*X-C1^2,X|cpx=Cpx);
6681: if(length(SQ)>1){
6682: SQ=sqrt2rat(SQ[0]);
6683: SQ2=getroot(X^2-SQ,X|cpx=Cpx);
6684: if(length(SQ2)>1){
6685: C1=SQ2[0]*X-C1/SQ2[0]/2;
6686: C0=getroot(X^2+CC/2+SQ/2+C1,X|cpx=Cpx);
6687: C1=getroot(X^2+CC/2+SQ/2-C1,X|cpx=Cpx);
6688: if(length(C0)>1&&length(C1)>1){
6689: C0=[sqrt2rat(C0[0]-C2),sqrt2rat(C0[1]-C2),
6690: sqrt2rat(C1[0]-C2),sqrt2rat(C1[1]-C2)];
6691: if(M==1) for(II=0;II<4;II++) S=cons([I,C0[II]],S);
6692: else for(II=I; II>0; II--) S=append(C0,S);
6693: continue;
6694: }
6695: }
6696: }
6697: }
6698: }
6699: if(M==1)
6700: S=cons([I,P],S);
6701: else for( ; I>0; I--) S=cons(P,S);
6702: }
6703: }
6704: S=qsort(S);
6705: if(M==1) S=reverse(S);
6706: return S;
6707: }
6708:
6709: def expat(F,L,V)
6710: {
6711: L = vweyl(L);
6712: if(V == "?"){
6713: Ans = [];
6714:
6715: F = nm(red(F));
6716: S = fromeul(toeul(F,L,"infty"),L,0);
6717: S = mycoef(S,mydeg(S,L[1]),L[1]);
6718: if(mydeg(S,L[0]) > 0)
6719: Ans = cons(["infty", expat(F,L,"infty")],Ans);
6720:
6721: S = mycoef(F,mydeg(F,L[1]), L[1]);
6722: R = getroot(S,L[0]);
6723: for(I = 0; I < length(R); I++){
6724: if(I > 0 && R[I-1] == R[I])
6725: continue;
6726: if(mydeg(R[I], L[0]) <= 0)
6727: Ans = cons([R[I], expat(F,L,R[I])], Ans);
6728: else
6729: Ans = cons([R[I]], Ans);
6730: }
6731: return Ans;
6732: }
6733: return getroot(subst(toeul(F,L,V),L[0],0),L[1]);
6734: }
6735:
6736: def polbyroot(P,X)
6737: {
6738: R = 1;
6739: while(length(P)){
6740: R *= X-car(P);
6741: if(type(R)>2) R = red(R);
6742: P = cdr(P);
6743: }
6744: return R;
6745: }
6746:
6747: def polbyvalue(P,X)
6748: {
6749: R = 1; S = 0;
6750: while(length(P)){
6751: T = car(P);
6752: V0 = T[1] - mysubst(S,[X,T[0]]);
6753: if(V0 != 0){
6754: if(type(R) > 2) R = red(R);
6755: V1 = mysubst(R,[X,T[0]]);
6756: if(V1 == 0){
6757: erno(0);
6758: return 0;
6759: }
6760: S += (V0/V1)*R;
6761: if(type(S) > 2) S = red(S);
6762: }
6763: R *= X - T[0];
6764: P = cdr(P);
6765: }
6766: return S;
6767: }
6768:
6769:
6770: def pcoef(P,L,Q)
6771: {
6772: if(L==0)
6773: return 1;
6774: Coef=TP=0;
6775: if(type(Q)>=4){
6776: TP=1;
6777: V=Q[0];
6778: if(type(V)==4)
6779: V=ltov(V);
6780: else V=dupmat(V);
6781: N=length(V);
6782: if(type(Q[1])==5) MR=dupmat(Q[1]);
6783: else{
6784: MR=newvect(N);
6785: for(K=Q[1], I=0; I< N; I++){
6786: MR[I] = car(K);
6787: K = cdr(K);
6788: }
6789: }
6790: }else{
6791: V=ltov(vars(P));
6792: N=length(V);
6793: MR=newvect(N);
6794: for(I=0;I<N;I++){
6795: MR[I]=mydeg(Q,V[I]);
6796: Q=mycoef(Q,MR[I],V[I]);
6797: }
6798: if(type(Q)>1) return 0;
6799: }
6800: if(L==1){
6801: for(I=0;I<N;I++)
6802: P=mycoef(P,MR[I],V[I]);
6803: return P;
6804: }
6805: for(I=1;I<N;I++){ /* sorted by required degrees */
6806: for(K1=MR[I],K2=V[I],J=I-1; J>=0 && MR[J]<K1; J--);
6807: for(II=I-1;II>J;II--){
6808: MR[II+1]=MR[II];V[II+1]=V[II];
6809: }
6810: MR[II+1]=K1;V[II+1]=K2;
6811: }
6812: for(NN=N; N>0 && MR[N-1]==0; N--);
6813: Mon=[];Coe=[];Q=P;
6814: while(Q!=0){
6815: M=newvect(N);
6816: for(R=Q,F=I=0,MT=1;I<NN;I++){
6817: K=mydeg(R,V[I]);
6818: R=mycoef(R,K,V[I]);
6819: if(I<N) M[I]=K;
6820: if(K>0) MT*=V[I]^K;
6821: if(K>MR[I]) F=1;
6822: }
6823: Q -= R*MT;
6824: if(F==0){
6825: Mon=cons(M,Mon);
6826: Coe=cons(R,Coe);
6827: }
6828: }
6829: Mon=ltov(reverse(Mon));
6830: Coe=ltov(reverse(Coe));
6831: Len=length(Mon);
6832: S=newvect(Len);
6833: for(JL=0; JL<Len;JL++){
6834: if(L*Mon[JL][0]<MR[0]) break;
6835: }
6836: S[0]=L;
6837:
6838: K0=Mon[0][0];
6839: K=L*K0-MR[0];
6840: for(I=II=0;II<Len && K>=0;II++){
6841: if((K1=K0-Mon[0][II])>0){
6842: while(K>K1 && S[I]>0){
6843: S[I]--;S[II]++;
6844: K-=K1;
6845: I=II;
6846: K0=Mon[0][II];
6847: }
6848: }else break;
6849: }
6850:
6851: I=0;
6852: while(1){
6853: for(T=T0=J=JP=0; J<Len; J++){
6854: if(S[J]!=0){
6855: if(T0==0 && J>=JL) return Coef;
6856: JP=J;T0=1;
6857: T+=S[J]*Mon[J][I];
6858: }
6859: }
6860: if(T==MR[I]){
6861: if(++I<N) continue;
6862: for(TT=1,J=1; J<=L; J++) /* find a solution */
6863: TT*=J;
6864: for(J=0;J<Len;J++){
6865: if(S[J]!=0){
6866: TT*=Coe[J]^S[J];
6867: for(II=S[J]; II>1; II--)
6868: TT/=II;
6869: }
6870: }
6871: Coef+=TT;
6872: if(TP==1 && type(Coef)==3) Coef=red(Coef);
6873: if(JP<Len-2 && S[JP]>1){
6874: S[JP]-=2;S[JP+1]++;S[JP+2]++;
6875: }else{
6876: for(JT=JP-1;JT>=0&&S[JT]==0;JT--);
6877: if(JT<0) break;
6878: if(JT==JP-1){
6879: S[JT]--;
6880: if(JP<Len-1)
6881: S[JP+1]++;
6882: else
6883: S[JP]++;
6884: }else{
6885: S[JT]--;
6886: S[JT+1]+=S[JP]+1;
6887: S[JP]=0;
6888: }
6889: }
6890: I=0;
6891: continue;
6892: }
6893: if(JP<Len-1){
6894: for(JP1=JP+1;JP1<Len-1;JP1++){
6895: if(Mon[JP1][I]!=Mon[JP][I]) break;
6896: }
6897:
6898: if(I>0 && Mon[JP1][0] < Mon[JP][0]){
6899: S[JP]--;S[Len-1]++;JP=JP-1;
6900: }else{
6901:
6902: S[JP]--;
6903: if(JP1<Len){
6904: S[JP1]++;
6905: }else{
6906: S[JP1-1]++;
6907: }
6908: }
6909: }
6910: if(JP==Len-1){
6911: for(JT=JP-1;JT>=0 && S[JT]==0;JT--);
6912: if(JT<0) break;
6913: S[JT]--;
6914: if(JT==JP-1){
6915: S[JP]++;
6916: }else{
6917: S[JT+1]+=S[JP]+1;
6918: S[JP]=0;
6919: }
6920: }
6921: I=0;
6922: }
6923: return Coef;
6924: }
6925:
6926: def prehombf(P,Q)
6927: {
6928: if((Mem=getopt(mem))!=1 && Mem!=-1)
6929: return prehombfold(P,Q);
6930: if(Q==0) Q=P;
6931: V=ltov(vars(P));
6932: N=length(V);
6933: for(I=1;I<N;I++){ /* sorted by required degrees */
6934: for(K=mydeg(P,V[I]),K1=V[I],J=I-1; J>=0 && mydeg(P,V[J])<K; J--);
6935: for(II=I-1;II>J;II--) V[II+1]=V[II];
6936: V[II+1]=K1;
6937: }
6938: S=newvect(N);T=newvect(N);U=newvect(N);
6939: for(R=P,M=1,Deg=I=0;I<N;I++){ /* extreme vector */
6940: Deg+=(S[I]=mydeg(R,V[I]));
6941: R=mycoef(R,S[I],V[I]);
6942: }
6943: DR=[[-1,0]];
6944: if((R1=N/Deg)!=1){
6945: DR=cons([-R1,0],DR);
6946: Sft=1;
6947: }else Sft=0;
6948: if(Deg%2==0) Sg=1;
6949: else Sg=-1;
6950: for(I=0,R=R2=1,QQ=Q; 2*I+Sft < Deg; I++){
6951: if(Mem==-1){
6952: print(I+1,0);print("/",0);print(idiv(Deg-Sft+1,2),0);print(" ",2);
6953: }
6954: Coef=0;
6955: Q=QQ;
6956: while(Q!=0){
6957: for(R=Q,J=0,RR=1;J<N;J++){
6958: T[J]=mydeg(R,V[J]);
6959: R=mycoef(R,T[J],V[J]);
6960: if(T[J]>0) RR*=V[J]^T[J];
6961: }
6962: Q-=R*RR;
6963: for(J=0,CC=R;J<N;J++){
6964: U[J]=I*S[J]+T[J];
6965: for(II=0; II<T[J]; II++)
6966: CC*=(U[J]-II);
6967: }
6968: CC*=pcoef(P,I+1,[V,U]);
6969: if(Mem==-1) print("*",2);
6970: Coef+=CC;
6971: }
6972: DR=cons([I,Coef],DR);
6973: DR=cons([-R1-1-I,Sg*Coef],DR);
6974: if(Mem==-1) print("");
6975: }
6976: P = polbyvalue(DR,s);
6977: return fctr(P);
6978: }
6979:
6980: def prehombfold(P,Q)
6981: {
6982: V = vars(P);
6983: if(Q==0) Q=P;
6984: for(Deg=0, R=P, V1=V, DD=[]; V1!=[]; V1=cdr(V1)){
6985: VT = car(V1);
6986: D = mydeg(R,VT);
6987: R = mycoef(R,D,VT);
6988: Deg += D;
6989: X = makev(["d",VT]);
6990: Q = subst(Q,VT,X);
6991: DD=cons([VT,X],DD);
6992: }
6993: DR=[[-1,0]];
6994: NV=length(V);
6995: if((R1=NV/Deg)!=1){
6996: DR=cons([-R1,0],DR);
6997: Sft=1;
6998: }else
6999: Sft=0;
7000: if(Deg%2==0)
7001: Sg=1;
7002: else Sg=-1;
7003: for(I = 0, R=R2=1; 2*I+Sft < Deg; I++){
7004: R = R2;
7005: R2 = R*P;
7006: S = appldo(Q,R2,DD);
7007: QQ = sdiv(S,R);
7008: DR=cons([I,QQ],DR);
7009: DR=cons([-R1-1-I,Sg*QQ],DR);
7010: }
7011: P = polbyvalue(DR,s);
7012: return fctr(P);
7013: }
7014:
7015: def sub3e(P0,P1,P2,N0,N1,N)
7016: {
7017: R = x^N0*(x-1)^N1*dx^N;
7018: for(V = I = 1, J = 1; I <= N; I++){
7019: S = 0;
7020: M = N-I;
7021: if(I <= N0){
7022: T = mycoef(P0,N0-I,x);
7023: S += T;
7024: R += T*x^(N0-I)*(x-1)^N1*dx^M;
7025: K1 = N0-I+1;
7026: }else
7027: K1 = 0;
7028: if(I <= N1){
7029: T = mycoef(P1,N1-I,x);
7030: S += T;
7031: R += T*x^N0*(x-1)^(N1-I)*dx^M;
7032: K2 = N0-1;
7033: }else
7034: K2 = N-I;
7035: for(K = K1; K <= K2; K++){
7036: if(K == K2){
7037: R += (mycoef(P2,N-I,x)-S)*x^K*(x-1)^(M-K)*dx^M;
7038: continue;
7039: }
7040: R += strtov("r"+rtostr(V))*x^K*(x-1)^(M-K)*dx^M;
7041: S += strtov("r"+rtostr(V++));
7042: }
7043: }
7044: if(V > 1)
7045: mycat([V-1, "accessory parameters: r1,r2,..."]);
7046: return R;
7047: }
7048:
7049: def fuchs3e(P,Q,R)
7050: {
7051: return getbygrs([R,P,Q],3);
7052: }
7053:
7054: def okubo3e(P,Q,R)
7055: {
7056: if(getopt(opt)==1){
7057: N=length(R);
7058: M1=N-length(P);M2=N-length(Q);
7059: V=(M1-1)*(M2-1);
7060: if(V>0) mycat([V, "accessory parameters"]);
7061: return getbygrs([R,cons([M1,0],P),cons([M2,0],Q)],3);
7062: }
7063: S = 0;
7064: V = -1;
7065: L = newvect(3,[[],[],[]]);
7066: N = newvect(3,[0,0,0]);
7067: if(type(R) < 4){
7068: I = -1;
7069: V = 3;
7070: }else{
7071: I = 2;
7072: V = -1;
7073: }
7074: for( ; I >= 0; I--){
7075: if(I == 2)
7076: U = R;
7077: else if(I == 1)
7078: U = Q;
7079: else
7080: U = P;
7081: for( ; length(U); U = cdr(U)){
7082: T = car(U);
7083: if( T == "?"){
7084: if(V < 0)
7085: V = I;
7086: else
7087: return 0;
7088: }else{
7089: if(I == 2)
7090: L[I] = cons(-T, L[I]);
7091: else
7092: L[I] = cons(T, L[I]);
7093: S += T;
7094: }
7095: N[I]++;
7096: }
7097: }
7098: if(V == 3){
7099: N[2] = N[0] + N[1];
7100: P2 = x^N;
7101: for(I = 1; I <= N; I++)
7102: P2 += makev([R,I])*x^(N-I);
7103: }else{
7104: if(N[0]+N[1] != N[2]){
7105: print("Number of exponents are wrong",0);
7106: return -1;
7107: }
7108: S -= N[0]*N[1];
7109: if(V < 0){
7110: if(S != 0){
7111: mycat(["Viorate Fuchs relation ->",S]);
7112: return -2;
7113: }
7114: }else{
7115: if(V != 2)
7116: S = -S;
7117: L[V] = cons(S, L[V]);
7118: }
7119: P2 = polinsft(polbyroot(L[2],x),x);
7120: }
7121: P0 = polinsft(mysubst(polbyroot(L[0],x),[x,x+N[1]]),x);
7122: P1 = polinsft(mysubst(polbyroot(L[1],x),[x,x+N[0]]),x);
7123: return sub3e(P0,P1,P2,N[0],N[1],N[2]);
7124: }
7125:
7126: /* N = 2*M (N-M = M) or 2*M+1 (N-M = M+1)
7127: 0 : 0 1 ..... M-1 B B+1 ... B+N-M-2 A
7128: 1 : C C+1 ... C+M-1 0 1 .... N-M-2 N-M-1
7129: */
7130: def eosub(A,B,C,N)
7131: {
7132: M = N%2;
7133: P = [];
7134: Q = [];
7135: P = cons(A,P);
7136: for(I = 0; I < N-M-1; I++)
7137: P = cons(B+I,P);
7138: for(I = 0; I < M; I++)
7139: Q = cons(C+I,Q);
7140: P = okubo3e(P,Q,s);
7141:
7142: C = newvect(2);
7143: L = newvect(2);
7144: C[1] = chkexp(P,[x,dx],0,b,N-M-1);
7145: C[0] = chkexp(P,[x,dx],1,c,M);
7146: for(LL = K = 0; K < 2; K++){
7147: L[K] = length(C[K]);
7148: C[K] = ltov(C[K]);
7149: if(L[K] > LL)
7150: LL = L[K];
7151: }
7152: JJ = 0;
7153:
7154: for(I = 1; Do; I++){
7155: Do = 0;
7156: S = makev(["r",I]);
7157: for(J = JJ; J < LL; J++){
7158: JJ = LL;
7159: for(K = 0; K < 2; K++){
7160: if(J >= L[K] || C[K][J] == 0)
7161: continue;
7162: if(J < JJ)
7163: JJ = J;
7164: if(Do == 1){
7165: CC = C[K];
7166: CC[J] = mysubst(CC[J], [S, Var]);
7167: continue;
7168: }
7169: if(mydeg(C[K][J]) >= 1){
7170: if(mydeg(C[K][J]) > 1){
7171: print("Internal error");
7172: return;
7173: }
7174: Var = getroot(C[K][J],S);
7175: Var = Var[0];
7176: CC = C[K];
7177: CC[J] = 0;
7178: P = mysubst(P, [S, Var]);
7179: Do = 1;
7180: J = JJ - 1;
7181: K++;
7182: }
7183: }
7184: }
7185: }
7186: if(JJ != L){
7187: print("Internal error (non Rigid)");
7188: return;
7189: }
7190: return P;
7191: }
7192:
7193: def even4e(X,Y){
7194: if(length(X) != 4 || length(Y) != 2){
7195: print("Usage: even4e([a,b,c,d],[e,f])");
7196: print("0: 0 1 e f");
7197: print("1; 0 1 * *+1");
7198: print("infty: a b c d");
7199: return;
7200: }
7201: S = -3;
7202: for(I = 0; I < 4; I++){
7203: S += X[I];
7204: if(I < 2)
7205: S += Y[I];
7206: }
7207: S = -S/2;
7208: P = okubo3e(Y,[S,"?"],X);
7209: T = chkexp(P,x,1,S,2);
7210: T = getroot(T[0],r1);
7211: return mysubst(P,[r1,T[0]]);
7212: }
7213:
7214: def odd5e(X,Y)
7215: {
7216: if(length(X) != 5 || length(Y) != 2){
7217: print("Usage: spec6e([a,b,c,d,e],[f,g])");
7218: print("0: 0 1 f g g+1");
7219: print("1: 0 1 2 * *+1");
7220: print("infty: a b c d e");
7221: return;
7222: }
7223: S = -4;
7224: for(I = 0; I < 5; I++){
7225: S += X[I];
7226: if(I < 2)
7227: S += Y[I];
7228: }
7229: S = -(S + Y[1])/2;
7230: P = okubo3e([Y[0],Y[1],Y[1]+1],[S,"?"],X);
7231: T = chkexp(P,x,1,S,2);
7232: T = getroot(T[0],r1);
7233: P = mysubst(P,[r1,T[0]]);
7234: T = chkexp(P,x,0,Y[1],2);
7235: T = getroot(T[0],r2);
7236: return mysubst(P,[r2,T[0]]);
7237: }
7238:
7239: def extra6e(X,Y)
7240: {
7241: if(length(X) != 6 || length(Y) != 2){
7242: print("Usage: extra6e([a,b,c,d,e,f],[g,h])");
7243: print("0: 0 1 g g+1 h h+1");
7244: print("1: 0 1 2 3 * *+1");
7245: print("infty: a b c d e f");
7246: return;
7247: }
7248: S = -5;
7249: for(I = 0; I < 6; I++){
7250: S += X[I];
7251: if(I < 2)
7252: S += 2*Y[I];
7253: }
7254: S = -S/2;
7255: P = okubo3e([Y[0],Y[0]+1,Y[1],Y[1]+1],[S,"?"],X);
7256: T = chkexp(P,x,1,S,2);
7257: T = getroot(T[0],r1);
7258: P = mysubst(P,[r1,T[0]]);
7259: T = chkexp(P,x,0,Y[0],2);
7260: T = getroot(T[0],r3);
7261: P = mysubst(P,[r3,T[0]]);
7262: T = chkexp(P,x,0,Y[1],2);
7263: T = getroot(T[0],r2);
7264: return mysubst(P,[r2,T[0]]);
7265: }
7266:
7267: def rigid211(X,Y,Z)
7268: {
7269: if(length(X) != 2 || length(Y) != 2 || length(Z) != 2){
7270: print("Usage: rigid211([a,b],[c,d],[e,f])");
7271: print("0: 0 1 a b");
7272: print("1: 0 1 c d");
7273: print("infty: e e+1 f *");
7274: return;
7275: }
7276: P = okubo3e(X,Y,[Z[0],Z[0]+1,Z[1],"?"]);
7277: T = chkexp(P,x,"infty",Z[0],2);
7278: T = getroot(T[0],r1);
7279: return mysubst(P,[r1,T[0]]);
7280: }
7281:
7282: def solpokuboe(P,L,N)
7283: {
7284: if(type(N) > 1 || ntype(N) != 0 || dn(N) != 1){
7285: mycat(["Irrigal argument :", N]);
7286: return 0;
7287: }
7288: L = vweyl(L);
7289: DD=N+1;
7290: for(U = S = L[0]^N; U != 0; ){
7291: D = mydeg(U,L[0]);
7292: if(D>=DD){
7293: mycat(["Internal Error",D,DD]);
7294: return -1;
7295: }
7296: DD=D;
7297: UU = L[0]^D;
7298: R = appldo(P,UU,L);
7299: if(mydeg(R,L[0]) > D){
7300: printf("Bad operator\n");
7301: return 0;
7302: }
7303: CC = mycoef(R,D,L[0]);
7304: if(D == N){
7305: P -= (E = CC);
7306: U = R-E*U;
7307: continue;
7308: }
7309: if(CC == 0){
7310: printf("No polynomial\n");
7311: return 0;
7312: }
7313: CC= mycoef(U,D,L[0])/CC;
7314: S = red(S - UU*CC);
7315: U = red(U - R*CC);
7316: }
7317: return [nm(S),E];
7318: }
7319:
7320: def stoe(M,L,N)
7321: {
7322: L = vweyl(L);
7323: Size = size(M);
7324: S = Size[0];
7325: NN = 0;
7326: if(type(N) == 4){
7327: NN=N[0]; N=N[1];
7328: }else if(N < 0){
7329: NN=-N; N=0;
7330: }
7331: if(S != Size[1] || N >= S || NN >= S)
7332: return;
7333: D = newmat(S+1,S+1);
7334: MN = dupmat(M);
7335: MD = newmat(S,S);
7336: DD = D[0];
7337: DD[N] = 1; DD[S] = 1;
7338: for(Lcm = I = 1; ; ){
7339: DD = D[I];
7340: MM = MN[N];
7341: for(J = 0; J < S; J++){
7342: DD[J] = MM[J];
7343: Lcm = lcm(dn(DD[J]),Lcm);
7344: }
7345: DD[S] = L[1]^I;
7346: for(J = 0; J <= S; J++)
7347: DD[J] = red(DD[J]*Lcm);
7348: if(I++ >= S)
7349: break;
7350: if(I==S && NN>0){
7351: DD = D[I];
7352: DD[0]=-z_zz; DD[NN]=1;
7353: break;
7354: }
7355: Mm = dupmat(MN*M);
7356: for(J = 0; J < S; J++){
7357: for(K = 0; K < S; K++)
7358: MN[J][K] = red(diff(MN[J][K],L[0])+Mm[J][K]);
7359: }
7360: }
7361: #if 0
7362: P = fctr(mydet2(D));
7363: #else
7364: P = fctr(det(D));
7365: #endif
7366: for(I = R = 1; I < length(P); I++){
7367: if(mydeg(P[I][0],L[1]) > 0)
7368: R *= P[I][0]^P[I][1];
7369: }
7370: if(NN > 0)
7371: R = -red(coef(R,0,z_zz)/coef(R,1,z_zz));
7372: return R;
7373: }
7374:
7375: def dform(L,X)
7376: {
7377: if(type(X)==2) X=[X];
7378: if(type(L[0])!=4) L=[L];
7379: if(type(X)==4) X=ltov(X);
7380: M=length(X);
7381: if(length(car(L))==2){
7382: R=newvect(M);
7383: for(LL=L; LL!=[]; LL=cdr(LL)){
7384: for(I=0; I<M; I++){
7385: RT=rmul(car(LL)[0],mydiff(car(LL)[1],X[I]));
7386: R[I] = (R[I]==0)?RT:radd(R[I],RT);
7387: }
7388: }
7389: Dif=getopt(dif);
7390: for(RR=[], I=M-1; I>=0; I--){
7391: if(Dif==1) RR=cons([1,R[I],X[I]],RR);
7392: else RR=cons([R[I],X[I]],RR);
7393: }
7394: if(Dif==1) RR=dform(RR,X);
7395: return RR;
7396: }else if(length(car(L))!=3) return L;
7397: N=M*(M-1)/2;
7398: R=newvect(N);
7399: S=newvect(N);
7400: for(LL=L; LL!=[]; LL=cdr(LL)){
7401: for(I=K=0; I<M; I++){
7402: for(J=I+1; J<M; J++, K++){
7403: if(LL==L) S[K]=[X[I],X[J]];
7404: LT=car(LL);
7405: R1=mydiff(LT[2],X[J]);
7406: R2=mydiff(-LT[2],X[I]);
7407: if(R2==0){
7408: if(R1==0) continue;
7409: R1=rmul(mydiff(LT[1],X[I]),R1);
7410: }else if(R1==0){
7411: R1=rmul(mydiff(LT[1],X[J]),R2);
7412: }else
7413: R1=rmul(mydiff(LT[1],X[I]),R1)+rmul(mydiff(LT[1],X[J]),R2);
7414: R1=rmul(LT[0],R1);
7415: R[K] = (R[K]==0)?R1:radd(R[K],R1);
7416: }
7417: }
7418: }
7419: for(RR=[],I=N-1; I>=0; I--)
7420: RR=cons([R[I],S[I][0],S[I][1]],RR);
7421: return RR;
7422: }
7423:
7424: def polinvsym(P,Q,Sym)
7425: {
7426: N = length(Q);
7427: T = polbyroot(Q,zz);
7428: for(I = 1; I <= N; I++){
7429: P = mysubst(P,[makev([Sym,I]), (-1)^I*coef(T,N-I,zz)]);
7430: }
7431: return P;
7432: }
7433:
7434: def polinsym(P,Q,Sym)
7435: {
7436: if(type(P) == 3){
7437: P = red(P);
7438: if(type(P) == 3){
7439: D = polinsym(dn(P),Q,Sym);
7440: if(D == 0)
7441: return 0;
7442: return polinsym(nm(P),Q,Sym)/D;
7443: }
7444: }
7445: N = length(Q);
7446: V = newvect(N+1);
7447: S = newvect(N+1);
7448: E = newvect(N+1);
7449: E0 = newvect(N+1);
7450: T = polbyroot(Q,zzz);
7451: for(J = 1; J <= N; J++){
7452: K = coef(T,N-J,zzz);
7453: if(J % 2)
7454: K = -K;
7455: S[J] = K;
7456: V[J] = makev([Sym,J]);
7457: }
7458: K = deg(P,Q[0]);
7459: for(J = 0; J <= N; J++)
7460: E0[J] = K+1;
7461: E[0] = K+1;
7462: while(deg(P,Q[0]) > 0){
7463: for(P0 = P, J = 1; J <= N; J++){
7464: E[J] = deg(P0,Q[J-1]);
7465: P0 = coef(P0,E[J],Q[J-1]);
7466: }
7467: /* P0*Q[0]^E[1]*Q[1]^E[2]*... E[1] >= E[2} >= ... */
7468: for(J = 1; J <= N; J++){
7469: if(E[J] < E0[J])
7470: break;
7471: if(E[J-1] < E[J])
7472: J = N;
7473: }
7474: if(J > N){
7475: print("Not symmetric");
7476: return 0;
7477: }
7478: for(J = 1; J <= N; J++)
7479: E0[J] = E[J];
7480: for(J = N; J > 1; J--){
7481: if(E[J] != 0)
7482: for(K = 1; K < J; K++)
7483: E[K] -= E[J];
7484: }
7485: for(R0 = P0, K = 1; K <= N; K++){
7486: if(E[K] > 0)
7487: P0 *= S[K]^E[K];
7488: R0 *= V[K]^E[K];
7489: }
7490: P += R0 - P0;
7491: }
7492: return P;
7493: }
7494:
7495: def tohomog(P,L,V)
7496: {
7497: while(length(L)>0){
7498: P = mysubst(P,[car(L),car(L)/V]);
7499: L = cdr(L);
7500: }
7501: P = red(P);
7502: N = mindeg(dn(P),V);
7503: if(N > 0)
7504: P = red(P*V^N);
7505: N = mindeg(dn(P),V);
7506: if(N > 0)
7507: P = red(P/(V^N));
7508: return P;
7509: }
7510:
7511: def substblock(P,X,Q,Y)
7512: {
7513: P = red(P);
7514: if(deg(dn(P),X) > 0)
7515: return substblock(nm(P),X,Q,Y)/substblock(dn(P),X,Q,Y);
7516: N = mydeg(Q,X);
7517: if(N < 1)
7518: return P;
7519: R = mycoef(Q,N,X);
7520: while(M = mydeg(P,X), M >= N)
7521: P = red(P - mycoef(P,M,X)*(Q-Y)*X^(M-N)/R);
7522: return P;
7523: }
7524:
7525: def okuboetos(P,L)
7526: {
7527: L = vweyl(L); X = L[0]; DX = L[1];
7528: N = mydeg(P,DX);
7529: C = mycoef(P,N,DX);
7530: K = mydeg(C,X);
7531: if(K > N){
7532: print("Irregular singularity at infinity")$
7533: return 0;
7534: }
7535: if(N > K)
7536: P *= x^(N-K);
7537:
7538: L = getroot(mycoef(P,N,DX),x);
7539: L = ltov(reverse(L));
7540: if(length(L) != N || N == 0){
7541: print("Cannot get exponents")$
7542: return 0;
7543: }
7544: if( type(LL = getopt(diag)) == 4 ){
7545: LL = ltov(LL);
7546: if(length(LL) != N){
7547: mycat(["Length of the option should be", N]);
7548: return 0;
7549: }
7550: Tmp = newvect(N);
7551: for(I = N-1; I >= 0; I--){
7552: for(LLT = LL[I], J = N-1; J >=0 ; J--){
7553: if(LLT == L[J] && Tmp[J] == 0){
7554: Tmp[J] = 1;
7555: break;
7556: }
7557: }
7558: if(J < 0){
7559: print("option is wrong");
7560: return 0;
7561: }
7562: }
7563: L = LL;
7564: }
7565: P /= mycoef(C,N,X);
7566: A = newmat(N,N);
7567: AT = newmat(N+1,N+1);
7568: Phi= newvect(N+1);
7569: Phi[0] = 1;
7570: for(J = 0; J < N; J++)
7571: Phi[J+1] = Phi[J]*(X-L[J]);
7572: for(ATT = AT[N], J = 0; J < N; J++)
7573: ATT[J] = mycoef(P,J,DX);
7574:
7575: for(K = 1; K <= N; K++){
7576: for(J = N; J >= K; J--){
7577: Aj = A[J-1];
7578: SIG = AT[J][J-K];
7579: for(I = 0; I <= K-2; I++)
7580: SIG += Aj[J-I-1]*AT[J-I-1][J-K];
7581: if(K == 1)
7582: DAT = mydiff(Phi[J-1],X);
7583: else
7584: DAT = mydiff(AT[J-1][J-K],X);
7585: Aj[J-K] = -SIG+(X-L[J-1])*DAT;
7586: Aj[J-K] /= Phi[J-K];
7587: Aj[J-K] = mysubst(Aj[J-K],[X,L[J-1]]);
7588: if(J < K+1) continue;
7589: ATj = AT[J-1];
7590: ATj[J-K-1] = SIG+Aj[J-K]*Phi[J-K];
7591: ATj[J-K-1] /= (X - L[J-1]);
7592: ATj[J-K-1] = red(ATj[J-K-1]-DAT);
7593: }
7594: }
7595:
7596: ATT = newmat(N,N);
7597: for(J = 0; J < N; J++){
7598: for(K = 0; K < N; K++){
7599: ATj = ATT[J];
7600: ATj[K] = AT[J][K];
7601: }
7602: ATj[J] = Phi[J];
7603: if(J < N-1){
7604: ATj = A[J];
7605: ATj[J+1] = 1;
7606: }
7607: }
7608: return [L,A,ATT];
7609: }
7610:
7611: def heun(X,P,R)
7612: {
7613: if(type(X) != 4 || length(X) != 5){
7614: print("Usage: huen([a,b,c,d,e],p,r)");
7615: print("0: 0 c");
7616: print("1: 0 d");
7617: print("p: 0 e");
7618: print("infty: a b");
7619: print("Fuchs relation: a+b+1 = c+d+e");
7620: return;
7621: }
7622: S = 1;
7623: V = -1;
7624: X = ltov(X);
7625: for(I = 0; I < 5; I++){
7626: if(X[I] == "?"){
7627: if(V >= 0)
7628: return;
7629: V = I;
7630: }else if(I < 2){
7631: S += X[I];
7632: }else
7633: S -= X[I];
7634: }
7635: if(V >= 0){
7636: if(V < 2)
7637: X[V] = -S;
7638: else
7639: X[V] = S;
7640: }else if(S != 0){
7641: mycat(["Fuch relation:", S,"should be zero!"]);
7642: return;
7643: }
7644: return
7645: x*(x-1)*(x-P)*dx^2
7646: + (X[2]*(x-1)*(x-P)+X[3]*x*(x-P)+X[4]*x*(x-1))*dx
7647: + X[0]*X[1]*(x-R);
7648: }
7649:
7650: def fspt(M,T)
7651: {
7652: if(type(M)==7) M=s2sp(M);
7653: if(T == 3) /* 3: cut 0 */
7654: return cutgrs(M);
7655: if(T == 4 || T== 5){ /* 4: short 5: long */
7656: for(MN = [] ; M != []; M = cdr(M)){
7657: MT = car(M);
7658: for(MNT = []; MT != []; MT = cdr(MT)){
7659: if(type(car(MT)) <= 3){
7660: if(T == 4) MNT = cons(car(MT),MNT);
7661: else MNT = cons([1,car(MT)],MNT);
7662: }else{
7663: if(T == 5 || car(MT)[0] > 1) MNT = cons(car(MT),MNT);
7664: else if(car(MT)[0] == 1) MNT = cons(car(MT)[1],MNT);
7665: }
7666: }
7667: MN = cons(reverse(MNT), MN);
7668: }
7669: return reverse(MN);
7670: }
7671: if(type(M[0][0]) == 4){
7672: for(MN = [] ; M != []; M = cdr(M)){
7673: MT = car(M);
7674: for(MNT = []; MT != []; MT = cdr(MT))
7675: MNT = cons(car(MT)[0], MNT);
7676: MN = cons(reverse(MNT), MN);
7677: }
7678: return fspt(reverse(MN),T);
7679: }
7680: if(T == 0) /* 0: sp */
7681: return M;
7682: for(MN = [] ; M != []; M = cdr(M)){
7683: MT = qsort(ltov(car(M)));
7684: L = length(MT);
7685: for(MNT = [], I = 0; I < L; I++)
7686: MNT = cons(MT[I], MNT);
7687: MN = cons(MNT, MN);
7688: }
7689: MN = reverse(MN);
7690: if(T==6) return MN; /* 7: sort */
7691: L = length(MN);
7692: for(M = MN; M != []; M = cdr(M)){
7693: for(I = 0, MT = car(M); MT != []; MT = cdr(MT))
7694: I += car(MT);
7695: if(OD == 0)
7696: OD = I;
7697: else if(OD != I || OD == 0)
7698: return 0;
7699: }
7700: ALL = [MN];
7701: RD=[];
7702: while(OD > 0){
7703: for(S = 0, MT = MN; MT != []; MT = cdr(MT))
7704: S += car(MT)[0];
7705: S -= (L-2)*OD;
7706: if(S <= 0){
7707: if(T==7) return [ALL[0],ALL[length(ALL)-1],RD];
7708: return (T==1)?MN:ALL;
7709: }
7710: RD=cons([S,0,0],RD);
7711: for(NP=0, M = [], MT = MN; MT != []; NP++, MT = cdr(MT)){
7712: MTT = car(MT);
7713: I = MTT[0] - S;
7714: if(I < 0){
7715: if(I+OD!=0) return 0;
7716: if(T==7) return [ALL[0],ALL[length(ALL)-1],cdr(RD)];
7717: return (T==1)?MN:ALL;
7718: }
7719: MTT = cdr(MTT);
7720: NC=1; DO=0;
7721: for(MNT = []; MTT != []; MTT = cdr(MTT)){
7722: if(MTT[0] > I){
7723: if(DO==0) RD=cons([MTT[0]-I,NP,NC++],RD);
7724: MNT = cons(MTT[0], MNT);
7725: }
7726: else if(MTT[0] <= I && I != 0){
7727: DO=1;
7728: MNT = cons(I, MNT);
7729: I = 0;
7730: if(MTT[0] > 0)
7731: MNT = cons(MTT[0], MNT);
7732: }
7733: }
7734: if(I > 0)
7735: MNT = cons(I,MNT);
7736: M = cons(reverse(MNT), M);
7737: }
7738: MN = reverse(M);
7739: ALL = cons(MN,ALL);
7740: OD -= S;
7741: }
7742: }
7743:
7744: def abs(X)
7745: {
7746: if(vars(X)!=[]) return todf(os_md.abs,[X]);
7747: if(type(X)==4){
7748: P=X[1];X=X[0];
7749: }else P=0;
7750: if(type(X)==1){
7751: if((T=ntype(X))<2 || T==3){
7752: if(X<0) X=-X;
7753: }else if(T==4) X=P?pari(abs,X,P):pari(abs,X);
7754: }
7755: return X;
7756: }
7757:
1.20 takayama 7758: def sgn(X)
7759: {
7760: if(X==0) return 0;
7761: if(type(X)==1){
7762: return (X>0)?1:-1;
7763: }
7764: if(type(X)==5) X=vtol(X);
7765: if(type(X)==4){
7766: for(W=0,Y=X;Y!=[];Y=cdr(Y))
7767: for(Z=cdr(Y);Z!=[];Z=cdr(Z))
7768: if(car(Y)>car(Z)) W++;
7769: if(getopt(val)==1) return W;
7770: return (iand(W,1))?-1:1;
7771: }
7772: }
7773:
1.6 takayama 7774: def calc(X,L)
7775: {
1.10 takayama 7776: if(type(X)<4||type(X)==7){
7777: if(type(L)==4||type(L)==7){
1.6 takayama 7778: V=L[1];
1.10 takayama 7779: if(type(X)!=7){
7780: if((L0=L[0])=="+") X+=V;
7781: else if(L0=="-") X-=V;
7782: else if(L0=="*") X*=V;
7783: else if(L0=="/") X/=V;
7784: else if(L0=="^") X^=V;
7785: }
7786: if((L0=L[0])==">") X=(X>V);
7787: else if(L0=="<") X=(X<V);
7788: else if(L0=="=") X=(X==V);
1.6 takayama 7789: else if(L0==">=") X=(X>=V);
7790: else if(L0=="<=") X=(X<=V);
7791: else if(L0=="!=") X=(X!=V);
1.10 takayama 7792: }else if(type(L)==7&&type(X)<4){
1.6 takayama 7793: if(L=="neg") X=-X;
7794: else if(L=="abs") X=abs(X);
7795: else if(L=="neg") X=-X;
7796: else if(L=="sqr") X*=X;
7797: else if(L=="inv") X=1/X;
7798: else if(L=="sgn"){
7799: if(X>0)X=1;
7800: else if(X<0) X=-1;
7801: }
7802: }
7803: }
7804: return X;
7805: }
7806:
1.23 takayama 7807: def tobig(X)
7808: {
7809: if((type(X)==1 && ntype(X)==3)||type(X)>3) return X;
7810: return eval(X*exp(0));
7811: }
7812:
1.6 takayama 7813: def isint(X)
7814: {
7815: if(X==0||(type(X)==1 && ntype(X)==0 && dn(X)==1)) return 1;
7816: return 0;
7817: }
7818:
7819: def israt(X)
7820: {
7821: if(X==0||(type(X)==1 && ntype(X)==0)) return 1;
7822: return 0;
7823: }
7824:
7825: def iscrat(X)
7826: {
7827: if(X==0 || (type(X)==1 && israt(real(X)) && israt(imag(X)))) return 1;
7828: return 0;
7829: }
7830:
7831: def isalpha(X)
7832: {
7833: return ((X>64&&X<91)||(X>96&&X<123))?1:0;
7834: }
7835:
7836: def isnum(X)
7837: {
7838: return (X>47&&X<58)?1:0;
7839: }
7840:
7841: def isalphanum(X)
7842: {
7843: return (isalpha(X)||isnum(X))?1:0;
7844: }
7845:
1.8 takayama 7846: def isdecimal(X)
7847: {
7848: if(type(X)!=7) return 0;
7849: F=S=0;
7850: L=strtoascii(X);
7851: while(L!=[]&&car(L)==32) L=cdr(L);
7852: if(L!=[]&&car(L)==45) L=cdr(L); /* - */
7853: while(L!=[]&&isnum(car(L))){
7854: F=1; L=cdr(L);
7855: }
7856: while(L!=[]&&car(L)<33){
7857: S=1;L=cdr(L);
7858: }
7859: if(L==[]) return F;
7860: else if(S||car(L)!=46) return 0; /* . */
7861: L=cdr(L);F=0;
7862: while(L!=[]&&isnum(car(L))){
7863: F=1; L=cdr(L);
7864: }
7865: while(L!=[]&&car(L)<33) L=cdr(L);
7866: return (L==[])?F:0;
7867: }
7868:
1.6 takayama 7869: def isvar(X)
7870: {
7871: return ([X]==vars(X)&&vtype(X)<3)?1:0;
7872: }
7873:
7874: def isyes(F)
7875: {
7876: if((CC=getopt(set))==1){
7877: IsYes=(type(F[0])==4)?F:[F];
7878: return 1;
7879: }else if(CC==0) return(IsYes);
7880: if(type(CC)!=7)
7881: CC=IsYes;
7882: for(;CC!=[]; CC=cdr(CC)){
7883: C=car(CC);
7884: V=call(C[0],cons(F,C[1]));
7885: if(type(C[2])!=4){
7886: if(V!=C[2]) break;
7887: }else{
7888: if(C[2][0]!="" && V<C[2][0]) break;
7889: if(C[2][1]!="" && V>C[2][1]) break;
7890: }
7891: }
7892: return (CC==[])?1:0;
7893: }
7894:
7895: def isall(FN,M)
7896: {
7897: if(type(M)<4 || type(M)>6) return ((*FN)(M)==0)?0:1;
7898: if(type(M)==4){
7899: for(;M!=[];M=cdr(M))
7900: if((*FN)(car(M))==0) return 0;
7901: }else if(type(M)==5){
7902: K=length(M);
7903: for(I=0;I<K;I++)
7904: if((*FN)(M[I])==0) return 0;
7905: }else if(type(M)==6){
7906: K=size(M)[0];
7907: for(I=0;I<K;I++)
7908: if (isall(FN,M[I])==0) return 0;
7909: }
7910: return 1;
7911: }
7912:
7913: def sproot(MP,T)
7914: {
7915: if((I=str_chr(T,0,","))>0){
7916: if(type(MP)==7) M=s2sp(MP);
7917: else M=chkspt(MP|opt=0);
7918: if(I==length(M[0])){
7919: N=s2sp(T);S=SM=SN=K=0;
7920: for(MM=M,NN=N;MM!=[];MM=cdr(MM),NN=cdr(NN),K++){
7921: for(MT=car(MM),NT=car(NN);MT!=[];MT=cdr(MT),NT=cdr(NT)){
7922: S+=car(MT)*car(NT);
7923: if(K==0){
7924: SM+=car(MT);SN+=car(NT);
7925: }
7926: }
7927: }
7928: return S-(length(M)-2)*SM*SN;
7929: }
7930: }
7931: MM=chkspt(MP|opt=7);
7932: if(T=="base") return MM;
7933: Keep=(getopt(keep)==1)?1:0;
7934: Null=getopt(null);
7935: Only=getopt(only);
7936: if(type(Only)!=1) Only=7;
7937: M0=MM[0];
7938: M1=MM[1];
7939: M=MM[2];
7940: if(T=="length") return length(M);
7941: if(T=="height"){
7942: for(J=2,S=M1[0][0],M2=M1; M2!=[]; M2=cdr(M2)){
7943: for(MT=cdr(car(M2)); MT!=[]; J++, MT=cdr(MT)){
7944: S+= J*car(MT);
7945: }
7946: J=1;
7947: }
7948: return S;
7949: }
7950: for(OD=0, MT=M1[0]; MT!=[]; MT=cdr(MT)) OD+=car(MT);
7951: if(T=="type"){
7952: R=newvect(OD+1);
7953: for(MT=M; MT!=[]; MT=cdr(MT)) R[MT[0][0]]++;
7954: for(RR=[],I=OD; I>0; I--)
7955: if(R[I]>0) RR=cons([R[I],I],RR);
7956: return RR;
7957: }
7958: if(T=="part"||T=="pair"||T=="pairs"){
7959: NP=length(M1);
7960: LM=newvect(NP);
7961: R=newvect(length(M));
7962: for(K=0; K<NP; K++) LM[K]=length(M1[K]);
7963: for(I=0,TM=M; TM!=[]; I++, TM=cdr(TM)){
7964: V=newvect(NP);
7965: for(K=0; K<NP; K++) V[K]=newvect(LM[K]);
7966: TP=car(TM);
7967: if(TP[2]==0){
7968: for(K=0;K<NP;K++) V[K][0]=1;
7969: for(J=0; J<I; J++){
7970: VJ=R[J][1];
7971: for(S=K=0;K<NP;K++) S+=VJ[K][0];
7972: for(OD=0,K=0;K<LM[0];K++) OD+=VJ[0][K];
7973: S-=(NP-2)*OD;
7974: for(K=0;K<NP;K++) VJ[K][0]-=S;
7975: }
7976: }else{
7977: K=TP[1]; P=TP[2];
7978: V[K][P-1]=-1; V[K][P]=1;
7979: for(J=0; J<I; J++){
7980: VJ=R[J][1];
7981: S=VJ[K][P]; VJ[K][P]=VJ[K][P-1]; VJ[K][P-1]=S;
7982: }
7983: }
7984: R[I]=[TP[0],V];
7985: }
7986: if(T=="pair"||T=="pairs"){
7987: MV=ltov(M1);
7988: for(K=0; K<NP; K++) MV[K] = ltov(MV[K]);
7989: for(RR=UU=SS=[],I=0; I<length(M); I++){
7990: V=newvect(NP); W=newvect(NP); U=newvect(NP);
7991: for(K=0; K<NP; K++){
7992: U[K]=newvect(LM[K]); V[K]=newvect(LM[K]); W[K]=newvect(LM[K]);
7993: }
7994: S=R[I][0];
7995: for(K=0; K<NP; K++){
7996: for(Q=J=0; J<LM[K]; J++){
7997: V[K][J] = S*(U[K][J] = R[I][1][K][J]);
7998: Q+=(W[K][J] = MV[K][J] - V[K][J]);
7999: }
8000: }
8001: if(Q>0 && iand(Only,1)==0) continue;
8002: if(Q==0 && iand(Only,2)==0) continue;
8003: if(Q<0 && iand(Only,4)==0) continue;
8004: for(K=0; K<NP; K++){
8005: V[K] = vtol(V[K]); W[K] = vtol(W[K]); U[K]=vtol(U[K]);
8006: }
8007: V=vtol(V); W=vtol(W);U=vtol(U);
8008: if(Q<0) S=-S;
8009: RR = cons([V,W], RR); UU = cons(U,UU); SS=cons(S,SS);
8010: }
8011: RR = reverse(RR); UU=reverse(UU); SS=reverse(SS);
8012: if(getopt(dviout)==1 && (Null!=1 || RR!=[])){
8013: Out=string_to_tb("\\begin{align}\\begin{split}"+s2sp(M1)+"&=");
8014: for(I=0,R=RR, U=UU; R!=[]; I++, R=cdr(R), U=cdr(U)){
8015: if(I>0) str_tb("\\\\\n &=",Out);
8016: if(T=="pairs"){
8017: if((S=SS[I])<0) S=-S;
8018: if(S>1) str_tb([my_tex_form(S),"("],Out);
8019: str_tb(s2sp(car(U)),Out);
8020: if(S>1) str_tb(")",Out);
8021: str_tb(" \\oplus ",Out);
8022: if(SS[I]<0){
8023: #ifdef USEMODULE
8024: str_tb(["-(",s2sp(mtransbys(os_md.abs,car(R)[1],[])),")"],Out);
8025: #else
8026: str_tb(["-(",s2sp(mtransbys(abs,car(R)[1],[])),")"],Out);
8027: #endif
8028: }else
8029: str_tb(s2sp(car(R)[1]),Out);
8030: }else
8031: str_tb([s2sp(car(R)[0])," \\oplus ",s2sp(car(R)[1])],Out);
8032: }
8033: str_tb("\n\\end{split}\\end{align}",Out);
8034: dviout(str_tb(0,Out)|keep=Keep);
8035: }
8036: return RR;
8037: }
8038: for(I=0; I<length(M); I++){
8039: for(K=0; K<NP; K++) R[I][1][K] = vtol(R[I][1][K]);
8040: R[I] = [R[I][0],vtol(R[I][1])];
8041: }
8042: R = vtol(R);
8043: return [M0,M1,R];
8044: }
8045: }
8046:
8047: def spgen(MO)
8048: {
8049: Eq=(getopt(eq)==1)?1:0;
8050: Sp=getopt(sp);
8051: if(type(Sp)==7) Sp=s2sp(Sp);
8052: St=getopt(str);
8053: LP=getopt(pt);
8054: F=getopt(std);
8055: if(F!=1&&F!=-1) F=0;
8056: if(type(LP)==4){
8057: L0=LP[0]; L1=LP[1];
1.29 takayama 8058: }else if(type(LP)==1){
8059: L0=L1=LP;
1.6 takayama 8060: }else{
8061: L0=0; L1=MO+1;
8062: }
8063: if(MO<=0){
8064: MO=-MO;
8065: if(iand(MO,1)==1) return [];
8066: if(MO>1){
8067: if(isMs()==0) return [];
8068: Cmd="okubo "+rtostr(-MO);
8069: MO/=2;
8070: if(L1>0) Cmd=Cmd+"+"+rtostr(L0)+"-"+rtostr(L1);
8071: else L1=MO+4;
8072: Cmd=Cmd+" B";
8073: Id=getbyshell(Cmd);
8074: if(Id<0) return [];
8075: B=[];
8076: while((S=get_line(Id)) !=0){
8077: P0=str_chr(S,1,":")+1;
8078: if(P0>1){
8079: P1=str_chr(S,P,"\n");
8080: if(P1<0) P1=str_len(S);
8081: B=cons(sub_str(S,P0,P1-1),B);
8082: }
8083: }
1.17 takayama 8084: close_file(Id);
1.6 takayama 8085: }else{
8086: MO/=2;
8087: if(L1<=1) L1=MO+4;
8088: BB=[
8089: ["11,11,11,11","111,111,111","1^4,1^4,22","1^6,222,33"],
8090: ["11,11,11,11,11","1^4,1^4,211","211,22,22,22","1^6,2211,33",
8091: "2211,222,222","22211,2^4,44","2^511,444,66","1^4,22,22,31",
8092: "2^5,3331,55","1^5,1^5,32","1^8,332,44","111,111,21,21","1^5,221,221"],
8093: ["11,11,11,11,11,11","1^4,1^4,1^4","1^4,22,22,22","111,111,111,21",
8094: "1^6,21^4,33","21^4,222,222","221^4,2^4,44","2^41^4,444,66",
8095: "1^5,1^5,311","1^8,3311,44","1^6,222,321","321,33,33,33",
8096: "3321,333,333","33321,3^4,66","3^721,666,99","2^5,3322,55",
8097: "1^6,1^6,42","222,33,33,42","1^a,442,55","1^6,33,33,51",
8098: "222,222,33,51","1^9,333,54","2^7,554,77","1^5,2111,221",
8099: "2^41,333,441","1^7,2221,43","211,211,22,22","2211,2211,222",
8100: "22211,22211,44","1^4,211,22,31","2^411,3331,55","1^4,1^4,31,31",
8101: "22,22,22,31,31","1^7,331,331","2221,2221,331","111,21,21,21,21"],
8102: ["11,11,11,11,11,11,11","111,111,111,111","1^6,1^6,33",
8103: "1^6,222,222","222,33,33,33","1^5,1^5,221",
8104: "1^4,211,22,22","1^4,1^4,22,31","22,22,22,22,31",
8105: "111,111,21,21,21","21^6,2^4,44","2221^6,444,66",
8106: "1^6,222,3111","3111,33,33,33","33111,333,333",
8107: "333111,3^4,66","3^5111,666,99","2^5,33211,55",
8108: "1^8,3221,44","3222,333,333","33222,3^4,66",
8109: "3^4222,666,99","1^6,1^6,411","222,33,33,411",
8110: "1^a,4411,55","2^4,2^4,431","431,44,44,44",
8111: "2^6,4431,66","4431,444,444","44431,4^4,88",
8112: "4^531,888,cc","1^a,433,55","1^7,1^7,52",
8113: "1^c,552,66","3^4,444,552","1^8,2^4,53",
8114: "1^8,44,44,71","3^5,555,771","21^4,2211,222",
8115: "221^4,22211,44","2221^4,3331,55","1^6,2211,321",
8116: "2^411,3322,55","1^7,322,331","2211,33,33,42",
8117: "3^42,4442,77","2211,222,33,51","3^51,5551,88",
8118: "2^611,554,77","2221,2221,322","2^41,2^41,54",
8119: "1^5,2111,2111","222111,333,441","1^7,22111,43",
8120: "1^5,1^5,41,41","1^9,441,441","22111,2221,331",
8121: "1^5,221,32,41","221,221,221,41","211,211,211,22",
8122: "2211,2211,2211","1^4,211,211,31","211,22,22,31,31",
8123: "1^4,22,31,31,31","1^5,32,32,32","221,221,32,32","21,21,21,21,21,21"],
8124: ["11,11,11,11,11,11,11,11","1^4,1^4,22,22","1^8,2^4,44",
8125: "1^6,2211,222","2211,33,33,33","111,111,111,21,21",
8126: "1^5,1^5,2111","1^4,211,211,22","1^4,1^4,211,31",
8127: "211,22,22,22,31","1^4,22,22,31,31","111,21,21,21,21,21",
8128: "221^8,444,66","2^5,331^4,55","1^8,32111,44",
8129: "32211,333,333","332211,3^4,66","3^42211,666,99",
8130: "2^5,32221,55","1^7,1^7,511","1^c,5511,66",
8131: "3^4,444,5511","541,55,55,55","5541,555,555",
8132: "55541,5^4,aa","5^541,aaa,ff","1^8,1^8,62",
8133: "1^a1^4,662,77","1^a,55,55,91","2^71,555,87",
8134: "21^6,22211,44","221^6,3331,55","1^6,2211,3111",
8135: "2^411,33211,55","1^7,3211,331","2211,33,33,411",
8136: "3^42,44411,77","22211,2^4,431","2^511,4431,66",
8137: "1^8,332,431","3^42,4433,77","1^8,22211,53",
8138: "2221,2221,3211","221^5,333,441","1^7,21^5,43",
8139: "1^b,443,65","21^5,2221,331","2^51,3332,65",
8140: "21^4,21^4,222","221^4,221^4,44","1^6,21^4,321",
8141: "2221^4,3322,55","21^4,33,33,42","21^4,222,33,51",
8142: "2^51^4,554,77","2^4,3311,3311","3^411,4442,77",
8143: "321,321,33,33","3321,3321,333","33321,33321,66",
8144: "222,321,33,42","1^6,321,33,51","222,222,321,51",
8145: "1^9,3321,54","1^7,322,322","3^422,5551,88",
8146: "1^6,33,42,42","1^6,222,42,51","33,33,33,42,51",
8147: "1^6,1^6,51,51","222,33,33,51,51","1^b,551,551",
8148: "1^5,221,311,41","2^41,3321,441","22111,2221,322",
8149: "2^51,443,551","222111,2^41,54","21^4,2211,2211",
8150: "1^5,311,32,32","3331,3331,442","2211,2211,33,51",
8151: "221,221,311,32","22111,22111,331","1^5,2111,32,41",
8152: "2111,221,221,41","2111,221,32,32","211,211,211,211",
8153: "211,211,22,31,31","1^4,211,31,31,31","22,22,31,31,31,31"],
8154: ["11,11,11,11,11,11,11,11,11","1^5,1^5,1^5","2^5,2^5,55",
8155: "111,111,111,111,21","2^41,333,333","1^4,1^4,211,22",
8156: "211,22,22,22,22","1^8,22211,44","1^4,1^4,1^4,31",
8157: "1^4,22,22,22,31","1^7,1^7,43","1^7,2221,331",
8158: "2221,2221,2221","1^6,21^4,222","21^4,33,33,33",
8159: "1^6,1^6,321","222,321,33,33","1^6,33,33,42",
8160: "222,222,33,42","1^6,222,33,51","222,222,222,51",
8161: "33,33,33,33,51","1^6,2211,2211","111,111,21,21,21,21",
8162: "1^5,1^5,32,41","1^5,221,221,41","1^5,221,32,32",
8163: "221,221,221,32","1^4,211,211,211","211,211,22,22,31",
8164: "1^4,211,22,31,31","1^4,1^4,31,31,31","22,22,22,31,31,31",
8165: "21,21,21,21,21,21,21","21^a,444,66","1^8,31^5,44",
8166: "321^4,333,333","3321^4,3^4,66","3^421^4,666,99",
8167: "2^5,322111,55","32^41,3^4,66","3332^41,666,99",
8168: "1^8,1^8,611","2^4,44,44,611","1^d,6611,77",
8169: "4^5,66611,aa","2^6,444,651","3^4,3^4,651",
8170: "651,66,66,66","3^6,6651,99","6651,666,666",
8171: "66651,6^4,cc","6^551,ccc,ii","2^8,655,88",
8172: "1^9,1^9,72","1^g,772,88","1^c,444,75",
8173: "2^6,3^4,75","1^c,66,66,b1","3^4,444,66,b1",
8174: "3^7,777,ba","1^7,2221,4111","2^41,333,4311",
8175: "1^9,2^41,63","21^8,3331,55","2^411,331^4,55",
8176: "1^7,31^4,331","2^411,32221,55","22211,2^4,422",
8177: "2^511,4422,66","1^8,332,422","2^5,3331,541",
8178: "22211,44,44,62","2^411,2^5,64","2^711,664,88",
8179: "1^a,3331,64","2221,2221,31^4","21^7,333,441",
8180: "333,333,441,81","2^6111,555,87","21^6,221^4,44",
8181: "221^6,3322,55","2^41^6,554,77","1^6,21^4,3111",
8182: "3111,321,33,33","33111,3321,333","333111,33321,66",
8183: "222,3111,33,42","1^6,3111,33,51","222,222,3111,51",
8184: "1^9,33111,54","2221^4,33211,55","1^7,3211,322",
8185: "3^4211,5551,88","2^4,3221,3311","333221,4442,77",
8186: "3222,3321,333","33222,33321,66","1^9,3222,54",
8187: "21^4,33,33,411","3^411,44411,77","222,321,33,411",
8188: "1^6,33,411,42","1^6,222,411,51","33,33,33,411,51",
8189: "221^4,2^4,431","2^41^4,4431,66","1^8,3311,431",
8190: "3^411,4433,77","33321,444,552","1^8,221^4,53",
8191: "3311,44,44,53","4^42,5553,99","2^4,3311,44,71",
8192: "3^421,555,771","4^52,7771,bb","3^611,776,aa",
8193: "2^41,33111,441","22111,2221,3211","2^41,3222,441",
8194: "2^61,4441,76","3331,3331,4411","22211,22211,431",
8195: "3331,3331,433","3^41,3^41,76","1^7,1^7,61,61",
8196: "1^d,661,661","21^5,2221,322","221^5,2^41,54",
8197: "2^51,33311,65","21^5,22111,331","3^41,4441,661",
8198: "1^7,331,43,61","2221,2221,43,61","2221,331,331,61",
8199: "21^4,21^4,2211","21^4,2211,33,51","22211,3311,3311",
8200: "1^5,311,311,32","2211,321,33,42","2211,222,321,51",
8201: "3322,3331,442","2211,222,42,42","2^411,442,442",
8202: "1^6,2211,42,51","2211,33,33,51,51","221,221,311,311",
8203: "1^5,2111,311,41","222111,3321,441","22111,22111,322",
8204: "222111,222111,54","2111,221,311,32","2111,2111,221,41",
8205: "1^5,221,41,41,41","2221,43,43,43","1^5,32,32,41,41",
8206: "331,331,43,43","221,221,32,41,41","221,32,32,32,41",
8207: "211,211,211,31,31","211,22,31,31,31,31","1^4,31,31,31,31,31"]];
8208: B=BB[MO];
8209: }
8210: if(St!=1){
8211: for(R=[]; B!=[]; B=cdr(B)){
8212: RT=F?s2sp(car(B)|std=F):s2sp(car(B));
8213: if(length(RT)<L0 || length(RT)>L1) continue;
8214: R=cons(RT,R);
8215: }
8216: return reverse(R);
8217: }else{
8218: if(L0<=3 && L1>=MO+4) return B;
8219: for(R=[]; B!=[]; B=cdr(B)){
8220: RT=s2sp(T=car(B));
8221: if(length(RT)<L0 || length(RT)>L1) continue;
8222: if(F) T=s2sp(s2sp(T|std=K));
8223: R=cons(T,R);
8224: }
8225: return reverse(R);
8226: }
8227: }
8228: MP=(L1<MO+1)?L1:MO+1;
8229: LL=newvect(MO+1);
8230: R=newvect(MP+2);
8231: R0=newvect(MP+2);
8232: for(I=1; I<=MO; I++) LL[I]=[];
8233: if(type(Sp)==4){
8234: if(getopt(basic)==1) Sp=chkspt(Sp[6]);
8235: R=chkspt(Sp);
8236: if(R[1]>MO) return 0;
8237: LL[R[1]]=R;
8238: K=R[1];
8239: }
8240: if(K==1||type(Sp)!=4){
8241: LL[1]=[[[1]]];
8242: for(I=2; I<=MO && I<MP;I++){
8243: for(T=[], J=0; J<I+1; J++)
8244: T=cons([I-1,1],T);
8245: LL[I]=cons(T,LL[I]);
8246: }
8247: K=2;
8248: }
8249: for(OD=K; OD<MO; OD++){
8250: for(LT=LL[OD]; LT!=[]; LT=cdr(LT)){
8251: for(II=0,L=car(LT); L!=[]; II++, L=cdr(L)){
8252: R0[II]=R[II]=car(L);
8253: }
8254: for(; ;){
8255: for(S=-2*OD, I=0; I<II; I++){
8256: S += OD;
8257: if(R[I]!=[]) S-=car(R[I]);
8258: }
8259: --I;
8260: for(;S+OD<=MO && I<=MP;S+=OD,I++){
8261: if(S<=0) continue;
8262: for(J=0;J<=I;J++){
8263: if(J>=II){
8264: if(S<OD) break;
8265: }else
8266: if(S+((R[J]==[])?0:car(R[J]))<car(R0[J])) break;
8267: }
8268: if(--J>=I){
8269: V=newvect(I);
8270: RRR=[];
8271: for(;J>=0;J--){
8272: if(J>=II) RR=[OD,S];
8273: else{
8274: K=length(R[J]);
8275: RR=[S+((K==0)?0:car(R[J]))];
8276: K=length(R0[J])-K;
8277: for(RT=R0[J]; RT!=[]; K--,RT=cdr(RT)){
8278: if(K!=0) RR=cons(car(RT),RR);
8279: }
8280: }
8281: RRR=cons(reverse(RR),RRR);
8282: }
8283: RRR=qsort(reverse(RRR));
8284: if(findin(RRR,LL[S+OD])<0)
8285: LL[S+OD]=cons(RRR,LL[S+OD]);
8286: }
8287: }
8288: for(K=0; K<II; K++){
8289: if(R[K]!=[]){
8290: S=car(R[K]);
8291: while((R[K]=cdr(R[K]))!=[] && car(R[K])==S);
8292: break;
8293: }else R[K]=R0[K];
8294: }
8295: if(K>=II) break;
8296: }
8297: }
8298: }
8299: if(L0>0 || L1<MO+1 || St==1 || F){
8300: for(J=1; J<=MO; J++){
8301: for(RT=[],R=LL[J];R!=[];R=cdr(R)){
8302: L=length(T=car(R));
8303: if(L<L0 || L>L1) continue;
8304: if(F) T=s2sp(T|std=F);
8305: RT=cons((St==1)?s2sp(T):T,RT);
8306: }
8307: LL[J] = reverse(RT);
8308: }
8309: }
8310: if(Eq==1) return LL[MO];
8311: return LL;
8312: }
8313:
8314: def spType2(L)
8315: {
8316: C=0;R=[];
8317: for(LT=L;LT!=[];LT=cdr(LT)){
8318: D=-1;LP=car(LT);
8319: for(LPT=LP;LPT!=[];LPT=cdr(LPT)){
8320: if(D==-1) D=car(LPT);
8321: else D=igcd(D,car(LPT));
8322: if(D==1){
8323: C++;break;
8324: }
8325: }
8326: if(C==2) return 0;
8327: R=cons(D,R);
8328: }
8329: if(C==0) return L;
8330: if(C==1){
8331: for(K=length(R)-1;R[K]!=1;K--);
8332: D=-1;
8333: for(I=length(R)-1;I>=0;I--){
8334: if(I==K) continue;
8335: if(D==-1) D=R[I];
8336: else D=igcd(D,R[I]);
8337: if(D==1) return 0;
8338: }
8339: }
8340: return L;
8341: }
8342:
8343:
8344: /* ret [#points, order, idx, Fuchs, reduction order, reduction exponents, fund] */
8345: def chkspt(M)
8346: {
8347: Opt= getopt(opt);
8348: Mat= getopt(mat);
8349: if(type(M)==7) M=s2sp(M);
1.28 takayama 8350: if(type(Opt) >= 0&&Opt!="idx"){
1.6 takayama 8351: if(type(Opt) == 7)
8352: Opt = findin(Opt, ["sp","basic","construct","strip","short","long","sort","root"]);
8353: if(Opt < 0){
8354: erno(2);
8355: return 0;
8356: }
8357: return fspt(M,Opt);
8358: }
8359: P = length(M);
8360: OD = -1;
8361: XM = newvect(P);
8362: Fu = 0;
8363: for( I = SM = SSM = 0; I < P; I++ ){
8364: LJ = length(M[I]);
8365: JM = JMV = 0;
8366: for(J = SM = 0; J < LJ; J++){
8367: MV = M[I][J];
8368: if(type(MV) == 4){
8369: Fu += MV[0]*MV[1];
8370: MV = MV[0];
8371: }
8372: if(MV > JMV){
8373: JM = J; JMV = MV;
8374: }
8375: SM += MV;
8376: SSM += MV^2;
8377: }
8378: if(OD < 0)
8379: OD = SM;
8380: else if(OD != SM){
1.28 takayama 8381: if(getopt(dumb)!=1) print("irregal partitions");
8382: return -1;
1.6 takayama 8383: }
8384: XM[I] = JM;
8385: }
8386: SSM -= (P-2)*OD^2;
8387: for(I = SM = JM = 0; I < P; I++){
8388: MV = M[I][XM[I]];
8389: if(type(MV) == 4){
8390: MV = MV[0]; JM = 1;
8391: }
8392: if(I == 0)
8393: SMM = MV;
8394: else if(SMM > MV)
8395: SMM = MV;
8396: SM += MV;
8397: }
8398: SM -= (P-2)*OD;
1.28 takayama 8399: if(Opt=="idx") return SSM;
1.6 takayama 8400: if(SM > SMM && SM != 2*OD){
1.28 takayama 8401: if(getopt(dumb)!=1) print("not realizable");
8402: return 0;
1.6 takayama 8403: }
8404: if(JM==1 && Mat!=1)
8405: Fu -= OD - SSM/2;
1.28 takayama 8406: return [P, OD, SSM, Fu, SM, XM, fspt(M,1)];
1.6 takayama 8407: }
8408:
8409: def cterm(P)
8410: {
8411: V = getopt(var);
8412: if(type(V) != 4)
8413: V=vars(P);
8414: for(; V !=[]; V = cdr(V))
8415: P = mycoef(P,0,car(V));
8416: return P;
8417: }
8418:
8419: def terms(P,L)
8420: {
8421: Lv=getopt(level);
8422: if(type(Lv)!=1) Lv=0;
8423: V=car(L);L=cdr(L);
8424: for(R=[],D=mydeg(P,V);D>=0; D--){
8425: if((Q=mycoef(P,D,V))==0) continue;
8426: if(L!=[]){
8427: R0=terms(Q,L|level=Lv+1);
8428: for(;R0!=[];R0=cdr(R0)) R=cons(cons(D,car(R0)),R);
8429: }else R=cons([D],R);
8430: }
8431: if(Lv>0) return R;
8432: R=qsort(R);
8433: Rev = getopt(rev); Dic=getopt(dic);
8434: if(Dic==1 && Rev==1) R=reverse(R);
8435: for(R0=[];R!=[];R=cdr(R)){
8436: for(RT=car(R),S=0;RT!=[];RT=cdr(RT)) S+=car(RT);
8437: R0=cons(cons(S,car(R)),R0);
8438: }
8439: if(Dic==1) return R0;
8440: if(Rev==1){
8441: for(R=[];R0!=[];R0=cdr(R0)){
8442: T=car(R0);
8443: R=cons(cons(-car(T),cdr(T)),R);
8444: }
8445: R0=R;
8446: }
8447: R0=qsort(R0);
8448: if(Rev==1){
8449: for(R=[];R0!=[];R0=cdr(R0)){
8450: T=car(R0);
8451: R=cons(cons(-car(T),cdr(T)),R);
8452: }
8453: R0=R;
8454: }
8455: return (Rev==1)?R0:reverse(R0);
8456: }
8457:
8458: def polcut(P,N,L)
8459: {
8460: if(type(L)==2) L=[L];
8461: M=getopt(top);
8462: if(type(M)!=1) M=0;
8463: T=terms(P,L);
8464: for(S=0;T!=[];T=cdr(T)){
8465: LT=car(T);
8466: if(LT[0]<M || LT[0]>N) continue;
8467: for(PW=1,LT=cdr(LT),V=L,Q=P;LT!=[];LT=cdr(LT),V=cdr(V)){
8468: Q=mycoef(Q,car(LT),car(V));PW*=car(V)^car(LT);
8469: }
8470: S+=Q*PW;
8471: }
8472: return S;
8473: }
8474:
8475: def redgrs(M)
8476: {
8477: Mat = getopt(mat);
8478: if(Mat!=1) Mat=0;
8479: R = chkspt(M|mat=Mat);
8480: if(type(R) < 4)
8481: return -1;
8482: if(R[4] <= 0)
8483: return 1-R[4];
8484: if(R[4] == 2*R[1])
8485: return 0;
8486: V = newvect(R[0]);
8487: Type = type(M[0][0]);
8488: if(Type > 3){
8489: Mu = Mat-1;
8490: for(I = 0; I < R[0]; I++)
8491: Mu += M[I][R[5][I]][1];
8492: }
8493: for(I = 0; I < R[0]; I++){
8494: IR = R[5][I]; L = []; MI = M[I]; MIE=MI[IR];
8495: for(J = length(MI)-1; J >= 0; J--){
8496: if(Type <= 3){
8497: VM = MI[J];
8498: if(J == IR){
8499: VM -= R[4];
8500: if(VM < 0) return -1;
8501: }
8502: L = cons(VM, L);
8503: }else{
8504: VM = MI[J][0];
8505: if(J == IR){
8506: VM -= R[4];
8507: if(VM < 0)
8508: return -1;
8509: if(I == 0)
8510: EV = 1-Mat-Mu;
8511: else
8512: EV = 0;
8513: }else{
8514: if(I == 0)
8515: EV = MI[J][1] - M[0][R[5][0]][1] + 1-Mat; /* + MX - Mu; */
8516: else
8517: EV = MI[J][1] - MIE[1] + Mu;
8518: }
8519: L = cons([VM,EV], L);
8520: /*
1.24 takayama 8521: if(R[2] >= 2){ */ /* rigid */
1.6 takayama 8522: /* P = dx^(R[1]);
8523: } */
8524: }
8525: }
8526: V[I] = L;
8527: }
8528: return [R[5], vtol(V)];
8529: }
8530:
8531: def cutgrs(A)
8532: {
8533: for(AL=[] ; A!=[]; A=cdr(A)){ /* AT: level 2 */
8534: for(ALT=[], AT=car(A); AT!=[]; AT=cdr(AT)){
8535: M = (type(car(AT)) < 4)?car(AT):car(AT)[0];
8536: if(M > 0)
8537: ALT = cons(car(AT), ALT); /* ALT: level 2 */
8538: }
8539: AL = cons(reverse(ALT), AL); /* AL: level 3 */
8540: }
8541: return reverse(AL);
8542: }
8543:
8544: def mcgrs(G, R)
8545: {
8546: NP = length(G);
8547: Mat = (getopt(mat)==1)?0:1;
1.24 takayama 8548: if(Mat==1 && type(SM=getopt(slm))==4){
8549: SM0=SM[0];SM1=anal2sp(SM[1],["*",-1]);
8550: if(findin(0,SM0)>=0){
8551: for(SM=[],I=length(G)-1;I>0;I--)
8552: if(findin(I,SM0)<0) SM=cons(I,SM);
8553: SM=[SM,SM1];
8554: G=mcgrs(G,R|slm=SM);
8555: return [G[0],anal2sp(G[1],["*",-1])];
8556: }
8557: }else SM0=0;
1.6 takayama 8558: for(R = reverse(R) ; R != []; R = cdr(R)){
8559: GN = [];
8560: L = length(G)-1;
8561: RT = car(R);
8562: if(type(RT) == 4){
1.24 takayama 8563: if(length(RT)==L&&RT[0]!=0){
8564: R=cons(cdr(RT),R);
8565: R=cons(RT[0],R);
8566: continue;
8567: } /* addition */
8568: RT = reverse(RT); S = ADS = 0;
1.6 takayama 8569: for(G = reverse(G); G != []; G = cdr(G), L--){
8570: AD = car(RT); RT = cdr(RT);
1.24 takayama 8571: if(L > 0){
1.6 takayama 8572: S += AD;
1.24 takayama 8573: if(SM && findin(L,SM0)>=0) ADS+=AD;
8574: }else
1.6 takayama 8575: AD = -S;
8576: for(GTN = [], GT = reverse(car(G)); GT != []; GT = cdr(GT))
8577: GTN = cons([car(GT)[0],car(GT)[1]+AD], GTN);
8578: GN = cons(GTN, GN);
8579: }
8580: G = GN;
1.24 takayama 8581: if(SM0){
8582: for(ST=reverse(SM1),SM1=[]; ST!=[]; ST=cdr(ST))
8583: SM1 = cons([car(ST)[0],car(ST)[1]+ADS], SM1);
8584: }
1.6 takayama 8585: continue;
8586: }
1.24 takayama 8587: if(RT==0) continue;
8588: VP = newvect(L+1); GV = ltov(G); /* middle convolution */
1.6 takayama 8589: for(I = S = OD = 0; I <= L; I++){
8590: RTT = (I==0)?(Mat-RT):0;
8591: VP[I] = -1;
1.24 takayama 8592: for(J = M = K = 0, GT = GV[I]; GT != []; GT = cdr(GT), J++){
1.6 takayama 8593: if(I == 0)
8594: OD += car(GT)[0];
8595: if(car(GT)[1] == RTT && car(GT)[0] > M){
8596: S += car(GT)[0]-M;
8597: VP[I] = J;
8598: }
8599: }
1.24 takayama 8600: }
8601: S -= (L-1)*OD;
8602: for(GN = []; L >= 0; L--){
8603: GT = GV[L];
8604: RTT = (L==0)?(-RT):RT;
8605: GTN = [(VP[L] >= 0 || S == 0)?[]:[-S,(L==0)?(Mat-RT):0]];
8606: for(J = 0; GT != []; GT = cdr(GT), J++){
8607: if(J != VP[L]){
8608: GTN = cons([car(GT)[0],car(GT)[1]+RTT], GTN);
8609: continue;
1.6 takayama 8610: }
1.24 takayama 8611: K = car(GT)[0] - S;
8612: if(K < 0){
8613: print("Not realizable");
8614: return;
8615: }
8616: GTN = cons([K,(L==0)?(Mat-RT):0], GTN);
8617: }
8618: if(VP[L]<0) GTN=cons([-S,(L==0)?(Mat-RT):0],GTN);
8619: GN = cons(reverse(GTN), GN);
8620: }
8621: if(SM0){
8622: for(M=0,L=length(G)-1;L>0;L--)
8623: if(findin(L,SM0)>=0&&VP[L]>=0) M+=GV[L][VP[L]][0];
8624: Mx=sp2anal(SM1,["max",1,0]);
8625: for(SM2=[],J=0;SM1!=[];J++,SM1=cdr(SM1)){
8626: if(J!=Mx[0]) SM2=cons([car(SM1)[0],car(SM1)[1]+RT],SM2);
8627: else if((V=car(SM1)[0]-M)!=0) SM2=cons([V,RT],SM2);
8628: }
8629: Mx=sp2anal(SM1,["max",1,0]);
8630: for(J=0;SM2!=[];J++,SM2=cdr(SM2)){
8631: if(J!=Mx[0]) SM1=cons(car(SM2),SM1);
8632: else if((V=car(SM1)[0]-S+M)!=0) SM1=cons([V,0],SM2);
1.6 takayama 8633: }
1.24 takayama 8634: if(Mx[0]<0) SM1=cons([-S,0],SM1);
1.6 takayama 8635: }
8636: G = cutgrs(GN);
8637: }
1.24 takayama 8638: return SM0?[G[0],SM1]:G;
1.6 takayama 8639: }
8640:
8641: /*
8642: F=0 : unify
8643: F=["add",S] :
8644: F=["sub",S] :
8645: F=["+",A,B] :
8646: F=["*",A,B] :
8647: F=["mul",K];
8648: F=["get",F,V] :
8649: F=["put",F,V] :
8650: F=["get1",F,V] :
8651: F=["put1",F,V] :
1.24 takayama 8652: F=["max"] :
8653: F=["max",F.V] :
1.6 takayama 8654: F=["put1"] :
8655: F=["val",F];
8656: F=["swap"];
8657: */
8658: def anal2sp(R,F)
8659: {
8660: if(type(F)==4&&type(F[0])==4){ /* multiple commands */
8661: for(;F!=[];F=cdr(F)) R=anal2sp(R,car(F));
8662: return R;
8663: }
8664: if(type(F)==7) F=[F];
8665: if(F==0){ /* unify */
8666: R=ltov(R);
8667: L=length(R);
8668: for(J=1;J<L;J++){
8669: for(I=0;I<J;I++){
8670: if(cdr(R[I])==cdr(R[J])){
8671: R[I]=cons(R[I][0]+R[J][0],cdr(R[I]));
8672: R[J]=cons(0,cdr(R[J]));
8673: break;
8674: }
8675: }
8676: }
8677: for(G=[],I=L-1;I>=0;I--)
8678: if(R[I][0]!=0) G=cons(R[I],G);
8679: if(length(G[0])==2){ /* sort by multiplicity */
8680: R=ltov(G);
8681: L=length(R);
8682: for(I=1;I<L;I++){
8683: for(J=I;J>0;J--){
8684: if(R[J-1][0]>R[J][0]) break;
8685: if(R[J-1][0]==R[J][0]){
8686: S1=rtostr(R[J-1][1]);S2=rtostr(R[J][1]);
8687: if((K=str_len(S1)-str_len(S2))<0) break;
8688: if(!K&&S1<S2) break;
8689: }
8690: S=R[J-1];R[J-1]=R[J];R[J]=S;
8691: }
8692: }
8693: G=vtol(R);
8694: }
8695: return G;
8696: }
8697: if(F[0]=="add") return append(R,F[1]);
1.24 takayama 8698: if(F[0]=="max"){
8699: if(length(F)==3) C=1;
8700: else C=0;
8701: M=-10^10;K=[-1];
8702: for(I=0;R!=[];R=cdr(R),I++){
8703: if(C>0&&car(R)[F[1]]!=F[2]) continue;
8704: if(M<car(R)[0]){
8705: M=car(R)[0];K=[I,car(R)];
8706: }
8707: }
8708: return K;
8709: }
1.6 takayama 8710: R=reverse(R);
8711: if(F[0]=="sub"){
8712: for(S=F[1];S!=[];S=cdr(S))
8713: R=cons(cons(-car(S)[0],cdr(car(S))),R);
8714: return reverse(R);
8715: }
8716: if(F[0]=="swap"){
8717: for(G=[];R!=[];R=cdr(R))
8718: G=cons([car(R)[0],car(R)[2],car(R)[1]],G);
8719: return G;
8720: }
8721: if(F[0]=="+"){
1.24 takayama 8722: L=length(F);
8723: for(G=[];R!=[];R=cdr(R)){
8724: for(S=[],I=L-1;I>0;I--) S=cons(car(R)[I]+F[I],S);
8725: G=cons(cons(car(R)[0],S),G);
8726: }
1.6 takayama 8727: return G;
8728: }
8729: if(F[0]=="*"){
1.24 takayama 8730: L=length(F);
8731: for(G=[];R!=[];R=cdr(R)){
8732: for(S=0,I=1;I<L;I++) S+=car(R)[I]*F[I];
8733: G=cons([car(R)[0],S],G);
8734: }
1.6 takayama 8735: return G;
8736: }
8737: if(F[0]=="mult"){
8738: K=F[1];
8739: for(G=[];R!=[];R=cdr(R)) G=cons(cons(K*car(R)[0],cdr(car(R))),G);
8740: return G;
8741: }
8742: if(F[0]=="get"){
8743: for(G=[];R!=[];R=cdr(R))
8744: if(car(R)[F[1]]==F[2]) G=cons(car(R),G);
8745: return G;
8746: }
8747: if(F[0]=="put"){
8748: if(F[1]==1){
8749: for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],F[2],car(R)[2]],G);
8750: }else{
8751: for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],car(R)[1],F[2]],G);
8752: }
8753: return G;
8754: }
8755: if(F[0]=="get1"){
8756: if(length(F)==2){
8757: for(G=[];R!=[];R=cdr(R)) G=cons([R[0][0],car(R)[F[1]]],G);
8758: return G;
8759: }
8760: for(G=[];R!=[];R=cdr(R))
8761: if(car(R)[F[1]]==F[2]) G=cons([R[0][0],car(R)[3-F[1]]],G);
8762: return G;
8763: }
8764: if(F[0]=="put1"){
8765: if(length(F)==1)
8766: for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],car(R)[1],car(R)[1]],G);
8767: else if(F[1]==1)
8768: for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],F[2],car(R)[1]],G);
8769: else{
8770: for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],car(R)[1],F[2]],G);
8771: }
8772: return G;
8773: }
8774: if(F[0]=="val"){
8775: V=(length(F)==1)?1:F[1];
8776: for(I=J=0;R!=[];R=cdr(R)){
8777: I+=car(R)[0];
8778: J+=car(R)[0]*car(R)[V];
8779: }
8780: return [I,J];
8781: }
8782: return 0;
8783: }
8784:
8785: /*
8786: G=0 get trivial common spct
8787: G="..,..," spectre type of 4 singular points
8788: P=["get"] all spct
8789: P=["get",L]
8790: L=n for variable x_n
8791: L=[m,n] for residue [m,n]
1.23 takayama 8792: L=[m,n,l] for residue [m,n,l]
1.6 takayama 8793: L=[[m,n],[m',n']] for common spct
1.23 takayama 8794: P=["eigen",I] decomposition of A_I
1.6 takayama 8795: P=["get0",[m,n],[m',n']] for the sum of residues
1.23 takayama 8796: P=["rest",[m,n]] restriction
1.6 takayama 8797: P=["swap",[m,n]] for symmetry
8798: P=["perm",[...]] for symmetry
8799: P=["deg"]
8800: P=["homog"]
8801: P=["sort"]
8802: P=[[[m,n],c],...] for addition
8803: P=[c] or [[c],...] for middle convolution wrt 0
8804: P=[m,c] or [[m,c],...] for general middle convolution
8805: P=[[a,b,c]] for special additions
8806: P=[[d,a,b,c]] for middle convotution and additions
8807: P=["multi",...] multiple commands
8808: P=0,1,3 : return sim. spectre of 4 singular points
8809: */
8810: def mc2grs(G,P)
8811: {
8812: if(G==0){
8813: G=[];
8814: for(I=4;I>=0;I--){
8815: V=lsort([0,1,2,3,4],[I],1);
8816: for(J=1;J<4;J++){
8817: for(T=[],K=3;K>0;K--)
8818: if(K!=J) T=cons(V[K],T);
8819: G=cons([[[V[0],V[J]],T],[1,0,0]],G);
8820: }
8821: }
8822: G=mc2grs(G,"sort");
8823: }else if(type(G)==7||(type(G)==4&&length(G)==4)){
8824: if(type(G)==7) G=s2sp(G);
8825: F=(getopt(top)==0)?1:0;
8826: K=[];
8827: if(type(P)==1&&iand(P,1)&&type(G[0][0])<4){
8828: G=s2sp(G|std=1);
8829: if(F) G=[G[1],G[2],G[3],G[0]];
8830: G=sp2grs(G,[d,c,b,a],[1,length(G[0]),-1]|mat=1);
8831: G=reverse(G);
8832: if(iand(P,3)==3){
8833: V=vars(G);
8834: for(H=L=[a,b,c,d];H!=[];H=cdr(H))
8835: if(findin(car(H),V)>=0) G=subst(G,car(H),makev([car(H),1]));
8836: G=shortv(G,[a,b,c,d]);
8837: V=vars(G);
8838: for(H=G[3];H!=[];H=cdr(H)){
8839: T=car(H)[1];
8840: if(type(T)>1&&!isvar(T)){
8841: K=[car(H)[0],T];
8842: break;
8843: }
8844: }
8845: }
8846: F=1;
8847: }
8848: if(F) G=[G[3],G[0],G[1],G[2]];
8849: S=cons(["anal",1],getopt());
8850: if(!(R=m2mc(G,0|option_list=S))) return R;
8851: for(G=0,R=cdr(R);R!=[];R=cdr(R)){
8852: TR=car(R)[0];
8853: if(TR[0]) G=mc2grs(G,[[TR[0]]]);
8854: G=mc2grs(G,[cdr(TR)]);
8855: }
8856: if(type(P)==1&&K!=[]){
8857: for(T=10;T<36;T++){
8858: if(findin(X=makev([T]),V)>=0) continue;
8859: F=K[0]*(X-K[1]);
8860: return [F,simplify(G,[F],4)];
8861: }
8862: }
8863: }
8864: if(type(P)<2) return G;
8865: F=0;
1.25 takayama 8866: if(type(P)==7||(type(P)==4&&
8867: (type(P[0])<4||(type(P[0])==4&&length(P[0])==2&&type(P[0][0])<4&&type(P[1])<4))
8868: )) P=[P];
1.6 takayama 8869: if((Dvi=getopt(dviout))!=1&&Dvi!=2&&Dvi!=-1) Dvi=0;
8870: Keep=(Dvi==2)?1:0;
8871: if(type(P)==4&&type(F=car(P))==7){
8872: if(F=="mult"){
8873: for(P=cdr(P);P!=[];P=cdr(P)) G=mc2grs(G,car(P)|option_list=getopt());
8874: return G;
8875: }
8876: if(F=="show"){
8877: for(R=str_tb(0,0);G!=[];){
8878: L=car(G);
8879: I=L[0][0];J=L[0][1];
8880: str_tb("[A_{"+rtostr(I[0])+rtostr(I[1])+"}:A_{"+rtostr(J[0])+rtostr(J[1])
8881: +"}]&=\\left\\{",R);
8882: for(L=cdr(L);;){
8883: S=car(L);
8884: str_tb("["+my_tex_form(S[1])+":"+my_tex_form(S[2])+"]",R);
8885: if(S[0]!=1) str_tb("_{"+rtostr(S[0])+"}",R);
8886: if((L=cdr(L))==[]) break;
8887: str_tb(",\\,",R);
8888: }
8889: str_tb("\\right\\}",R);
8890: if((G=cdr(G))==[]) break;
8891: str_tb(",\\\\\n",R);
8892: }
8893: R=texbegin("align*",str_tb(0,R));
8894: if(Dvi!=-1) dviout(R|keep=Keep);
8895: return R;
8896: }
8897: if(F=="show0"){
1.26 takayama 8898: if(type(Fig=getopt(fig))>0){
8899: PP=[[-1.24747,-5.86889],[1.24747,-5.86889],[3.52671,-4.8541],[5.19615,-3],
8900: [5.96713,-0.627171],[5.70634,1.8541],[4.45887,4.01478],[2.44042,5.48127],
8901: [0,6],[-2.44042,5.48127],[-4.45887,4.01478],[-5.70634,1.8541],
8902: [-5.96713,-0.627171],[-5.19615,-3],[-3.52671,-4.8541]];
8903: PL=[[1.8,-5.2],[5.7,-1.7],[3.2,5],[-3.6,4.7],[2.2,3],[-2.8,2.8],
8904: [-1.5,-1.4],[-3.2,-2.5],[0.76,-1.4],[-2,0.2]];
8905: PC=["black,dashed","green,dashed","red,dashed","blue,dashed",
8906: "black","cyan","green","blue","red","magenta"];
8907: N=["1","2","3","4","5","6","7","8","9","a","b","c","d","e","f"];
8908: LL=[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[7,10,13],[4,11,14],[5,8,15],[1,12,15],
8909: [2,9,14],[3,6,13]];
8910: TB=str_tb("\\draw\n",TB);
8911: if(type(Fig)==4){
8912: if(type(car(Fig))==1){
8913: PP=ptaffine(car(Fig)/12,PP);PL=ptaffine(car(Fig)/12,PL);
8914: Fig=cdr(Fig);
8915: }
8916: if(Fig!=[]&&length(Fig)==10) PC=Fig;
8917: }
8918: for(R=mc2grs(G,"show0"|dviout=-1),I=0;R!="";I++){ /* 頂点 */
8919: J=str_chr(R,0,",");
8920: if(J>0){
8921: S=str_cut(R,0,J-1);
8922: R=str_cut(R,J+1,1000);
8923: }else{
8924: S=R;R="";
8925: }
8926: T=(str_chr(S,0,"1")==0)?"":"[red]";
8927: str_tb(["node",T,"(",N[I],") at ",xypos(PP[I]),"{$",S,"$}\n"],TB);
8928: }
8929: for(S=PC,P=PL,I=0;I<4;I++){
8930: for(J=I+1;J<5;J++,S=cdr(S),P=cdr(P)){ /* 線の番号 */
8931: SS=car(S);
8932: if((K=str_chr(SS,0,","))>0) SS=sub_str(SS,0,K-1);
8933: str_tb(["node[",SS,"] at ",xypos(car(P)),
8934: "{$[",rtostr(I),rtostr(J),"]$}\n"],TB);
8935: }
8936: }
8937: str_tb(";\n",TB);
8938: for(I=0;I<10;I++){ /* 線 */
8939: S=car(PC);P0=car(PC);L0=car(LL);PC=cdr(PC);LL=cdr(LL);
8940: C=[N[L0[0]-1],N[L0[1]-1],N[L0[2]-1]];
8941: str_tb(["\\draw[",S,"] (", C[0],")--(",C[1],") (",
8942: C[0],")--(",C[2],") (",C[1],")--(",C[2],");\n"],TB);
8943: }
8944: R=str_tb(0,TB);
8945: if(TikZ==1&&Dvi!=-1) dviout(xyproc(R)|dviout=1,keep=Keep);
8946: return R;
8947: }
1.6 takayama 8948: for(S="",L=[];G!=[];G=cdr(G)){
8949: for(TL=[],TG=cdr(car(G));TG!=[];TG=cdr(TG)) TL=cons(car(TG)[0],TL);
8950: TL=msort(TL,[-1,0]);
8951: if(Dvi){
8952: if(S!="") S=S+",";
8953: for(I=J=0,T=append(TL,[[0]]);T!=[];T=cdr(T)){
8954: if(car(T)==I) J++;
8955: else{
8956: if(I>0&&J>0){
8957: if(I>9) S=S+"("+rtostr(I)+")";
8958: else S=S+rtostr(I);
8959: if(J>1){
8960: if(J>9) S=S+"^{"+rtostr(J)+"}";
8961: else S=S+"^"+rtostr(J);
8962: }
8963: }
8964: I=car(T);J=1;
8965: }
8966: }
8967: }
8968: L=cons(TL,L);
8969: }
8970: if(Dvi){
8971: if(Dvi!=-1) dviout(S|eq=0);
8972: return S;
8973: }
8974: return reverse(L);
8975: }
8976: if(F=="sort"){
8977: G=ltov(G);L=length(G);
8978: for(I=0;I<L;I++){
8979: S=G[I][0];
8980: if(S[0][0]>S[0][1]) S=[[S[0][1],S[0][0]],S[1]];
8981: if(S[1][0]>S[1][1]) S=[S[0],[S[1][1],S[1][0]]];
8982: if(S[0]>S[1]){
8983: F=0;S=[S[1],S[0]];
8984: }
8985: if(S!=G[I][0]){
8986: if(F==0) G[I]=cons(S,anal2sp(cdr(G[I]),"swap"));
8987: else G[I]=cons(S,cdr(G[I]));
8988: }
8989: for(J=I;J>0;J--){
8990: if(G[J-1][0]<G[J][0]) break;
8991: S=G[J-1];G[J-1]=G[J];G[J]=S;
8992: }
8993: }
8994: return vtol(G);
8995: }
8996: if(F=="get"||F=="get0"){
8997: if(Dvi!=0) F="get";
8998: if(length(P)==1||type(P[1])<2){
8999: L=[];
9000: if(length(P)==1){
9001: for(I=3;I>=0;I--){
9002: for(J=4;J>I;J--) L=cons(mc2grs(G,[F,[I,J]]),L);
9003: }
9004: }else{
9005: for(I=P[1],J=4;J>=0;J--){
9006: if(I==J) continue;
9007: L=cons(mc2grs(G,[F,(I<J)?[I,J]:[J,I]]),L);
9008: }
9009: }
9010: if(Dvi){
9011: if(length(L)==10){
9012: R=ltov(L);
9013: if(R[6][0]==[1,4]){
9014: S=R[6];R[6]=R[7];R[7]=S;
9015: L=vtol(R);
9016: }
9017: }
9018: for(R=S=[],L=reverse(L);L!=[];L=cdr(L)){
9019: T=car(L);
9020: R=cons(cdr(T),R);
9021: if(S==[]) S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}\\\\\n";
9022: else S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}&"+S;
9023: }
9024: L=ltotex(R|opt="GRS",pre=S);
1.26 takayama 9025: if(type(D=getopt(div))==1 || type(D)==4) L=divmattex(L,D);
1.6 takayama 9026: if(Dvi>0) dviout(L|eq=0,keep=Keep);
9027: }
9028: return L; /* get all spct */
9029: }
9030: if(type(T=P[1])==4){
9031: if(F=="get0"&&length(P)==3&&type(I=P[1])==4&&type(J=P[2])==4){
9032: if(I[0]>I[1]) I=[I[1],I[0]];
9033: if(J[0]>J[1]) J=[J[1],J[0]];
9034: if(I[0]>I[0]){S=I;I=J;J=S;};
9035: K=lsort(I,J,0);
9036: if(length(K)==4){
1.24 takayama 9037: S=mc2grs(G,["get0",[I,J]]);
1.6 takayama 9038: return anal2sp(S,[["*",1,1],0]);
9039: }
9040: I=lsort(K,lsort(I,J,2),1);
9041: S=lsort([0,1,2,3,4],K,1);
1.24 takayama 9042: D=mc2grs(G,"deg");
1.6 takayama 9043: if(findin(4,S)<0) D=-D;
1.24 takayama 9044: J=mc2grs(G,["get0",[I,S]]);
1.6 takayama 9045: if(I[0]>S[0]) J=sp2grs(J,"swap");
9046: return anal2sp(J,[["+",0,D],["*",-1,1]]);
9047: }
9048: if(type(car(T))==4){
9049: if(T[0][0]>T[0][1]) T=[[T[0][1],T[0][0]],T[1]];
9050: if(T[1][0]>T[1][1]) T=[T[0],[T[1][1],T[1][0]]];
9051: if(T[0][0]>T[1][0]) T=[T[1],T[0]];
9052: for(PG=G;PG!=[];PG=cdr(PG))
9053: if(car(PG)[0]==T) return (F=="get")?car(PG):cdr(car(PG));
9054: return []; /* get common spct */
9055: }
1.23 takayama 9056: if(length(T)==3){
9057: T0=T;T=lsort([0,1,2,3,4],T,1);
9058: if(length(T)!=2) return [];
9059: }else T0=0;
1.6 takayama 9060: if(T[0]>T[1]) T=[T[1],T[0]];
9061: for(FT=0,PG=G;PG!=[];PG=cdr(PG)){
9062: if(car(PG)[0][0]==T){
9063: FT=1;break;
9064: }
9065: if(car(PG)[0][1]==T){
9066: FT=2;break;
9067: }
9068: }
9069: if(!FT) return [];
9070: L=anal2sp(cdr(car(PG)),[["get1",FT],0]);
1.23 takayama 9071: if(T0!=0){
9072: if((K=mc2grs(G,"deg"))!=0){
9073: if(T[1]!=4) K=-K;
9074: R=reverse(L);
9075: for(L=[];R!=[];R=cdr(R)) L=cons([car(R)[0],car(R)[1]+K],L);
9076: }
9077: T=T0;
9078: }
1.6 takayama 9079: return (F=="get")?cons(T,L):L;
9080: }
9081: }
1.27 takayama 9082: if(F=="rest"||F=="eigen"||F=="rest0"||F=="rest1"){
1.23 takayama 9083: if(F!="eigen") G=mc2grs(G,"homog");
1.26 takayama 9084: if(length(P)==1){
9085: for(R=[],I=0;I<4;I++){
9086: for(J=I+1;J<5;J++){
9087: S=mc2grs(G,[F,[I,J]]);
1.27 takayama 9088: if(S!=[]) R=cons(cons([I,J],S),R);
1.26 takayama 9089: }
9090: }
9091: R=reverse(R);
9092: if(Dvi){
9093: TB=str_tb(0,0);
1.27 takayama 9094: if(F=="rest0"||F=="rest1"){
1.26 takayama 9095: for(T=R;;){
9096: TT=car(T);
9097: S=rtostr(car(TT)[0])+rtostr(car(TT)[1]);
9098: str_tb(["[",S,"]","&: "],TB);
9099: for(TR=[],TT=cdr(TT);TT!=[];TT=cdr(TT))
9100: TR=cons(car(TT)[1],TR);
9101: for(TR=qsort(TR);TR!=[];TR=cdr(TR))
9102: str_tb([s2sp(car(TR)|short=1,std=-1),"\\ \\ "],TB);
9103: if((T=cdr(T))==[]) break;
9104: str_tb("\\\\\n",TB);
9105: }
9106: }else{
9107: TB=str_tb(0,0);
9108: for(T=R;;){
9109: TT=car(T);
9110: S=rtostr(car(TT)[0])+rtostr(car(TT)[1]);
9111: str_tb(["[",S,"]",":\\ "],TB);
9112: for(TR=[],TT=cdr(TT);;){
9113: T0=car(TT);
9114: str_tb(["&",my_tex_form(car(T0)),"&&\\to\\ \n",
9115: ltotex(cdr(T0)|opt="GRS")],TB);
9116: if((TT=cdr(TT))==[]) break;
9117: str_tb("\\\\\n",TB);
9118: }
9119: if((T=cdr(T))==[]) break;
9120: str_tb("\\allowdisplaybreaks\\\\\n",TB);
9121: }
9122: }
9123: R=texbegin("align*",str_tb(0,TB));
9124: if(Dvi!=-1) dviout(R|keep=Keep);
9125: }
9126: return R;
9127: }
1.23 takayama 9128: I=P[1];
9129: if(I[0]>I[1]) I=[I[1],I[0]];
9130: L=lsort([0,1,2,3,4],I,1);
1.29 takayama 9131: if(F=="rest"&&length(P)==3){
9132: J=P[2];if(J[0]>J[1]) J=[J[1],J[0]];
9133: L=lsort(L,J,1);
9134: if(length(L)!=1) return 0;
9135: return [mc2grs(G,["get0",I]),mc2grs(G,["get0",[I[0],J[0]],[I[1],J[1]]]),
9136: mc2grs(G,["get0",[I[0],J[1]],[I[1],J[0]]]),mc2grs(G,["get0",[I[0],I[1],L[0]]])];
9137: }
1.23 takayama 9138: L=[[L[0],L[1]],[L[0],L[2]],[L[1],L[2]]];
1.24 takayama 9139: if(F!="eigen"){
9140: if(I==[0,4]) L=reverse(L);
9141: else{
9142: for(V=[],J=2;J>=0;J--){
9143: if(L[J][0]==0) V=cons([L[J][1],J],V);
9144: else{
9145: for(K=4;K>=0;K--){
9146: if(findin(K,L[J])<0){
9147: V=cons([K,J],V);break;
9148: }
9149: }
9150: }
9151: }
9152: V=qsort(V);
9153: L=[L[V[0][1]],L[V[1][1]],L[V[2][1]]];
9154: }
9155: }
1.23 takayama 9156: for(LL=[],T=L;T!=[];T=cdr(T))
9157: LL=cons(mc2grs(G,["get0",[I,car(T)]]),LL);
9158: LL=reverse(LL);
9159: for(R=[],Q=mc2grs(G,["get0",I]);Q!=[];Q=cdr(Q)){
1.24 takayama 9160: for(T=[],J=2;J>=0;J--){
9161: V=anal2sp(LL[J],["get1",(I[0]<L[J][0])?1:2,car(Q)[1]]);
9162: if(F=="rest"){
9163: if(I[0]==0){
9164: if(I[1]!=4){
9165: if(L[J][1]!=4) V=anal2sp(V,["+",-car(Q)[1]]);
9166: }else if (L[J][0]!=2) V=anal2sp(V,["+",-car(Q)[1]]);
9167: }else if(L[J][0]!=0) V=anal2sp(V,["+",-car(Q)[1]]);
9168: }
9169: T=cons(V,T);
9170: }
1.23 takayama 9171: R=cons(cons(car(Q)[1],T),R);
9172: }
1.27 takayama 9173: if(F=="rest0"||F=="rest1"){
9174: for(L=[];R!=[];R=cdr(R)){
9175: TR=cdr(car(R));
1.28 takayama 9176: if(F=="rest1"&&chkspt(TR|opt="idx")==2) continue;
1.27 takayama 9177: L=cons([car(R)[0],s2sp(chkspt(TR|opt=6))],L);
9178: }
1.23 takayama 9179: R=reverse(L);
9180: }
9181: return R;
9182: }
1.6 takayama 9183: if(F=="deg"){
9184: for(S=I=0;I<3;I++){
9185: for(J=I+1;J<4;J++){
9186: L=mc2grs(G,["get0",[I,J]]);
9187: L=anal2sp(L,"val");
9188: S+=L[1];
9189: }
9190: }
9191: return S/L[0];
9192: }
1.27 takayama 9193: if(F=="spct"||F=="spct1"){
9194: K=(F=="spct")?5:6;
1.6 takayama 9195: G=mc2grs(G,"get");
1.27 takayama 9196: M=newmat(5,K);
1.6 takayama 9197: for(;G!=[];G=cdr(G)){
9198: GT=car(G);I=GT[0][0];J=GT[0][1];
9199: for(S=0,L=[],GT=cdr(GT);GT!=[];GT=cdr(GT)){
9200: L=cons(car(GT)[0],L);
9201: }
9202: L=reverse(qsort(L));
9203: M[I][J]=M[J][I]=L;
9204: }
9205: for(D=0,GT=M[0][1];GT!=[];GT=cdr(GT)) D+=car(GT);
9206: for(I=0;I<5;I++){
9207: S=-2*D^2;
9208: for(J=0;J<5;J++){
9209: if(I==J) continue;
9210: for(L=M[I][J];L!=[];L=cdr(L)) S+=car(L)^2;
9211: }
9212: M[I][I]=S;
1.27 takayama 9213: if(K==6){
9214: for(S=[],J=4;J>=0;J--)
9215: if(I!=J) S=cons(M[I][J],S);
9216: R=chkspt(S|opt=2);
9217: M[I][5]=((L=length(R))>1)?s2sp(R[L-2]|short=1):"";
9218: }
1.6 takayama 9219: }
9220: if(Dvi){
9221: S=[];
9222: for(I=4;I>=0;I--){
1.27 takayama 9223: L=(K==6)?[M[I][5]]:[];
9224: L=cons(M[I][I],L);
1.6 takayama 9225: for(J=4;J>=0;J--){
9226: if(I==J) L=cons("",L);
9227: else L=cons(s2sp([M[I][J]]),L);
9228: }
9229: S=cons(L,S);
9230: }
1.27 takayama 9231: T=(K==6)?["reduction"]:[];
9232: S=cons(append([x0,x1,x2,x3,x4,"idx"],T),S);
9233: M=ltotex(S|opt="tab",hline=[0,1,z],
9234: vline=(K==6)?[0,1,z-2,z-1,z]:[0,1,z-2,z-1,z],
1.26 takayama 9235: left=["","$x_0$","$x_1$","$x_2$","$x_3$","$x_4$"]);
1.6 takayama 9236: if(Dvi>0) dviout(M|keep=Keep);
9237: }
9238: return M;
9239: }
9240: if(F=="swap"||F=="perm"){
9241: if(F=="perm") TR=P[1];
9242: else{
9243: TR=newvect(5,[0,1,2,3,4]);
9244: K=P[1][0];L=P[1][1];
9245: TR[K]=L;TR[L]=K;
9246: if(TR[4]!=4) G=mc2grs(G,"deg");
9247: }
9248: V=newvect(2);
9249: for(L=[],T=G;T!=[];T=cdr(T)){
9250: TP=car(T)[0];
9251: for(TQ=[],I=1;I>=0;I--){
9252: V=[TR[TP[I][0]],TR[TP[I][1]]];
9253: if(V[0]>V[1]) V=[V[1],V[0]];
9254: TQ=cons(V,TQ);
9255: }
9256: if(TQ[0][0]<TQ[1][0]){
9257: L=cons(cons(TQ,cdr(car(T))),L);
9258: continue;
9259: }
9260: TQ=[[TQ[1],TQ[0]]];
9261: for(TP=cdr(car(T));TP!=[];TP=cdr(TP))
9262: TQ=cons([car(TP)[0],car(TP)[2],car(TP)[1]],TQ);
9263: L=cons(reverse(TQ),L);
9264: }
9265: return mc2grs(L,"sort");
9266: }
9267: if(F=="homog"){
9268: V=mc2grs(G,"deg");
9269: return mc2grs(G,[[[2,3],-V]]);
9270: }else if(F=="deg"){
9271: R=mc2grs(G,4);
9272: for(V=0;R!=[];R++){
9273: for(TR=cdr(R);TR!=[];TR=cdr(TR))
9274: V+=car(TR)[0]*car(TR)[1];
9275: }
9276: return -V;
9277: }
9278: }
9279: if(type(F)!=4) return 0;
9280: if(type(P[0])!=4) P=[P];
9281: for(;P!=[];P=cdr(P)){
9282: if(type((S=P[0])[0])==4){ /* addition */
9283: T=P[0][0];
9284: if(T[0]>T[1]) T=[T[1],T[0]];
9285: T1=[T[0],4];T2=[T[1],4];
9286: for(L=[],PG=reverse(G);PG!=[];PG=cdr(PG)){
9287: R=car(PG);R0=R[0];F=0;K=P[0][1];
9288: if(R0[0]==T) F=1;
9289: else if(R0[1]==T) F=2;
9290: else if(getopt(unique)!=1){
9291: K=-K;
9292: if(R0[0]==T1||R0[0]==T2) F=1;
9293: else if(R0[1]==T1||R0[1]==T2) F=2;
9294: }
9295: if(F==0) L=cons(R,L);
9296: else{
9297: R1=anal2sp(cdr(R),(F==1)?["+",K,0]:["+",0,K]);
9298: L=cons(cons(R0,R1),L);
9299: }
9300: }
9301: G=L;
9302: }else if(type(S[0])<4){
9303: if(length(S)==1){ /* mc wrt0 4:cases */
9304: U=mc2grs(G,"deg");
9305: C=P[0][0];
9306: L=[];
9307: /* [[0,1],[2,3]] : [K=[0,k],J=[i,j]], S=[k,4] : 3 cases */
9308: for(K=1;K<4;K++){
9309: J=lsort([1,2,3],[K],1);
9310: K4=[K,4];K0=[0,K];
9311: G0=mc2grs(G,["get0",[K0,J]]);
9312: LT=anal2sp(G0,["+",C,0]);
9313: G0=mc2grs(G,["get0",J]);
9314: L0=anal2sp(G0,["put1",1,0]);
9315: LT=anal2sp(LT,["add",L0]);
9316: G0=mc2grs(G,["get0",K4]);
9317: L0=anal2sp(G0,[["put1",1,0],["+",0,U]]);
9318: LT=anal2sp(LT,["add",L0]);
9319: G0=mc2grs(G,["get0",[[0,J[0]],K4]]);
9320: L0=anal2sp(G0,[["get",1,0],["+",0,U]]);
9321: LT=anal2sp(LT,["sub",L0]);
9322: G0=mc2grs(G,["get0",[[0,J[1]],K4]]);
9323: L0=anal2sp(G0,[["get",1,0],["+",0,U]]);
9324: LT=anal2sp(LT,["sub",L0]);
9325: G0=mc2grs(G,["get0",[K0,J]]);
9326: L0=anal2sp(G0,[["get",1,0],["+",C,0]]);
9327: LT=anal2sp(LT,["sub",L0]);
9328: G0=mc2grs(G,["get0",[[0,4],J]]);
9329: L0=anal2sp(G0,[["+",-C,0],["get",1,0]]);
9330: LT=anal2sp(LT,[["sub",L0],0]);
9331: L=cons(cons([K0,J],LT),L);
9332: }
9333: /* [[0,1],[2,4]] : [K,I]=[[0,k],[i,4]] S=[j,k] : 6 cases */
9334: for(K=1;K<4;K++){
9335: for(I=1;I<4;I++){
9336: if(I==K) continue;
9337: for(J=1;J<4;J++) if(J!=I&&J!=K) break;
9338: I4=[I,4];S=(J<K)?[J,K]:[K,J];K0=[0,K];
9339: G0=cdr(mc2grs(G,["get",[K0,I4]]));
9340: LT=anal2sp(G0,["+",C,0]);
9341: G0=cdr(mc2grs(G,["get",I4]));
9342: L0=anal2sp(G0,["put1",1,0]);
9343: LT=anal2sp(LT,["add",L0]);
9344: G0=cdr(mc2grs(G,["get",S]));
9345: L0=anal2sp(G0,[["put1",1,0],["+",0,-C-U]]);
9346: LT=anal2sp(LT,["add",L0]);
9347:
9348: G0=cdr(mc2grs(G,["get",[[0,I],S]]));
9349: L0=anal2sp(G0,[["get",1,0],["+",0,-C-U]]);
9350: LT=anal2sp(LT,["sub",L0]);
9351: G0=cdr(mc2grs(G,["get",[[0,J],I4]]));
9352: L0=anal2sp(G0,["get",1,0]);
9353: LT=anal2sp(LT,["sub",L0]);
9354: G0=cdr(mc2grs(G,["get",[K0,I4]]));
9355: L0=anal2sp(G0,[["get",1,0],["+",C,0]]);
9356: LT=anal2sp(LT,["sub",L0]);
9357: G0=cdr(mc2grs(G,["get",[[0,4],S]]));
9358: L0=anal2sp(G0,[["get",1,C],["+",-C,-C-U]]);
9359: LT=anal2sp(LT,[["sub",L0],0]);
9360: L=cons(cons([K0,I4],LT),L);
9361: }
9362: }
9363: /* [[0,4],[2,3]] : [[0,4],J]=[[0,4],[i,j]] 3 cases */
9364: for(K=3;K>0;K--){
9365: J=lsort([1,2,3],[K],1);
9366: G0=mc2grs(G,["get0",[[0,4],J]]);
9367: LT=anal2sp(G0,["+",-C,0]);
9368: G0=mc2grs(G,["get0",J]);
9369: L0=anal2sp(G0,["put1",1,-C]);
9370: LT=anal2sp(LT,["add",L0]);
9371: G0=mc2grs(G,["get0",[K,4]]);
9372: L0=anal2sp(G0,[["put1",1,-C],["+",0,U]]);
9373: LT=anal2sp(LT,["add",L0]);
9374:
9375: G0=mc2grs(G,["get0",[[0,J[0]],[K,4]]]);
9376: L0=anal2sp(G0,[["get",1,0],["+",-C,U]]);
9377: LT=anal2sp(LT,["sub",L0]);
9378: G0=mc2grs(G,["get0",[[0,J[1]],[K,4]]]);
9379: L0=anal2sp(G0,[["get",1,0],["+",-C,U]]);
9380: LT=anal2sp(LT,["sub",L0]);
9381: G0=mc2grs(G,["get0",[[0,K],J]]);
9382: L0=anal2sp(G0,[["get",1,0],["+",-C,0]]);
9383: LT=anal2sp(LT,["sub",L0]);
9384: G0=mc2grs(G,["get0",[[0,4],J]]);
9385: L0=anal2sp(G0,[["get",1,C],["put",1,0]]);
9386: LT=anal2sp(LT,[["sub",L0],0]);
9387: L=cons(cons([[0,4],J],LT),L);
9388: }
9389: /* [[1,2],[3,4]] : [J,K]=[[i,j],[k,4]] 3 cases */
9390: for(K=3;K>0;K--){
9391: J=lsort([1,2,3],[K],1);
9392: if(K>1)
9393: LT=mc2grs(G,["get0",[J,[K,4]]]);
9394: else{
9395: LT=mc2grs(G,["get0",[[K,4],J]]);
9396: LT=anal2sp(LT,"swap");
9397: }
9398: G0=mc2grs(G,["get0",J]);
9399: L0=anal2sp(G0,[["put1"],["+",0,-C-U]]);
9400: LT=anal2sp(LT,["add",L0]);
9401: G0=mc2grs(G,["get0",[K,4]]);
9402: L0=anal2sp(G0,[["put1"],["+",U,0]]);
9403: LT=anal2sp(LT,["add",L0]);
9404:
9405: G0=mc2grs(G,["get0",[[0,J[0]],[K,4]]]);
9406: L0=anal2sp(G0,[["get1",1,0],["put1"],["+",U,0]]);
9407: LT=anal2sp(LT,["sub",L0]);
9408: G0=mc2grs(G,["get0",[[0,J[1]],[K,4]]]);
9409: L0=anal2sp(G0,[["get1",1,0],["put1"],["+",U,0]]);
9410: LT=anal2sp(LT,["sub",L0]);
9411: G0=mc2grs(G,["get0",[[0,K],J]]);
9412: L0=anal2sp(G0,[["get1",1,0],["put1"],["+",0,-C-U]]);
9413: LT=anal2sp(LT,["sub",L0]);
9414: G0=mc2grs(G,["get0",[[0,4],J]]);
9415: L0=anal2sp(G0,[["get1",1,C],["put1"],["+",0,-C-U]]);
9416: LT=anal2sp(LT,[["sub",L0],0]);
9417: if(K==1){
9418: LT=anal2sp(LT,"swap");
9419: L=cons(cons([[K,4],J],LT),L);
9420: }else L=cons(cons([J,[K,4]],LT),L);
9421: }
9422: G=L;
9423: }else if(length(S)==2){ /* general mc */
9424: if(S[1]!=0){
9425: I=S[0];
9426: if(I!=0) G=mc2grs(G,["swap",[0,I]]);
9427: G=mc2grs(G,[S[1]]);
9428: if(I!=0) G=mc2grs(G,["swap",[0,I]]);
9429: }
9430: }else if(length(S)==3||length(S)==4){ /* addition */
9431: for(I=1;I<4;I++,S=cdr(S))
9432: if(S[0]) G=mc2grs(G,[[[0,I],S[0]]]);
9433: if(length(S)==1 && S[0]) /* mc */
9434: G=mc2grs(G,[S[0]]);
9435: }
9436: }
9437: }
9438: return mc2grs(G,"sort");
9439: }
9440:
9441: def mcmgrs(G,P)
9442: {
9443: if(type(G)<2){
9444: if(G>1){
9445: N=G+2;G=[];
9446: for(I=1;I<=N;I++){
9447: for(J=1;J<N;J++){
9448: if(I==J) continue;
9449: for(K=J+1;K<=N;K++){
9450: if(I==K) continue;
9451: G=cons([[[0,I],[J,K]],[1,0,0]],G);
9452: }
9453: }
9454: }
9455: for(I=1;I<=N;I++){
9456: for(J=1;J<I;J++) G=cons([[[0,I],[0,J,I]],[1,0,0]],G);
9457: for(J=I+1;J<=N;J++) G=cons([[[0,I],[0,I,J]],[1,0,0]],G);
9458: }
9459: return reverse(G);
9460: }
9461: return 0;
9462: }
9463: if(type(G)==7) G=os_md.s2sp(G);
9464: if(type(G)!=4||type(G[0])!=4) return 0;
9465: if(type(G[0][0])!=4){ /* spectre type -> GRS */
9466: G=s2sp(G|std=1);
9467: L=length(G);
9468: for(V=[],I=L-2;I>=0;I--) V=cons(makev([I+10]),V);
9469: V=cons(makev([L+9]),V);
9470: G=sp2grs(G,V,[1,length(G[0]),-1]|mat=1);
9471: if(getopt(short)!=0){
9472: V=append(cdr(V),[V[0]]);
9473: G=shortv(G,V);
9474: }
9475: R=chkspt(G|mat=1);
9476: if(R[2] != 2 || R[3] != 0 || !(R=getbygrs(G,1|mat=1))) return 0;
9477: if(getopt(anal)==1) return R; /* called by mcmgrs() */
9478: if(!(G=mcmgrs(L-2,0))) return 0;
9479: for(R=cdr(R);R!=[];R=cdr(R)){
9480: TR=car(R)[0];
9481: if(TR[0]) G=mcmgrs(G,[[TR[0]]]);
9482: G=mcmgrs(G,[cdr(TR)]);
9483: }
9484: }
9485: L=length(G);
9486: for(N=4;N<25;N++){
9487: K=N^2*(N-1)/2;
9488: if(K>L) return 0;
9489: if(K==L) break;
9490: }
9491: if(type(P)<2) return G;
9492: F=0;
9493: if(type(P)==7||(type(P)==4&&type(P[0])<4)) P=[P];
9494: if((Dvi=getopt(dviout))!=1&&Dvi!=2&&Dvi!=-1) Dvi=0;
9495: Keep=(Dvi==2)?1:0;
9496: if(type(P)==4 && type(F=car(P))==7){
9497: if(F=="mult"){
1.24 takayama 9498: for(P=cdr(P);P!=[];P=cdr(P)) G=mc2grs(G,car(P)|option_list=getopt());
1.6 takayama 9499: return G;
9500: }
9501: if(F=="get"||F=="get0"){
9502: if(Dvi!=0) F="get";
9503: if(length(P)==2){
9504: if(type(P[1])==4){
9505: if(type(P[1][1])==4){ /* [[,],[,]] */
9506: for(PG=reverse(G);PG!=[];PG=cdr(PG)){
9507: TP=car(PG);
9508: if(TP[0]==P[1]) return (F=="get")?TP:cdr(TP);
9509: }
9510: return [];
9511: }
9512: if(P[1][0]==0){
9513: if(length(P[1])==2){ /* [0,] */
9514: for(J=1;J<=N;J++) if(J!=P[1][1]) break;
9515: for(K=J+1;K<=N;K++) if(K!=P[1][1]) break;
9516: L=mcmgrs(G,["get0",[P[1],[J,K]]]);
9517: L=anal2sp(L,["get1",1]);
9518: }else{ /* [0,*,*] */
9519: L=mcmgrs(G,["get0",[[P[1][0],P[1][1]],P[1]]]);
9520: L=anal2sp(L,["get1",2]);
9521: }
9522: }else{ /* [,] */
9523: for(J=1;J<=N;J++) if(J!=P[1][0]&&J!=P[1][1]) break;
9524: L=mcmgrs(G,["get0",[[0,J],P[1]]]);
9525: L=anal2sp(L,["get1",2]);
9526: }
9527: L=anal2sp(L,0);
9528: if(F=="get") L=cons(P[1],L);
9529: return L;
9530: }else{ /* I */
9531: for(L=[],I=P[1],J=0;J<=N;J++){
9532: if(I==J) continue;
9533: II=(I<J)?[I,J]:[J,I];
9534: L=cons(mcmgrs(G,[F,II]),L);
9535: }
9536: }
9537: }else{
9538: for(L=[],I=0;I<N;I++){
9539: for(J=I+1;J<=N;J++) L=cons(mcmgrs(G,[F,[I,J]]),L);
9540: }
9541: }
9542: if(Dvi){
9543: for(R=S=[];L!=[];L=cdr(L)){
9544: T=car(L);
9545: R=cons(cdr(T),R);
9546: if(S==[]) S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}\\\\\n";
9547: else S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}&"+S;
9548: }
9549: L=ltotex(R|opt="GRS",pre=S);
9550: if(type(V=getopt(div))!=4) V=[];
9551: if(V==[]&&(K=length(R))>10)
9552: for(I=9;I<K;I+=9) V=cons(I,V);
9553: V=reverse(V);
9554: if(V!=[]) L=divmattex(L,V);
9555: if(Dvi>0){
9556: if(V!=[]) dviout(L|keep=Keep);
9557: else dviout(L|eq=0,keep=Keep);
9558: }
9559: }else L=reverse(L);
9560: return L;
9561: }
9562: if(F=="show"){
9563: for(R=str_tb(0,0);G!=[];){
9564: L=car(G);
9565: I=L[0][0];J=L[0][1];
9566: str_tb("[A_{"+rtostr(I[0])+rtostr(I[1])+"}:A_{"+rtostr(J[0])+rtostr(J[1]),R);
9567: if(length(J)==3) str_tb(rtostr(J[2]),R);
9568: str_tb("}]&=\\left\\{",R);
9569: for(L=cdr(L);;){
9570: S=car(L);
9571: str_tb("["+my_tex_form(S[1])+":"+my_tex_form(S[2])+"]",R);
9572: if(S[0]!=1) str_tb("_{"+rtostr(S[0])+"}",R);
9573: if((L=cdr(L))==[]) break;
9574: str_tb(",\\,",R);
9575: }
9576: str_tb("\\right\\}",R);
9577: if((G=cdr(G))==[]) break;
9578: str_tb(texcr(43),R);
9579: }
9580: R=texbegin("align*",str_tb(0,R));
9581: if(Dvi!=-1) dviout(R|keep=Keep);
9582: return R;
9583: }
9584: if(F=="show0"){
9585: for(C=N*(N-1)*(N-2)/2,S="",L=[];G!=[];G=cdr(G)){
9586: for(TL=[],TG=cdr(car(G));TG!=[];TG=cdr(TG)) TL=cons(car(TG)[0],TL);
9587: TL=msort(TL,[-1,0]);
9588: if(Dvi){
9589: if(S!=""){
9590: if(--C==0) S=S+";";
9591: else S=S+",";
9592: }
9593: for(I=J=0,T=append(TL,[[0]]);T!=[];T=cdr(T)){
9594: if(car(T)==I) J++;
9595: else{
9596: if(I>0&&J>0){
9597: if(I>9) S=S+"("+rtostr(I)+")";
9598: else S=S+rtostr(I);
9599: if(J>1){
9600: if(J>9) S=S+"^{"+rtostr(J)+"}";
9601: else S=S+"^"+rtostr(J);
9602: }
9603: }
9604: I=car(T);J=1;
9605: }
9606: }
9607: }
9608: L=cons(TL,L);
9609: }
9610: if(Dvi){
9611: if(Dvi!=-1) dviout(S|eq=0);
9612: return S;
9613: }
9614: return reverse(L);
9615: }
9616: if(F=="spct"){
9617: G=mcmgrs(G,"get");
9618: M=newmat(N+1,N+1);
9619: for(;G!=[];G=cdr(G)){
9620: GT=car(G);I=GT[0][0];J=GT[0][1];
9621: for(S=0,L=[],GT=cdr(GT);GT!=[];GT=cdr(GT)){
9622: L=cons(car(GT)[0],L);
9623: }
9624: L=reverse(qsort(L));
9625: M[I][J]=M[J][I]=L;
9626: }
9627: for(D=0,GT=M[0][1];GT!=[];GT=cdr(GT)) D+=car(GT);
9628: for(I=0;I<=N;I++){
9629: S=-(N-2)*D^2;
9630: for(J=0;J<=N;J++){
9631: if(I==J) continue;
9632: for(L=M[I][J];L!=[];L=cdr(L)) S+=car(L)^2;
9633: }
9634: M[I][I]=S;
9635: }
9636: if(Dvi){
9637: S=[];
9638: for(LS=[],I=N;I>=0;I--){
9639: L=[M[I][I]];
9640: for(J=N;J>=0;J--){
9641: if(I==J) L=cons("",L);
9642: else L=cons(s2sp([M[I][J]]),L);
9643: }
9644: S=cons(L,S);
9645: LS=cons("$x_"+rtostr(I)+"$",LS);
9646: }
9647: S=cons(append(LS,["idx"]),S);
9648: M=ltotex(S|opt="tab",hline=[0,1,z],vline=[0,1,z-1,z],left=cons("",LS));
9649: if(Dvi>0) dviout(M|keep=Keep);
9650: }
9651: return M;
9652: }
9653: if(F=="deg"){
9654: for(S=I=0;I<N-1;I++){
9655: for(J=I+1;J<N;J++){
9656: L=mcmgrs(G,["get0",[I,J]]);
9657: L=anal2sp(L,"val");
9658: S+=L[1];
9659: }
9660: }
9661: return S/L[0];
9662: }
9663: }
9664: L=[];
9665: if(type(F)!=4) return 0;
9666: if(type(P[0])!=4||length(P[0])==2) P=[P];
9667: for(;P!=[];P=cdr(P)){
9668: if(type(T=(S=car(P))[0])==4){ /* addition */
9669: if((K=P[0][1])!=0){
9670: if(T[0]>T[1]) T=[T[1],T[0]];
9671: T1=[T[0],N];T2=[T[1],N];
9672: T01=cons(0,T1);T02=cons(0,T2);
9673: for(PG=G;PG!=[];PG=cdr(PG)){
9674: R=car(PG);R0=R[0];K1=K2=0;
9675: TP=R0[0];
9676: if(TP==T) K1=K;
9677: else if(TP==T1||TP==T2) K1=-K;
9678: if(length(TP=R0[1])==2){
9679: if(TP==T) K2=K;
9680: else if(TP==T1||TP==T2) K2=-K;
9681: }else{
9682: S=0;
9683: if(findin(T[0],TP)>=0) S++;
9684: if(findin(T[1],TP)>=0) S++;
9685: if(S>0&&TP[2]==N) K2=-K;
9686: else if(S==2) K2=K;
9687: }
9688: R1=anal2sp(cdr(R),["+",K1,K2]);
9689: L=cons(cons(R0,R1),L);
9690: }
9691: G=reverse(L);
9692: }
9693: }else if(length(S)==1){ /* middle convolution */
9694: C=S[0];L=[];
9695: for(I=1;I<=N;I++){
9696: for(J=1;J<=N;J++){
9697: if(I==J) continue;
9698: for(K=J+1;K<=N;K++){ /* [[0,I],[J,K]] */
9699: if(I==K)continue;
9700: T=[[0,I],JK=[J,K]];
9701: if(I==N){
9702: LT=mcmgrs(G,["get0",T]);
9703: G0=mcmgrs(G,["get0",JK]);
9704: L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]);
9705: G0=mcmgrs(G,["get0",[0,J,K]]);
9706: LT=anal2sp(LT,["add",L0]);
9707: L0=anal2sp(G0,["put1",1,0]);
9708: LT=anal2sp(LT,["add",L0]);
9709: for(V=1;V<=N;V++){
9710: if(V==I){
9711: G0=mcmgrs(G,["get0",T]);
9712: L0=anal2sp(G0,["get",1,C]);
9713: }else if(V==J||V==K){
9714: G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]);
9715: L0=anal2sp(G0,["get",1,0]);
9716: }else{
9717: G0=mcmgrs(G,["get0",[[0,V],JK]]);
9718: L0=anal2sp(G0,["get",1,0]);
9719: }
9720: LT=anal2sp(LT,["sub",L0]);
9721: }
9722: LT=anal2sp(LT,["+",-C,0]);
9723: }else if(K==N){
9724: LT=mcmgrs(G,["get0",T]);
9725: LT=anal2sp(LT,["+",C,0]);
9726: G0=mcmgrs(G,["get0",JK]);
9727: L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]);
9728: LT=anal2sp(LT,["add",L0]);
9729: G0=mcmgrs(G,["get0",[0,J,K]]);
9730: L0=anal2sp(G0,[["put1",1,0],["+",0,-C]]);
9731: LT=anal2sp(LT,["add",L0]);
9732: for(V=1;V<=N;V++){
9733: if(V==I){
9734: G0=mcmgrs(G,["get0",T]);
9735: L0=anal2sp(G0,[["get",1,0],["+",C,0]]);
9736: }else if(V==J){
9737: G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]);
9738: L0=anal2sp(G0,[["get",1,0],["+",0,-C]]);
9739: }else if(V==N){
9740: G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]);
9741: L0=anal2sp(G0,[["get",1,C],["+",-C,-C]]);
9742: }else{
9743: G0=mcmgrs(G,["get0",[[0,V],JK]]);
9744: L0=anal2sp(G0,["get",1,0]);
9745: }
9746: LT=anal2sp(LT,["sub",L0]);
9747: }
9748: }else{
9749: G0=mcmgrs(G,["get0",T]);
9750: LT=anal2sp(G0,["+",C,0]);
9751: G0=mcmgrs(G,["get0",JK]);
9752: L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]);
9753: LT=anal2sp(LT,["add",L0]);
9754: G0=mcmgrs(G,["get0",[0,J,K]]);
9755: L0=anal2sp(G0,["put1",1,0]);
9756: LT=anal2sp(LT,["add",L0]);
9757: for(V=1;V<=N;V++){
9758: if(V==I){
9759: G0=mcmgrs(G,["get0",T]);
9760: L0=anal2sp(G0,[["get",1,0],["+",C,0]]);
9761: }else if(V==J||V==K){
9762: G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]);
9763: L0=anal2sp(G0,["get",1,0]);
9764: }else if(V==N){
9765: G0=mcmgrs(G,["get0",[[0,V],JK]]);
9766: L0=anal2sp(G0,[["get",1,C],["+",-C,0]]);
9767: }else{
9768: G0=mcmgrs(G,["get0",[[0,V],JK]]);
9769: L0=anal2sp(G0,["get",1,0]);
9770: }
9771: LT=anal2sp(LT,["sub",L0]);
9772: }
9773: }
9774: LT=anal2sp(LT,0);
9775: L=cons(cons(T,LT),L);
9776: }
9777: T=[[0,I],(I<J)?[0,I,J]:[0,J,I]]; /* [0,I], [0,I,J] */
9778: JK=(I<J)?[I,J]:[J,I];
9779: if(I==N){
9780: G0=mcmgrs(G,["get0",T]);
9781: LT=anal2sp(G0,["+",-C,0]);
9782: G0=mcmgrs(G,["get0",JK]);
9783: L0=anal2sp(G0,[["put1",1,-C],["mult",N-3]]);
9784: LT=anal2sp(LT,["add",L0]);
9785: G0=mcmgrs(G,["get0",T[1]]);
9786: L0=anal2sp(G0,["put1",1,-C]);
9787: LT=anal2sp(LT,["add",L0]);
9788: for(V=1;V<=N;V++){
9789: if(V==J){
9790: G0=mcmgrs(G,["get0",T]);
9791: L0=anal2sp(G0,[["get",1,0],["+",-C,0]]);
9792: }else if(V==N){
9793: G0=mcmgrs(G,["get0",[[0,V],T[1]]]);
9794: L0=anal2sp(G0,[["get",1,C],["+",-C,0]]);
9795: }else{
9796: G0=mcmgrs(G,["get0",[[0,V],JK]]);
9797: L0=anal2sp(G0,[["get",1,0],["+",-C,0]]);
9798: }
9799: LT=anal2sp(LT,["sub",L0]);
9800: }
9801: LT=anal2sp(LT,["+",0,C]);
9802: }else if(J==N){
9803: G0=mcmgrs(G,["get0",T]);
9804: LT=anal2sp(G0,["+",C,0]);
9805: G0=mcmgrs(G,["get0",T[0]]);
9806: L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]);
9807: LT=anal2sp(LT,["add",L0]);
9808: G0=mcmgrs(G,["get0",T[1]]);
9809: L0=anal2sp(G0,["put1",1,0]);
9810: LT=anal2sp(LT,["add",L0]);
9811: for(V=1;V<=N;V++){
9812: if(V==I){
9813: G0=mcmgrs(G,["get0",T]);
9814: L0=anal2sp(G0,[["get",1,0],["+",C,0]]);
9815: }else if(V==N){
9816: G0=mcmgrs(G,["get0",[[0,V],T[1]]]);
9817: L0=anal2sp(G0,[["get",1,C],["+",-C,0]]);
9818: }else{
9819: G0=mcmgrs(G,["get0",[[0,V],JK]]);
9820: L0=anal2sp(G0,["get",1,0]);
9821: }
9822: LT=anal2sp(LT,["sub",L0]);
9823: }
9824: LT=anal2sp(LT,["+",0,-C]);
9825: }else{
9826: G0=mcmgrs(G,["get0",T]);
9827: LT=anal2sp(G0,["+",C,C]);
9828: G0=mcmgrs(G,["get0",JK]);
9829: L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]);
9830: LT=anal2sp(LT,["add",L0]);
9831: G0=mcmgrs(G,["get0",T[1]]);
9832: L0=anal2sp(G0,[["put1",1,0],["+",0,C]]);
9833: LT=anal2sp(LT,["add",L0]);
9834: for(V=1;V<=N;V++){
9835: if(V==I){
9836: G0=mcmgrs(G,["get0",T]);
9837: L0=anal2sp(G0,[["get",1,0],["+",C,C]]);
9838: }else if(V==J){
9839: G0=mcmgrs(G,["get0",[[0,V],T[1]]]);
9840: L0=anal2sp(G0,[["get",1,0],["+",0,C]]);
9841: }else if(V==N){
9842: G0=mcmgrs(G,["get0",[[0,V],JK]]); L0=anal2sp(G0,[["get",1,C],["+",-C,0]]);
9843: }else{
9844: G0=mcmgrs(G,["get0",[[0,V],JK]]);
9845: L0=anal2sp(G0,["get",1,0]);
9846: }
9847: LT=anal2sp(LT,["sub",L0]);
9848: }
9849: }
9850: LT=anal2sp(LT,0);
9851: L=cons(cons(T,LT),L);
9852: }
9853: }
9854: for(G0=G=[];L!=[];L=cdr(L)){
9855: if(length(car(L)[0][1])==2) G0=cons(car(L),G0);
9856: else G=cons(car(L),G);
9857: }
9858: G=append(G0,G);
9859: }else{
9860: if(length(S)==N-1||length(S)==N){ /* [a_1,...,a_{N-1},c] */
9861: for(I=1;I<N;S=cdr(S),I++) G=mcmgrs(G,[[0,I],car(S)]);
9862: if(length(S)==1) G=mcmgrs(G,[S[0]]);
9863: }else return 0;
9864: }
9865: }
9866: return G;
9867: }
9868:
9869:
9870: def delopt(L,S)
9871: {
9872: if((Inv=getopt(inv))!=1) Inv=0;
9873: for(R=[];L!=[];L=cdr(L)){
9874: if(type(car(L))!=4) F=0;
9875: else if(type(S)==4) F=(findin(car(L)[0],S)<0)?0:1;
9876: else F=(car(L)[0]==S)?1:0;
9877: if(F==Inv) R=cons(car(L),R);
9878: }
9879: return reverse(R);
9880: }
9881:
9882: def str_char(S,N,L)
9883: {
9884: if(type(S)==7){
9885: if(type(L)==1) L=asciitostr([L]);
9886: return str_chr(S,N,L);
9887: }
9888: if(type(L)==7) L=strtoascii(L)[0];
9889: if(type(S)==4){
9890: M=N;
9891: while(M-->0) S=cdr(S);
9892: M=findin(L,S);
9893: return (M>=0)?findin(L,S)+N:-1;
9894: }else if(type(S)==5){
9895: K=length(S);
9896: for(I=N;I<K;I++)
9897: if(S[I]==L) return I;
9898: }
9899: return -1;
9900: }
9901:
9902: def str_pair(S,N,I,J)
9903: {
9904: if(type(I)==7) I=(II=strtoascii(I))[0];
9905: if(type(J)==7) J=(JJ=strtoascii(J))[0];
9906: if(type(S)==7) S=strtoascii(S);
9907: if(getopt(inv)==1){
9908: if(II!=0){
9909: I=asciitostr(reverse(II));
9910: IL=length(II);
9911: }else IL=1;
9912: if(JJ!=0) J=asciitostr(reverse(JJ));
9913: R=str_pair(reverse(S),length(S)-N-1,J,I);
9914: if(R>=0) R=length(S)-IL-R;
9915: return R;
9916: }
9917: if((SJIS=getopt(sjis))!=1) SJIS=0;
9918: if((II!=0&&length(II)>1)||(JJ!=0&&length(JJ)>1)){
9919: for(;;){
9920: MJ=str_str(S,N|top=JJ,sjis=SJIS);
9921: if(MJ>=0){
9922: MI=str_str(S,II|top=N,sjis=SJIS);
9923: if(MI<0 || MI>MJ){
9924: if(C==0) return MJ;
9925: C--; N=MJ+length(II);
9926: }else if(MI>=0){
9927: C++; N=MI+length(JJ);
9928: }
9929: }
9930: return -1;
9931: }
9932: }
9933: if(type(S)==4){
9934: M=N;
9935: while(M-->0) S=cdr(S);
9936: while(S!=[]){
9937: if(car(S)==I) C++;
9938: else if(car(S)==J){
9939: if(C==0) return N;
9940: C--;
9941: }
9942: S=cdr(S);N++;
9943: }
9944: }else if(type(S)==5){
9945: K=length(S);
9946: for(T=N;T<K && C>=0;T++){
9947: if(S[T]==I) C++;
9948: else if(S[T]==J){
9949: if(C==0) return T;
9950: C--;
9951: }
9952: }
9953: }
9954: return -1;
9955: }
9956:
9957:
9958: def str_cut(S,I,J)
9959: {
9960: if(type(S)==7) return sub_str(S,I,J);
9961: if((JJ=length(S))<=J) J=JJ-1;
9962: if(type(S)==5){
9963: for(L=[],K=J; K>=I; K--) L=cons(S[K],L);
9964: }else if(type(S)==4){
9965: J-=I;
9966: while(I-->0) S=cdr(S);
9967: for(L=[];J-->=0;S=cdr(S)) L=cons(car(S),L);
9968: L=reverse(L);
9969: }
9970: return asciitostr(L);
9971: }
9972:
9973: def str_str(S,T)
9974: {
9975: if(S==0) return -1;
9976: if(type(S) == 7)
9977: S = strtoascii(S);
9978: if(type(J=getopt(top))!=1 || J<0) J=0;
9979: LS=length(S);
9980: if(LS-J<1) return -1;
9981: if(type(S)==4){
9982: LS-=(J0=J);
9983: for( ; J>0 && S!=[]; S=cdr(S),J--);
9984: }
9985: if(type(JJ=getopt(end))!=1 && JJ!=0) JJ=LS;
9986: else JJ-=J0;
9987: if((SJIS=getopt(sjis))!=1) SJIS=0;
9988: if(JJ-J<0) return -1;
9989: /* search from J-th to JJ-th */
9990: if(type(T)==1) T=[T];
9991: else if(type(T)==7) T = strtoascii(T);
9992: else if(type(T)==4 && type(T[0])>3){
9993: for(K=(KF=-1)-J0; T!=[]; F++,T=cdr(T)){
9994: JK=str_str(S,car(T)|top=J,end=JJ,sjis=SJIS);
9995: if(JK>=0){
9996: JJ=(K=JK)-1; KF=F;
9997: if(J>JJ) break;
9998: }
9999: }
10000: return [KF,J0+K];
10001: }
10002: if(type(T)==4) T=ltov(T);
10003: LT = length(T);
10004: if(LT>0){
10005: LE = LS-LT;
10006: LP = T[0];
10007: if(JJ==0 ||(type(JJ)==1 && JJ<LE)) LE=JJ;
10008: if(type(S)==5){
10009: for(; J <= LE; J++){
10010: if(S[J] != LP){
10011: if(SJIS && (V=S[J])>128){
10012: if(V<160 || (V>223 && V<240)) J++;
10013: }
10014: continue;
10015: }
10016: for(I = 1; I < LT && S[I+J] == T[I]; I++);
10017: if(I >= LT) return J;
10018: }
10019: }else if(type(S)==4){
10020: for(; J<=LE; S=cdr(S),J++){
10021: if(car(S) != LP){
10022: if(SJIS && (V=S[J])>128){
10023: if(V<160 || (V>223 && V<240)) J++;
10024: }
10025: continue;
10026: }
10027: for(ST=cdr(S), I = 1; I < LT && car(ST) == T[I]; I++, ST=cdr(ST));
10028: if(I >= LT) return J0+J;
10029: }
10030: }
10031: }
10032: return -1;
10033: }
10034:
10035: def str_times(S,N)
10036: {
10037: if(!isint(N)) return "";
10038: if(type(S)==7){
10039: for(Tb=str_tb(0,0);N-->0;)
10040: str_tb(S,Tb);
10041: return str_tb(0,Tb);
10042: }
10043: if(type(S)==4){
10044: for(LT=[],I=0;I<N;I++){
10045: if(type(car(S))==7){
10046: LT=cons(car(S),LT);
10047: S=cdr(S);
10048: if(S==[]) S=[[""]];
10049: }else if(type(car(S))==4){
10050: ST=car(S);
10051: for(J=0;I<N;I++){
10052: if(J==length(ST)) J=0;
10053: LT=cons(ST[J++],LT);
10054: }
10055: }
10056: }
10057: return reverse(LT);
10058: }
10059: return S;
10060: }
10061:
10062: def ssubgrs(M,L)
10063: {
10064: if(type(L)==7) L=s2sp(L);
10065: for(S=0, L=L, M=M; L!=[]; L=cdr(L), M=cdr(M)){
10066: for(LT=car(L), MT=car(M); LT!=[]; LT=cdr(LT), MT=cdr(MT)){
10067: S += car(LT)*car(MT)[1];
10068: }
10069: }
10070: return S;
10071: }
10072:
10073: def s2os(S)
10074: {
10075: return str_subst(S,[["\\","\\\\"],["\"","\\\""]],0);
10076: }
10077:
10078: def l2os(S)
10079: {
10080: if(type(S)==6)
10081: S=m2ll(S);
10082: else if(type(S)==5)
10083: S=vtol(S);
10084: else if(type(S)==7) return "\""+s2os(S)+"\"";
10085: else if(type(S)<4) return rtostr(S);
10086: if(type(S)==4){
10087: for(F=0,Tb=str_tb("[",0);S!=[];S=cdr(S)){
10088: if(F++) str_tb(", ",Tb);
10089: str_tb(l2os(car(S)),Tb);
10090: }
10091: str_tb("]",Tb);
10092: return str_tb(0,Tb);
10093: }
10094: return 0;
10095: }
10096:
10097: def r2os(S)
10098: {
10099: if(type(S)==6){
10100: for(T="",S=m2ll(S);S!=[];S=cdr(S)){
10101: if(T!="") T=T+","+r2os(car(S));
10102: else T=r2os(car(S));
10103: }
10104: return "mat("+T+")\n";
10105: }else if(type(S)==5){
10106: for(T="",S=v2l(S);S!=[];S=cdr(S)){
10107: if(T!="") T=T+","+r2os(car(S));
10108: else T=r2os(car(S));
10109: }
10110: return "vect("+T+")\n";
10111: }else if(type(S)<4) return rtostr(S);
10112: else if(type(S)==4){
10113: for(T="";S!=[];S=cdr(S)){
10114: if(T!="") T=T+","+r2os(car(S));
10115: else T=r2os(car(S));
10116: }
10117: return "["+T+"]";
10118: }else if(type(S)==7) return "\""+s2os(S)+"\"";
10119: return "";
10120: }
10121:
10122: def s2euc(S)
10123: {
10124: for(R=[],CR=0,L=strtoascii(S);L!=[];L=cdr(L)){
10125: if((C=car(L)) == 0x1b && length(L)>1) {
10126: if((C=car(L=cdr(L)))==0x24 && length(L)>1){ /* $ */
10127: if((C = car(L=cdr(L))) == 0x40 || C == 0x42) { /* @, B */
10128: Mode = 1;
10129: } else return 0;
10130: }else if(C == 0x28 && length(L)>1) { /* ( */
10131: if((C = car(L=cdr(L)))== 0x42 || C == 0x4a) { /* B, J */
10132: Mode = 0;
10133: }else if(C == 0x49) { /* I */
10134: Mode = 2;
10135: }else{
10136: R=cons(0x1b,R);R=cons(0x28,R);R=cons(C,R);
10137: }
10138: }else if (C == 0x26 && length(L)>1 && car(cdr(L))==0x1b) { /* & ESC */
10139: L=cdr(L);
10140: }else{
10141: R=cons(0x1b,R);R=cons(C,R);
10142: }
10143: }else if(C == 0x0e) {
10144: Mode = 2;
10145: }else if(C == 0x0f) {
10146: Mode = 0;
10147: }else if(Mode == 1 && C>0x20 && C<0x7f && length(L)>1) { /* JIS KANJI */
10148: D=car(L=cdr(L));
10149: if(D>0x20 && D<0x7f) {
10150: R=cons(ior(C,0x80),R);R=cons(ior(D,0x80),R);
10151: } else return 0;
10152: }else if(Mode == 2 && C > 0x1f && C < 0x60) { /* JIS KANA */
10153: R=cons(0x8e,R); R=cons(ior(C,0x80),R);
10154: }else if(((C>0x80 && C<0xa0) || (C>0xdf && C<0xf0)) && length(L)>1) { /* ShiftJIS */
10155: D=car(L=cdr(L));
10156: if(D>0x3f && D<0xfd && D!=0x7f) {
10157: T=sjis2jis([C,D]);
10158: R=cons(ior(T[0],0x80),R); R=cons(ior(T[1],0x80),R);
10159: }else return 0;
10160: }else if(C>0x9f && C<0xe0) { /* HanKana */
10161: R=cons(0x8e,R); R=cons(C,R);
10162: }else if(C == 0x0a){
10163: CR++;
10164: }else if(C == 0x0d){
10165: R=cons(0x0d,R);
10166: CR=0;
10167: }else{
10168: while(CR-->0) R=cons(0x0d,R);
10169: R=cons(C,R);
10170: }
10171: }
10172: while(CR-->0) R=cons(0x0d,R);
10173: return asciitostr(reverse(R));
10174: }
10175:
10176: def s2sjis(S)
10177: {
10178: for(R=[],CR=0,L=strtoascii(S);L!=[];L=cdr(L)){
10179: if((C=car(L)) == 0x1b && length(L)>1) {
10180: if((C=car(L=cdr(L)))==0x24 && length(L)>1){ /* $ */
10181: if((C = car(L=cdr(L))) == 0x40 || C == 0x42) { /* @, B */
10182: Mode = 1;
10183: } else return 0;
10184: }else if(C == 0x28 && length(L)>1) { /* ( */
10185: if((C = car(L=cdr(L)))== 0x42 || C == 0x4a) { /* B, J */
10186: Mode = 0;
10187: }else if(C == 0x49) { /* I */
10188: Mode = 2;
10189: }else{
10190: R=cons(0x1b,R);R=cons(0x28,R);R=cons(C,R);
10191: }
10192: }else if (C == 0x26 && length(L)>1 && car(cdr(L))==0x1b) { /* & ESC */
10193: L=cdr(L);
10194: }else{
10195: R=cons(0x1b,R);R=cons(C,R);
10196: }
10197: }else if(C == 0x0e) {
10198: Mode = 2;
10199: }else if(C == 0x0f) {
10200: Mode = 0;
10201: }else if(Mode == 1 && C>0x20 && C<0x7f && length(L)>1) { /* JIS KANJI */
10202: D=car(L=cdr(L));
10203: if(D>0x20 && D<0x7f) {
10204: T=jis2sjis([C,D]);
10205: R=cons(T[0],R);R=cons(T[1],R);
10206: } else return 0;
10207: }else if(Mode == 2 && C > 0x1f && C < 0x60) { /* JIS KANA */
10208: R=cons(ior(C,0x80),R);
10209: }else if(C>0xa0 && C<0xff && length(L)>1) { /* EUC */
10210: D=car(L=cdr(L));
10211: if(D>0xa0 && D<0xff) {
10212: T=jis2sjis([iand(C,0x7f),iand(D,0x7f)]);
10213: R=cons(T[0],R);R=cons(T[1],R);
10214: }else return 0;
10215: }else if(C == 0x0a){
10216: CR++;
10217: }else if(C == 0x0d){
10218: R=cons(0x0a,R);R=cons(0x0d,R);
10219: CR=0;
10220: }else{
10221: while(CR-->0){
10222: R=cons(0x0a,R);R=cons(0x0d,R);
10223: }
10224: R=cons(C,R);
10225: }
10226: }
10227: while(CR-->0){
10228: R=cons(0x0a,R);R=cons(0x0d,R);
10229: }
10230: return asciitostr(reverse(R));
10231: }
10232:
10233: def r2ma(S)
10234: {
10235: return evalma(S|inv=1);
10236: }
10237:
10238: def evalma(S)
10239: {
10240: L0=["\n","\d","{","}","[","]","Log","Exp","Sinh","Cosh","Tanh","Sin","Cos","Tan",
10241: "ArcSin","ArcCos","ArcTan"];
10242: L1=["", "" ,"[","]","(",")","log","exp","sinh","cosh","tanh","sin","cos","tan",
10243: "asin", "acos", "atan"];
10244: if(getopt(inv)==1){
10245: if(type(S)==6) S=m2ll(S);
10246: else if(type(S)==5) S=vtol(S);
10247: if(type(S)==4){
10248: for(L=[];S!=[];S=cdr(S)){
10249: if(type(car(S))==6) L=cons(m2ll(car(S)),L);
10250: else if(type(car(S))==5) L=cons(vtol(car(S)),L);
10251: else L=cons(car(S),L);
10252: }
10253: S=reverse(L);
10254: }else return 0;
10255: return str_subst(rtostr(S),cdr(cdr(L1)),cdr(cdr(L0)));
10256: }
10257: if(S==0){
10258: print("Mathematica text (terminated by ;) ?");
10259: purge_stdin();
10260: Tb=str_tb(0,0);
10261: for(;;){
10262: S=get_line();
10263: str_tb(S,Tb);
10264: if(str_char(S,0,";")>=0) break;
10265: }
10266: S=str_tb(0,Tb);
10267: }
10268: /*
10269: while((P=str_chr(S,0,";"))>=0){
10270: V0=evalma(str_cut(S,0,P+1));
10271: S=str_cut(S,P+1,length(S));
10272: }
10273: if((P=str_char(S,0,"="))>=0){
10274: X=strtoascii(str_cut(S,0,P));
10275: L=length(X);
10276: for(P0=P1=-1,I=0;I<L;I++){
10277: if(L(I)<=32) continue;
10278: if(isalphanum(L[I])){
10279: if(P0<0){
10280: if(isnum(L[I])) break;
10281: P0=I;
10282: }
10283: else if(P1!=I+1) break;
10284: P1=I;
10285: }
10286: }
10287: if(I==L && P0>=0){
10288: for(I==P0;I-->0;) X=cdr(X);
10289: if((X0=car(X))>96) X0-=32;
10290: Y=[X0];X=cdr(X);
10291: for(I=P1-P0;I-->0;X=cdr(X))
10292: Y=cons(car(X),Y);
10293: Y=cons(61,Y);
10294: Var=asciitostr(reverse(Y));
10295: S=str_cut(S,P,length(S));
10296: }
10297: }
10298: */
10299: S=eval_str(str_subst(S,L0,L1));
10300: if(type(S)==4){
10301: for(L=-1,T=S;T!=[];T=cdr(T)){
10302: if(type(T0=car(T))>4) break;
10303: if(type(T0)<4){
10304: if(L>=0) break;
10305: L=-2;continue;
10306: }
10307: if(L<-2) break;
10308: if(L==-1) L=length(T0);
10309: else if(L!=length(T0)) break;
10310: }
10311: if(T==[]){
10312: if(L>0) S=s2m(S);
10313: else S=ltov(S);
10314: }
10315: }
10316: /*
10317: if(S==0 && V0!=0) return V0;
10318: if(type(Var)==7){
10319: T=rtostr(S);
10320: if(type(S)==7) T="\""+T+"\"";
10321: S=eval_str(Var+T);
10322: mycat(["Define",Var]);
10323: }
10324: */
10325: return S;
10326: }
10327:
10328: def i2hex(N)
10329: {
10330: Opt=getopt();
10331: if(type(N)==4 && isint(car(N))){
10332: #ifdef USEMODULE
10333: L=mtransbys(os_md.i2hex,N,[]|option_list=Opt);
10334: #else
10335: L=mtransbys(i2hex,N,[]|option_list=Opt);
10336: #endif
10337: return rtostr(L);
10338: }
10339: if(!isint(N) || N<0) return 0;
10340: if(!N) L=[];
10341: else{
10342: Cap=(getopt(cap)==1)?32:0;
10343: for(L=[];N!=0;N=ishift(N,4)){
10344: J=iand(N,15);
10345: L=cons(((J>9)?(87-Cap):48)+J,L);
10346: }
10347: }
10348: if(!isint(Min=getopt(min))) Min=2;
10349: for(Min-=length(L);Min-->0;)
10350: L=cons(48,L);
10351: if(getopt(num)==1){
10352: L=cons(120,L);L=cons(48,L);
10353: }
10354: return asciitostr(L);
10355: }
10356:
10357: def sjis2jis(L)
10358: {
10359: L1=L[1];
10360: if((L0=L[0])<=0x9f){
10361: if(L1<0x9f) L0=L0*2-0xe1;
10362: else L0=(L0*2)-0xe0;
10363: }else{
10364: if(L1<0x9f) L0=L0*2-0x161;
10365: else L0=L0*2-0x160;
10366: }
10367: if(L1<0x7f) return [L0,L1-0x1f];
10368: else if(L1<0x9f) return [L0,L1-0x20];
10369: return [L0,L1-0x7e];
10370: }
10371:
10372: def jis2sjis(L)
10373: {
10374: L1=L[1];
10375: if(iand(L0=L[0],1)){
10376: if(L1<0x60) L=[L1+0x1f];
10377: else L=[L1+0x20];
10378: }else L=[L1+0x7e];
10379: if(L0<0x5f) return cons(ishift(L0+0xe1,1),L);
10380: return cons(ishift(L0+0x161,1),L);
10381: }
10382:
10383: def verb_tex_form(P)
10384: {
10385: L = reverse(strtoascii(rtostr(P)));
10386: for(SS = []; L != []; L = cdr(L)){
10387: Ch = car(L); /* ^~\{} */
10388: if(Ch == 92 || Ch == 94 || Ch == 123 || Ch == 125 || Ch == 126){
10389: SS = append([92,Ch,123,125],SS); /* \Ch{} */
10390: if(Ch != 94 && Ch != 126) /* \char` */
10391: SS = append([92,99,104,97,114,96],SS);
10392: continue;
10393: }
10394: SS = cons(Ch, SS);
10395: if((Ch >= 35 && Ch <= 38) || Ch == 95) /* #$%&_ */
10396: SS = cons(92, SS); /* \Ch */
10397: }
10398: return asciitostr(SS);
10399: }
10400:
10401: def tex_cuteq(S,P)
10402: {
10403: if(P==0) return 0;
10404: if(S[P]==125){ /* } */
10405: if((Q=str_pair(S,P-1,"{","}"|inv=1))<0) return -1;
10406: if(Q<2||S[Q-1]!=95) return Q;
10407: return tex_cuteq(S,Q-2);
10408: }
10409: if(!isalphanum(S[Q=P--])) return -1;
10410: while(P>0&&isalphanum(S[P])) P--;
10411: if(S[P]==92){ /* \ */
10412: if(P==0) return P;
10413: else P--;
10414: }
10415: if(S[P]!=95||P==0) return Q; /* _ */
10416: return tex_cuteq(S,P-1);
10417: }
10418:
10419:
10420: def texket(S)
10421: {
10422: if(!isint(F=getopt(all))) F=0;
10423: if(type(S)==7){
10424: L=str_len(S);
10425: SS=strtoascii(S);
10426: }else{
10427: L=length(S);
10428: SS=S;
10429: }
10430: for(T="",I=I0=0;I<L-1;){
10431: J=str_char(SS,I,"(");
10432: if(J<0) break;
10433: if(J<L-1 && J>4 && str_str(SS,"\\left"|top=J-5,end=J-1)>=0){
10434: I=J+1;continue;
10435: }
10436: if((K=str_pair(SS,J+1,"(",")"))>=0){
10437: KK=str_char(SS,J+2,"(");
10438: if(KK>K||KK<0){
10439: if(F!=1){
10440: if(!F){
10441: for(N=J+1;N<K;N++) /* + - _ { } */
10442: if(!isalphanum(P=SS[N])&&findin(P,[32,43,45,95,123,125])<0) break;
10443: }else N=K;
10444: if(N==K){
10445: I=K+1;continue;
10446: }
10447: }
10448: T=T+str_cut(SS,I0,J-1)+"\\left"+str_cut(SS,J,K-1)+"\\right)";
10449: I0=I=K+1;
10450: }else{
10451: T=T+str_cut(SS,I0,J-1)+"\\left("+texket(str_cut(SS,J+1,K-1)|all=F) +"\\right)";
10452: I0=I=K+1;
10453: }
10454: }else break;
10455: }
10456: return T+str_cut(SS,I0,L);
10457: }
10458:
10459:
10460: def my_tex_form(S)
10461: {
10462: if(getopt(skip) != 1){
10463: if(type(S)==1 && S<0) return "-"+print_tex_form(-S);
10464: if(type(S)==6) return mtotex(S);
10465: S = print_tex_form(S);
10466: for(F=Top=0;(L=str_str(S,"\\verb`"|top=Top))>=0;Top=LV+1){
10467: F++;
10468: if(Top==0) Tb = string_to_tb("");
10469: LV = str_chr(S, L+6, "`");
10470: if(LV<0) LV=str_len(S);
10471: str_tb([my_tex_form(sub_str(S, Top, L-1)|skip=1), "\\texttt{"], Tb);
10472: str_tb([verb_tex_form(sub_str(S,L+6, LV-1)),"}"], Tb);
10473: Top=LV+1;
10474: }
10475: if(F>0){
10476: str_tb(my_tex_form(sub_str(S, Top,str_len(S)-1)|skip=1), Tb);
10477: return tb_to_string(Tb);
10478: }
10479: }
10480: if(S==0) return "";
10481: S = ltov(strtoascii(S));
10482: L = length(S)-1;
10483: while(L >= 1 && S[L] == 10)
10484: L--;
10485: if((Fr=getopt(frac))!=0 && Fr!=1) Fr=2;
10486: for(I = L+1, T = K = 0, SS = []; --I >= 0; ){
10487: if(S[I] == 32 && I!=L){
10488: if(I==L) continue;
10489: if(findin(S[I+1], [32,40,41,43,45,123,125]) >= 0 /* " ()+-{}" */
10490: || (S[I+1] >= 49 && S[I+1] <= 57)) /* 1 - 9 */
10491: if(I == 0 || S[I-1] >= 32) continue;
10492: }
10493: if(Fr && S[I]>=48 && S[I]<=57){ /* 2/3 -> \tfrac{2}{3} */
10494: for(K=0,II=I; II>=0; II--){
10495: if(S[II]>=48 && S[II]<=57) continue;
10496: if(S[II]==47){ /* / */
10497: if(K>0) break;
10498: K=II;
10499: }else break;
10500: }
10501: if(K>II+1){
10502: SS=cons(125,SS);
10503: for(J=I; J>K; J--) SS=cons(S[J],SS);
10504: if(AMSTeX){
10505: SS=cons(123,SS);SS=cons(125,SS);
10506: }else{
10507: for(J=[114,101,118,111,92];J!=[];J=cdr(J)) /* \over */
10508: SS=cons(car(J),SS);
10509: }
10510: for(J=K-1;J>II;J--) SS=cons(S[J],SS);
10511: SS=cons(123,SS);
10512: if(AMSTeX){
10513: J=(Fr==2)?[99,97,114,102,116,92]:[99,97,114,102,92];
10514: for(;J!=[];J=cdr(J)) /* \tfrac */
10515: SS=cons(car(J),SS);
10516: }
10517: I=II+1;
10518: }else{
10519: for(;I>II;I--) SS = cons(S[I], SS);
10520: I++;
10521: }
10522: continue;
10523: }
10524: SS = cons(S[I], SS);
10525: }
10526: SS=str_subst(SS,"\\\\\n\\end{pmatrix}","\n\\end{pmatrix}"|raw=1);
10527: Subst=getopt(subst);
10528: Sub0=["{asin}","{acos}","{atan}"];
10529: Sub1=["\\arcsin ","\\arccos","\\arctan "];
10530: if(type(Subst) == 4){
10531: Sub0=append(Sub0,Subst[0]);Sub1=append(Sub1,Subst[1]);
10532: }
10533: SS = str_subst(SS,Sub0,Sub1|raw=1);
10534: S = ltov(SS);
10535: L = length(S);
10536: SS = [];
10537: while(--L >= 0){
10538: if(S[I=L] == 125){
10539: while(--I >= 0 && S[I] == 125);
10540: J = 2*I - L;
10541: if(J >= 0 && S[I] != 123){
10542: for(K = J; K < I && S[K] == 123; K++);
10543: if(K == I){
10544: if(J-- <= 0 || S[J] < 65 || S[J] > 122 || (S[J] > 90 && S[J] < 97)){
10545: SS = cons(S[I],SS);
10546: L = J+1;
10547: continue;
10548: }
10549: }
10550: }
10551: }
10552: SS = cons(S[L],SS);
10553: }
10554: RT=getopt(root);
10555: for(Top=0;;Top++){ /* ((x+1))^{y} , 1/y=2,3,...,9 */
10556: #if 1
10557: P=str_str(SS,["))^","^{\\tfrac{1}"]|top=Top);
10558: if(P[0]<0) break;
10559: Sq=0;
10560: if(P[0]==0){
10561: P=P[1];
10562: if((Q=str_pair(SS,P,"(",")"|inv=1))<0||SS[Q+1]!=40) continue;
10563: if((RT==2||(RT!=0 && P-Q<33)) && str_str(SS,"{\\tfrac{1}"|top=P+3,end=P+3)==P+3
10564: && SS[P+14]==125){
10565: if((Sq=SS[P+13]-48)<2||Sq>9) Sq=0;
10566: }
10567: F=2;
10568: }else{
10569: P=P[1];
10570: if(SS[P+12]!=125||(Sq=(SS[P+11]-48))<2||Sq>9) break;
10571: if(SS[P-1]==125){
10572: if((Q=str_pair(SS,P-2,"{","}"|inv=1))<0) break;
10573: if(Q>1&&SS[Q-1]==95){
10574: if((Q=tex_cuteq(SS,Q-2))<0) break;
10575: F=0;
10576: }else F=1;
10577: }else{
10578: if(!isalphanum(SS[Q=P-1]) || (Q=tex_cuteq(SS,Q))<0) break;
10579: F=0;
10580: }
10581: if(RT!=2&&P-Q>32) break;
10582: }
10583: #else
10584: if((P=str_str(SS,"))^"|top=Top))<0 || (Q=str_pair(SS,P,"(",")"|inv=1))<0) break;
10585: else F=2;
10586: Sq=0;
10587: if((RT==2||(RT!=0 && P-Q<33)) && str_str(SS,"{\\tfrac{1}"|top=P+3,end=P+3)==P+3
10588: && SS[P+14]==125){
10589: if((Sq=SS[P+13]-48)<2||Sq>9) Sq=0;
10590: }
10591: #endif
10592: for(I=0,S=[];SS!=[];SS=cdr(SS),I++){
10593: if(I==Q){
10594: if(Sq){
10595: S=append([116,114,113,115,92],S);
10596: if(Sq>2) S=append([93,Sq+48,91],S);
10597: S=cons(123,S);
10598: if(F==2) SS=cdr(SS);
10599: else if(F==0) S=cons(car(SS),S);
10600: }else if(F==2&&P-Q==3){ /* (2)^x -> 2^x*/
10601: SS=cdr(SS);SS=cdr(SS);
10602: S=cons(123,S);S=cons(car(SS),S);S=cons(125,S);
10603: SS=cdr(SS);SS=cdr(SS);
10604: I+=3;
10605: }
10606: continue;
10607: }else if(I==P){
10608: if(Sq){
10609: if(F>0) S=cdr(S);
10610: S=cons(125,S);
10611: if(F==2) SS=cdr(SS);
10612: for(J=0;J<12;J++) SS=cdr(SS);
10613: }
10614: continue;
10615: }
10616: S=cons(car(SS),S);
10617: }
10618: SS=reverse(S);
10619: Top=P;
10620: }
10621: S=asciitostr(SS);
10622: if((K=getopt(ket))==1) S=texket(S);
10623: else if(K==2) S=texket(S|all=1);
10624: return S;
10625: }
10626:
10627: def smallmattex(S)
10628: {
10629: return str_subst(S,[["\\begin{pmatrix}","\\left(\\begin{smallmatrix}"],
10630: ["\\end{pmatrix}","\\end{smallmatrix}\\right)"],
10631: ["\\begin{Bmatrix}","\\left\\{\\begin{smallmatrix}"],
10632: ["\\end{Bmatrix}","\\end{smallmatrix}\\right\\}"],
10633: ["\\begin{bmatrix}","\\left[{\\begin{smallmatrix}"],
10634: ["\\end{bmatrix}","\\end{smallmatrix}\\right]"],
10635: ["\\begin{vmatrix}","\\left|\\begin{smallmatrix}"],
10636: ["\\end{vmatrix}","\\end{smallmatrix}\\right|"],
10637: ["\\begin{Vmatrix}","\\left\\|\\begin{smallmatrix}"],
10638: ["\\end{Vmatrix}","\\end{smallmatrix}\\right\\|"],
10639: ["\\begin{matrix}","\\begin{smallmatrix}"],
10640: ["\\end{matrix}","\\end{smallmatrix}"]],0);
10641: }
10642:
10643:
10644: def divmattex(S,T)
10645: {
10646: TF=["matrix","pmatrix","Bmatrix","bmatrix","vmatrix","Vmatrix"];
10647: TG=[0,"(","\\{","[","|","\\|"];
10648: TH=[0,")","\\}","]","|","\\|"];
10649: if(type(S)!=7) S=mtotex(S);
10650: S=strtoascii(S0=S);
10651: if((P0=str_str(S,"\\begin{"))<0 || (P1=str_str(S,"}"|top=P0+7))<0)
10652: return S0;
10653: F=str_cut(S,P0+7,P1-1);
10654: if((K=findin(F,TF))<0) return S0;
10655: Q=str_str(S,"\\end{"+F+"}");
10656: if(Q<0) return S0;
10657: for(J=P1+1;S[J]<33;J++);
10658: for(L0=L=[],I=J;J<Q;J++){
10659: if(S[J]==38){ /* & */
10660: if(I>=J) L0=cons(0,L0);
10661: else L0=cons(str_cut(S,I,J-1),L0);
10662: I=J+1;
10663: }
10664: if(S[J]==92&&S[J+1]==92){ /* \\ */
10665: if(I>=J) L0=cons(0,L0);
10666: else L0=cons(str_cut(S,I,J-1),L0);
10667: L=cons(reverse(L0),L);
10668: L0=[];
10669: J++;
10670: for(I=J+1;S[I]<33;I++);
10671: }
10672: }
10673: J--;
10674: if(S[J]<33) J--;
10675: if(I<=J) L0=cons(str_cut(S,I,J),L0);
10676: if(length(L0)>0) L=cons(reverse(L0),L);
10677: L=lv2m(reverse(L)); /* get matrix */
10678: if(T==0) return L;
1.26 takayama 10679: if(type(T)==1) T=[T];
1.6 takayama 10680: Size=size(L);S0=Size[0];
10681: if(type(T[0])!=4){
10682: S1=Size[1];
10683: T=append(T,[S1]);
10684: for(TT=[],I=0;T!=[];T=cdr(T)){
10685: J=car(T);
10686: if(J>S1) J=S1;
10687: for(T0=[];J>I;J--) T0=cons(J-1,T0);
10688: if(T0!=[]) TT=cons(T0,TT);
10689: I=car(T);
10690: }
10691: T=reverse(TT);
10692: }
10693: SS=length(T);
10694: St=str_tb(0,0);
10695: if(SS==1) St=str_tb("\\begin{"+F+"}\n",St);
10696: else{
10697: if(K>0) St=str_tb("&\\left"+TG[K],St);
10698: St=str_tb("\\begin{matrix}\n",St);
10699: }
10700: for(;T!=[];T=cdr(T)){
10701: for(I=0;I<S0;I++){
10702: for(J=0,TT=car(T);TT!=[];TT=cdr(TT),J++){
10703: if(J>0) St=str_tb("&",St);
10704: if(L[I][car(TT)]!=0) St=str_tb(L[I][car(TT)],St);
10705: }
10706: if(I<S0-1) St=str_tb("\\\\",St);
10707: St=str_tb("\n",St);
10708: }
10709: if(length(T)>1)
10710: St=str_tb("\\end{matrix}\\right.\\\\\n&\\quad\\left.\\begin{matrix}\n",St);
10711: else{
10712: if(SS==1) St=str_tb("\\end{"+F+"}\n",St);
10713: else St=str_tb("\\end{matrix}\\right"+TH[K]+"\n",St);
10714: }
10715: }
10716: S=str_tb(0,St);
10717: if(SS==1) return S;
10718: return texbegin("align*",S);
10719: }
10720:
10721: def str_subst(S, L0, L1)
10722: {
10723: if(type(S) == 7)
10724: S = strtoascii(S);
10725: if(type(S) == 4)
10726: S = ltov(S);
10727: SE = length(S);
10728: if(L1 == 0){
10729: for(L1 = L = [], L0 = reverse(L0); L0 != []; L0 = cdr(L0)){
10730: L = cons(car(L0)[0], L);
10731: L1 = cons(car(L0)[1], L1);
10732: }
10733: L0 = L;
10734: }
10735: if(type(L0)==7) L0 = [strtoascii(L0)];
10736: else{
10737: for(LT = []; L0 != []; L0 = cdr(L0))
10738: LT = cons(strtoascii(car(L0)), LT);
10739: L0 = ltov(LT);
10740: }
10741: E0 = length(L0);
10742: if(type(L1)==7) L1 = [strtoascii(L1)];
10743: else{
10744: for(LT = []; L1 != []; L1 = cdr(L1))
10745: LT = cons(strtoascii(car(L1)), LT);
10746: L1 = ltov(LT);
10747: }
10748: if(getopt(inv)==1){
10749: L2=L0;L0=L1;L0=L2;
10750: }
10751: if((SJIS=getopt(sjis))!=1) SJIS=0;
10752: for(J = JJ = 0, ST = []; J < SE; J++){
10753: SP = S[J];
10754: for(I = E0-1; I >= 0; I--){
10755: if(SP != L0[I][0] || J + (K = length(L0[I])) > SE)
10756: continue;
10757: while(--K >= 1)
10758: if(L0[I][K] != S[J+K]) break;
10759: if(K > 0) continue;
10760: for(KE = length(L1[I]), K = 0 ;K < KE; K++)
10761: ST = cons(L1[I][K],ST);
10762: J += length(L0[I])-1;
10763: break;
10764: }
10765: if(I < 0){
10766: ST = cons(S[J],ST);
10767: if(SJIS && (V=S[J])>128){
10768: if(V<160 || (V>223 && V<240)) ST = cons(S[J++],ST);
10769: }
10770: }
10771: }
10772: if(getopt(raw)==1) return reverse(ST);
10773: return asciitostr(reverse(ST));
10774: }
10775:
10776: def dviout0(L)
10777: {
10778: Cmd=["TikZ","TeXLim","TeXEq","DVIOUT","XYPrec","XYcm","XYLim","Canvas"];
10779: if(type(Opt=getopt(opt))==7){
10780: if((F=findin(Opt,Cmd)) < 0) return -1;
10781: if(L==-1){
10782: if(F<=3){
10783: if(F==0) V=TikZ;
10784: else if(F==1) V=TeXLim;
10785: else if(F==2) V=TeXEq;
10786: else V=iand(DVIOUTF,1);
10787: }else{
10788: if(F==4) V=XYPrec;
10789: else if(F==5) V=XYcm;
10790: else if(F==6) V=XYLim;
10791: else V=Canvas;
10792: }
10793: return V;
10794: }
10795: if(F==0) TikZ=L;
10796: else if(F==2) TeXEq=L;
10797: else if(F==3){
10798: if(iand(DVIOUTF,1)==L)
10799: mycat0(["DVIOUTA=\"", DVIOUTA,"\""],1);
10800: else dviout0(4);
10801: return 1;
10802: }else if(F==7&&type(L)==4)
10803: Canvas=L;
10804: else if(L>0){
10805: if(F==1) TeXLim=L;
10806: else if(F==4) XYPrec=L;
10807: else if(F==5) XYcm=L;
10808: else if(F==6) XYLim=L;
10809: }
10810: mycat0([Cmd[F],"=",L],1);
10811: return 1;
10812: }
10813: if(type(L) == 4){
10814: for( ; L != []; L = cdr(L)) dviout0(car(L));
10815: return 1;
10816: }
10817: if(type(L) == 7){
10818: if(L=="") dviout(" \n"|keep=1);
10819: else if(L=="cls") dviout0(0);
10820: else if(L=="show") dviout(" ");
10821: else if(L=="?") dviout0(3);
10822: else dviout("\\"+L+"\n"|keep=1);
10823: return 1;
10824: }
10825: if(L == 0)
10826: dviout(" "|keep=1,clear=1);
10827: else if(L == 1)
10828: dviout(" ");
10829: else if(L == 2)
10830: dviout(" "|clear=1);
10831: else if(L>10)
10832: dviout("\\setcounter{MaxMatrixCols}{"+rtostr(L)+"}%"|keep=1);
10833: else if(L < 0)
10834: dviout(" "|delete=-L,keep=1);
10835: else if(L == 3){
10836: mycat0(["DIROUT =\"", DIROUT,"\""],1);
10837: mycat0(["DVIOUTH=\"", DVIOUTH,"\""],1);
10838: mycat0(["DVIOUTA=\"", DVIOUTA,"\""],1);
10839: mycat0(["DVIOUTB=\"", DVIOUTB,"\""],1);
10840: mycat0(["DVIOUTL=\"", DVIOUTL,"\""],1);
10841: mycat(["Canvas =", Canvas]);
10842: mycat(["TeXLim =", TeXLim]);
10843: mycat(["TeXEq =", TeXEq]);
10844: mycat(["AMSTeX =", AMSTeX]);
10845: mycat(["TikZ =", TikZ]);
10846: mycat(["XYPrec =", XYPrec]);
10847: mycat(["XYcm =", XYcm]);
10848: mycat(["XYLim =", XYLim]);
10849: }else if(L==4){
10850: Tmp=DVIOUTA; DVIOUTA=DVIOUTB; DVIOUTB=Tmp;
10851: mycat0(["DVIOUTA=\"", DVIOUTA,"\""],1);
10852: DVIOUTF++;
10853: }else if(L==5){
10854: if(!iand(DVIOUTF,1)) dviout0(4);
10855: }else if(L==6){
10856: TikZ=1;mycat("TikZ=1");
10857: }else if(L==7){
10858: TikZ=0;mycat("TikZ=0");
10859: }
10860: return 1;
10861: }
10862:
10863: def myhelp(T)
10864: {
10865: /* extern DVIOUT; */
10866: /* extern HDVI; */
10867: /* extern DVIOUTH; */
10868:
10869: if(type(T)==2){
10870: if(T==getbygrs){
10871: getbygrs(0,0);
10872: return 0;
10873: }
10874: else if(T==m2mc){
10875: m2mc(0,0);
10876: return 0;
10877: }
10878: else if(T==mgen){
10879: mgen(0,0,0,0);
10880: return 0;
10881: }
10882: else T=rtostr(T);
10883: }
10884: if(type(T)==4 && typeT[0]==7){
10885: if(length(T)==2 && type(T[1])==1){
10886: DVIOUTH="start "+T[0]+" -"+rtostr(T[1])+"-hyper:0x90 \"%ASIRROOT%\\help\\os_muldif.dvi\" #r:%LABEL%";
10887: }else if(str_len(T[0])>2) DVIOUTH=T[0];
10888: mycat(["DVIOUTH="+DVIOUTH,"\nmyhelp(fn) is set!"]);
10889: return 0;
10890: }
10891: if(T==0){
10892: mycat([
10893: "myhelp(t) : show help\n",
10894: #ifdef USEMODULE
10895: " t : -1 (dvi), 1 (pdf) or os_md.getbygrs, os_md.m2mc, os_md.mgen\n",
10896: #else
10897: " t : -1 (dvi), 1 (pdf) or getbygrs, m2mc, mgen\n",
10898: #endif
10899: " \"fn\" : Help of the function fn\n",
10900: " [path,n] : path of dviout, n = # dviout\n",
10901: " [DVIOUTH] : Way to jump to the help of a function\n",
10902: " default: start dviout -2 \"%ASIRTOOT%\\help\\os_muldif.dvi\" #r:%LABEL%"
10903: ]);
10904: return 0;
10905: }
10906: if(type(T)==7){
10907: if(str_str(T,"os_md.")==0) T=str_cut(T,6,str_len(T)-1);
10908: Dr=str_subst(DVIOUTH,["%ASIRROOT%","%LABEL%"],[get_rootdir(),"r:"+str_subst(T,"_","")]);
10909: shell(Dr);
10910: return 0;
10911: }
10912: Dr=get_rootdir();
10913: if(T==-1) Dr+="\\help\\os_muldif.dvi";
10914: else Dr+="\\help\\os_muldif.pdf";
10915: if(!isMs()) Dr=str_subst(Dr,"\\","/");
10916: shell(Dr);
10917: return 0;
10918: }
10919:
10920: def isMs()
10921: {
10922: if(type(Tmp=getenv("TEMP"))!=7) {
10923: if (type(Tmp=getenv("TMP")) != 7) Tmp=getenv("HOME");
10924: }
10925: if(type(Tmp)==7 && str_chr(Tmp,0,"\\")==2) return 1;
10926: else return 0;
10927: }
10928:
10929: def tocsv(L)
10930: {
10931: if(type(L)==6) L=m2ll(L);
10932: else if(type(L)==5) L=vtol(L);
10933: Null=getopt(null);
10934: Tb=str_tb(0,0);
10935: for(LL=L; LL!=[]; LL=cdr(LL)){
10936: LT=car(LL);
10937: if(type(LT)==5) LT=vtol(LT);
10938: if(type(LT)<4) LT=[LT];
10939: for(N=0; LT!=[]; LT=cdr(LT),N++){
10940: if(N) str_tb(", ",Tb);
10941: if((T=car(LT))==Null) continue;
10942: if(type(T)==7){
10943: K=str_len(T);
10944: T=str_subst(T,["\""],["\"\""]);
10945: if(str_len(T)>K||str_char(T,0,",")>=0) T="\""+T+"\"";
10946: str_tb(T,Tb);
10947: }else str_tb(rtostr(T),Tb);
10948: }
10949: str_tb("\n",Tb);
10950: }
1.16 takayama 10951: S=str_tb(0,Tb);
10952: if(type(EXE=getopt(exe))!=1&&EXE!=0&&type(EXE)!=7) return S;
10953: if(type(F)!=7){
1.18 takayama 10954: fcat(-1,0);
1.16 takayama 10955: F="risaout";
10956: if(EXE>=2&&EXE<=9) F+=rtostr(EXE);
10957: F=DIROUTD+F+".csv";
10958: }else F=S;
10959: if(EXE!=0 && access(F)) remove_file(F);
10960: fcat(F,S|exe=1);
10961: return 1;
1.6 takayama 10962: }
10963:
10964: def readcsv(F)
10965: {
10966: if((ID=open_file(F))<0) return -1;
10967: SJIS=isMs();
10968: L=[];
10969: if(type(V=getopt(eval))!=4){
10970: if(V=="all") V=1;
10971: else if(type(V)==1) V=[V];
10972: else V=[];
10973: }
1.9 takayama 10974: Eq=getopt(eq);
1.6 takayama 10975: Sp=getopt(sp);
10976: if(type(T=getopt(col))!=1) T=0;
10977: Null=getopt(null);
1.9 takayama 10978: if(type(Null)<0) Null=(Eq==1)?0:"";
1.6 takayama 10979: while((S=get_line(ID))!=0){
10980: S=strtoascii(S);
10981: N=length(S);
10982: for(I=J=F=0,LL=LT=[];I<N;I++){
10983: C=S[I];
10984: if(F==0){
10985: if(C<=32) continue;
10986: if(C==34){F=2;continue;}
10987: F=1;
10988: }
10989: if(F==2 && C==34){
10990: if(I<N-1&& S[I+1]==34){
10991: LT=cons(34,LT);I++;continue;
10992: }
10993: F=-2;
10994: }
10995: if(F==1){
10996: if((C==44&&Sp!=1)||(C<=32&&Sp==1)) F=-1;
10997: else if(C<32 && C!=9) continue;
10998: }
10999: if(SJIS && I<N-1 && ((C>128 && C<160)||(C>223 && C<240))){
11000: LT=cons(C,LT);LT=cons(S[++I],LT);continue;
11001: }
11002: if(F>0){
11003: LT=cons(C,LT);continue;
11004: }
11005: LS=asciitostr(reverse(LT));
1.9 takayama 11006: if(V==1||findin(++J,V)>=0){
11007: if(Eq==1) LS=(LS=="")?Null:eval_str(LS);
11008: else LS=(isdecimal(LS))?eval_str(LS):((LS=="")?Null:LS);
11009: }
1.6 takayama 11010: if(!T || T==J) LL=cons(LS,LL);
11011: if(F==-2) while(++I<N && Sp!=1 && S[I]!=44);
11012: F=0;LT=[];
11013: }
11014: if(I<=N && (Sp!=1 || length(LT)>0)){ /* lastline */
11015: LS=asciitostr(reverse(LT));
1.9 takayama 11016: if(V==1||findin(++J,V)>=0){
11017: if(Eq==1) LS=(LS=="")?Null:eval_str(LS);
11018: else LS=(isdecimal(LS))?eval_str(LS):((LS=="")?Null:LS);
11019: }
1.6 takayama 11020: if(!T || T==J) LL=cons(LS,LL);
11021: }
11022: L=cons(reverse(LL),L);
11023: }
11024: close_file(ID);
11025: if(T) L=m2l(L|flat=1);
1.16 takayama 11026: L=reverse(L);
11027: return L;
1.6 takayama 11028: }
11029:
11030: def showbyshell(S)
11031: {
11032: Id = getbyshell(S);
11033: if(Id<0) return Id;
11034: while((S=get_line(Id))!=0) print(S,2);
11035: return close_file(Id);
11036: }
11037:
11038:
11039: def getbyshell(S)
11040: {
11041: /* extern DIROUT; */
11042:
11043: Home=getenv("HOME");
11044: if(type(Home)!=7) Home="";
11045: if(type(Tmp=getenv("TEMP"))!=7 && type(Tmp=getenv("TMP")) != 7)
11046: Tmp=str_subst(DIROUT,["%HOME%","%ASIRROOT%"],[Home,get_rootdir()]);
11047: Sep=isMs()?"\\":"/";
11048: F=Tmp+Sep+"muldif.tmp";
1.16 takayama 11049: if(type(S)<=1 && S>=0) close_file(S);
1.6 takayama 11050: remove_file(F);
11051: if(type(S)<=1) return -1;
11052: shell(S+" > \""+F+"\"");
11053: return open_file(F);
11054: }
11055:
11056: def show(P)
11057: {
11058: T=type(P);
11059: S=P;
11060: Var=getopt(opt);
11061: if(Var=="verb"){
11062: dviout("{\\tt"+verb_tex_form(T)+"}\n\n");
11063: return;
11064: }
11065: if(type(Var)<0) Var=getopt(var);
11066: if(T==6){
11067: if((Sp=getopt(sp))==1 || Sp==2)
11068: S=mtotex(P|lim=1,small=2,sp=Sp,null=1,mat="B");
11069: else if(type(Var)==4 || type(Var)==7)
11070: S=mtotex(P|lim=1,small=2,var=Var);
11071: else
11072: S=mtotex(P|lim=1,small=2);
11073: Size=size(P);
11074: Size=(Size[0]>Size[1])?Size[0]:Size[1];
11075: if(Size>10) dviout0(Size);
11076: }else if(T<=3){
11077: X=0;
11078: if(Var=="pfrac") X=var(P);
11079: else X=getopt(pfrac);
11080: if(isvar(X)){
11081: pfrac(P,X|dviout=1);
11082: return;
11083: }
11084: Opt=cons(["dviout",1],getopt());
11085: if(type(Var)==2||type(Var)==4||type(Var)==7) fctrtos(P|option_list=Opt);
11086: else{
11087: if(isdif(P)!=0) Opt=cons(["var","dif"],Opt);
11088: else Opt=cons(["br",1],Opt);
11089: fctrtos(P|option_list=Opt);
11090: }
11091: return;
11092: }else if(T==4){
11093: if(type(Var)==4 || type(Var)==7){
11094: S=ltotex(P|option_list=getopt());
11095: if(Var=="text"){
11096: dviout(S);
11097: return;
11098: }
11099: }else{
11100: for(F=0,L=P;L!=[] && F!=-1;L=cdr(L)){
11101: LL=car(L);
11102: if(type(LL)==4){
11103: if(F==0){
11104: T=type(LL[0]);
11105: if(T==4) F=2; /* [[[? */
11106: else if(T==1 || T==0) F=1; /* [[num,.. */
11107: }
11108: if(F==1){
11109: if(length(LL)!=2 || !isint(LL[0]) || LL[0]<0 || type(LL[1])>3)
11110: F=-1; /* [[num,rat],[num,rat],...] */
11111: }else if(F==2){
11112: for(LLT=LL; LLT!=[] && F!=-1; LLT=cdr(LLT)){
11113: LLL=car(LLT); /* [[[num,rat],[num,rat],...],[[..],..]],....] */
11114: if(length(LLL)!=2 || !isint(LLL[0]) || LLL[0]<0 || type(LLL[1])>3)
11115: F=-1;
11116: }
11117: }
11118: }else if((F==0 || F==7) && type(LL)==7){
11119: F=7;
11120: }else F=-1;
11121: }
11122: if(F==1) S=ltotex(P|opt="spt");
11123: else if(F==2){
11124: M=mtranspose(lv2m(S));
11125: show(M|sp=1); /* GRS */
11126: return;
11127: }else if(F==7) S=ltotex(P|opt="spts");
11128: else{
11129: for(F=0,L=P;L!=[] && F!=-1;L=cdr(L)){
11130: LL=car(L);
11131: if(type(LL)!=4){
11132: F=-1; break;
11133: }
11134: for(LLT=LL; LLT!=[] && F!=-1; LLT=cdr(LLT)){
11135: T=type(LLL=car(LLT));
11136: if(T<7 && T!=4) F0++;
11137: else if(T==7){
11138: if(str_char(LLL,0,"\\")<0) F1++;
11139: else F2++;
11140: }else F=-1;
11141: }
11142: }
11143: }
11144: if(F==0 && F0>0 && (F1+F2)>0){ /* list of list of eq and str */
11145: if(F2>0) S=ltotex(P|opt=["cr","spts0"],str=1);
11146: else S=ltotex(P|opt=["cr","spts"]);
11147: }else{
11148: for(S="[";;){
11149: S+=my_tex_form(car(P));
11150: if((P=cdr(P))==[]){
11151: S+="]";break;
11152: }
11153: S+=",";
11154: }
11155: }
11156: }
11157: }else if(T==7){
11158: if(Var=="raw" ||
11159: (Var !="eq" && str_chr(P,0,"\\")<0 && str_char(P,0,"^")<0 && str_char(P,0,"_")<0
11160: && str_char(P,0,"&")<0)){
11161: dviout(P+"\n\n");
11162: return;
11163: }
11164: }
11165: dviout(S|eq=5);
11166: }
11167:
11168:
11169: /* options : eq = 1 - 8, clear=1, keep=1, delete=1, title=s,
11170: fctr=1, begin=s */
11171: def dviout(L)
11172: {
11173: /* extern AMSTeX, TeXEq, DIROUT, DVIOUTA, DVIOUTB, DVIOUTL; */
11174:
11175: MyEq = [
11176: ["\\[\n ","\\]"],
11177: ["\\begin{align}\n","\\end{align}"],
11178: ["\\begin{gather}\n ","\\end{gather}"],
11179: ["\\begin{multline}\n ","\\\\[-15pt]\\end{multline}"],
11180: ["\\begin{align}\\begin{split}\n &","\\end{split}\\end{align}"],
11181: ["\\begin{align*}\n &","\\end{align*}"],
11182: ["\\begin{gather*}\n ","\\end{gather*}"],
11183: ["\\begin{equation}\n ","\\end{equation}"]
11184: ];
11185: if(!chkfun("print_tex_form", "names.rr"))
11186: return 0;
11187: Home=getenv("HOME");
11188: if(type(Home)!=7) Home="";
11189: Dir=str_subst(DIROUT,["%HOME%","%ASIRROOT%","\\"],[Home,get_rootdir(),"/"]);
11190: Dirout=Dir+(AMSTeX?"/out.tex":"/out0.tex");
11191: Risaout=(AMSTeX)?"risaout":"risaout0";
11192: Dirisa=Dir+"/"+Risaout+".tex";
11193: Viewer="dviout";
11194: SV=["c:/w32tex/dviout","c:/dviout"];
11195: Risatex=str_subst(AMSTeX?DVIOUTA:DVIOUTL,
11196: ["%HOME%","%ASIRROOT%","%TikZ%"],[Home,get_rootdir(),rtostr(TikZ)]);
11197: if(isMs() && !access(Risatex)){
11198: for(TV=SV; TV!=[]; TV=cdr(TV)){
11199: VV=car(TV)+"/dviout.exe";
11200: if(access(VV)){
11201: Viewer=str_subst(VV,"/","\\");
11202: break;
11203: }
11204: }
11205: output(Risatex);
11206: print("cd \""+str_subst(Dir,"/","\\")+"\"");
11207: print("latex -src=cr,display,hbox,math,par "+Risaout);
11208: print("start "+Viewer+" -1 \""+Dr+"\\tex\\"+Risaout+"\" 1000");
11209: output();
11210: }
11211: if(access(Dirisa) == 0){
11212: D0="\""+(isMs()?str_subst(Dir,"/","\\")+"\"":Dir);
11213: shell("mkdir "+D0);
11214: output(Dirisa);
11215: if(AMSTeX){
11216: print("\\documentclass[a4paper]{amsart}");
11217: print("\\usepackage{amsmath,amssymb,amsfonts}");
11218: }else
11219: print("\\documentclass[a4paper]{article}");
11220: print("\\pagestyle{empty}\n\\begin{document}\n\\thispagestyle{empty}");
11221: print(AMSTeX?"\\input{out}\n\\end{document}":"\\input{out0}\n\\end{document}");
11222: output();
11223: }
11224: if((K = getopt(delete)) >= 1){ /* delete */
11225: LC = 0;
11226: if(type(K) == 1 && K > 10) K = 10;
11227: if(type(K) == 4){
11228: K = qsort(K);
11229: LC = 1; /* specific lines */
11230: }
11231: Done = 1;
11232: Id = open_file(Dirout);
11233: if(Id >= 0){
11234: Buf = Buf0 = Buf1 = Key = "";
11235: PE = 0;
11236: if(type(K) == 1)
11237: BufE = newvect(K--);
11238: Dout = Dirout+"0";
11239: remove_file(Dout);
11240: output(Dout);
11241: while((S = get_line(Id)) != 0){
11242: if(LC){
11243: while(K != [] && car(K) < LC)
11244: K = cdr(K);
11245: if(K == [] || car(K) > LC)
11246: output(S);
11247: }
11248: if(Key == ""){
11249: if((P0 = str_str(S,"\\begin{")) == 0){
11250: Key = sub_str(S,7,str_str(S,"}")-1);
11251: if(findin(Key,["align", "gather","multline", "equation","align*"]) < 0)
11252: Key = "";
11253: else{
11254: Key = "\\end{"+Key+"}";
11255: if(!LC){
11256: if(Buf != ""){
11257: if(PE < K)
11258: BufE[PE++] = Buf1+Buf;
11259: else{
11260: if(K > 0){
11261: print(BufE[0]);
11262: for(I = 1; I < K; I++)
11263: BufE[I-1]=BufE[I];
11264: BufE[K-1] = Buf1+Buf;
11265: }else
11266: print(Buf1+Buf);
11267: Done = 0;
11268: }
11269: Buf1 = Buf0;
11270: Buf = Buf0 ="";
11271: }
11272: }
11273: }
11274: }
11275: if(Key == "" && !LC) Buf0 += S;
11276: }
11277: if(Key != ""){
11278: if(!LC) Buf += S;
11279: if(str_str(S,Key) >= 0){
11280: Key = "";
11281: if(LC) LC++;
11282: }
11283: }
11284: }
11285: output();
11286: close_file(Id);
11287: }
11288: if(Done==0){
11289: Id = open_file(Dout);
11290: if(Id >= 0){
11291: remove_file(Dirout);
11292: output(Dirout);
11293: while((S = get_line(Id)) != 0)
11294: print(S,0);
11295: output();
11296: close_file(Id);
11297: }
11298: remove_file(Dout);
11299: }else L=" ";
11300: }
11301: if(getopt(clear) == 1 || Done == 1){ /* clear */
11302: remove_file(Dirout);
11303: if(L == "" || L == " "){
11304: output(Dirout);
11305: print("\\centerline{Risa/Asir}");
11306: output();
11307: }
11308: }
11309: if(L != " "){
11310: Eq=1;
11311: Eqo = getopt(eq);
11312: Fc = getopt(fctr);
11313: if(Fc == 1 && (type(L) == 2 || type(L) == 3)){
11314: L = fctrtos(L|TeX=1);
11315: if(type(L) == 4)
11316: L = "\\fact{"+L[0]+"}{"+L[1]+"}";
11317: if(type(Eqo) != 0 && type(Eqo) !=7){
11318: Eqo=0;
11319: }
11320: }
11321: if(type(L) != 4 || getopt(mult) != 1)
11322: L = [L];
11323: if(type(Eqo)!=7 && (Eqo<1 || Eqo>8))
11324: Eqo = (AMSTeX==1)?TeXEq:1;
11325: Title = getopt(title);
11326: if(type(Title) == 7){
11327: output(Dirout);
11328: print(Title);
11329: output();
11330: }
11331: Sb = getopt(subst);
11332: for( ; L != []; L = cdr(L)){
11333: Eq = 1;
11334: if(type(LT=car(L)) != 7 && type(LT) != 21)
11335: LT = my_tex_form(LT);
11336: else if(type(getopt(eq)) < 0)
11337: Eq = 0;
11338: if(type(Sb) == 4)
11339: LT = str_subst(LT,Sb[0],Sb[1]);
11340: output(Dirout);
11341: if(Eq == 1){
11342: if(type(Eqo)==7)
11343: print(texbegin(Eqo,LT));
11344: else if(Eqo >= 1 && Eqo <= 8){
11345: mycat0([MyEq[Eqo-1][0],LT,"%"],1);
11346: print(MyEq[Eqo-1][1]);
11347: }else print(LT);
11348: }else print(LT);
11349: output();
11350: }
11351: }
11352: if(str_char(Risatex,0," ")>=0 && str_char(DVIOUTA,0," ")<0 && str_char(DVIOUTB,0," ")<0
11353: && str_char(DVIOUTL,0," ")<0)
11354: Risatex="\""+Risatex+"\"";
11355: if(getopt(keep) != 1) shell(Risatex);
11356: return 1;
11357: }
11358:
11359: def rtotex(P)
11360: {
11361: S = my_tex_form(P);
11362: return (str_len(S) == 1)?S:"{"+S+"}";
11363: }
11364:
11365: def mtotex(M)
11366: {
11367: /* extern TexLim; */
11368:
11369: MB=mat(["(",")","p"],["\\{","\\}","B"],["[","]","b"],["|","|","v"],
11370: ["\\|","\\|","V"], [".",".",""]);
11371: if(type(MT=getopt(mat))==7){
11372: MT=findin(MT,["p","B","b","v","V",""]);
11373: if(MT<0) MT=0;
11374: }
11375: else MT=0;
11376: MT=MB[MT];
11377: if((F=getopt(small))!=1 && F!=2) F=0;
11378: Lim=getopt(lim);
11379: if(type(Lim)==1){
11380: if(Lim<30 && Lim!=0) Lim = TexLim;
11381: }else Lim=0;
11382: FL=getopt(len);
11383: Rw=getopt(raw);
11384: Sp=getopt(sp);
11385: Idx=getopt(idx);
11386: if(type(Idx)==4) Idx=ltov(Idx);
11387: if(type(Idx)==6 && length(Idx)==0) Idx=-1;
11388: Var=getopt(var);
11389: if(Lim>0) FL=1;
11390: Null=getopt(null);
11391: if(Null!=1 && Null!=2) Null=0;
11392: if(type(M)==5) M=lv2m([V]);
11393: else if(type(M)!=6) return monototex(M);
11394: S=size(M);
11395: if(FL==1){
11396: L=newmat(S[0],S[1]); LL=newvect(S[1]);
11397: }
11398: SS=newmat(S[0],S[1]);
11399: for(I=0; I<S[0]; I++){
11400: for(J=0; J<S[1]; J++){
11401: if(type(P=M[I][J])<=3){
11402: if(P!=0 || Null == 0 || (Null==2 && I==J)){
11403: SS[I][J]=(type(Var)>1)?fctrtos(P|TeX=2,lim=0,var=Var):fctrtos(P|TeX=2,lim=0);
11404: if(type(P)==1 && str_str(SS[I][J],"\\frac{-"|end=0)==0)
11405: SS[I][J]="-\\frac{"+str_cut(SS[I][J],7,100000);
11406: }
11407: }else if(type(P)==6){
11408: ST= mtotex(P|small=1,len=1);
11409: SS[I][J]=ST[0];
11410: L[I][J]=ST[1];
11411: }else if(type(P)==7){
11412: if(Rw==1) SS[I][J]=P;
11413: else SS[I][J]="\\text{"+P+"\}";
11414: }else if(type(P)==4 && length(P)==2 && P[0]>0 && (Sp==1 || Sp==2)){
11415: if(P[0]==1){
11416: SS[I][J]=fctrtos(P[1]|TeX=2,lim=0);
11417: }else{
11418: ST=my_tex_form(P[0]);
11419: if(Sp==2) ST="("+ST+")";
11420: SS[I][J]="["+fctrtos(P[1]|TeX=2,lim=0)+"]_";
11421: if(str_len(ST)<2) SS[I][J]+=ST;
11422: else SS[I][J]+="{"+ST+"}";
11423: }
11424: }else
11425: SS[I][J]=my_tex_form(P);
11426: if(FL==1) L[I][J]=texlen(SS[I][J]);
11427: }
11428: }
11429: if(Lim>0 || FL==1){
11430: for(LLL=J=0; J<S[1];J++){
11431: for(I=K=0; I<S[0];I++){
11432: if(K<L[I][J]) K=L[I][J];
11433: }
11434: LLL+=(LL[J]=K);
11435: }
11436: }
11437: if(Lim>0){
11438: if(F==2 && LLL>Lim-2*S[1]-2) F=1;
11439: if(F==1)
11440: Lim=idiv(Lim*6,5);
11441: if(LLL<=Lim-(2-F)*S[I]-2) Lim=0;
11442: }
11443: Mat=(F==1)?"smallmatrix}":"matrix}";
11444: if(F==1) Out=str_tb("\\left"+MT[0]+"\\begin{",0);
11445: else Out=str_tb((Lim==0)?"\\begin{"+MT[2]:"\\left"+MT[0]+"\\begin{",0);
11446: Out = str_tb(Mat,Out);
11447: for(I=II=LT=0; II<=S[0]; II++){
11448: if(Lim==0) II=S[0];
11449: if(II<S[0]){
11450: K=LL[II]+(2-F);
11451: if(I==II){
11452: LT+=K;
11453: continue;
11454: }
11455: if(LT+K<Lim-2) continue;
11456: LT=K;
11457: }
11458: for(I0=I; I<II; I++){
11459: if(I==I0){
11460: str_tb((I==0)?
11461: "\n ":
11462: "\\right.\\\\\n \\allowdisplaybreaks\\\\\n &\\ \\left.\\begin{"+Mat+"\n ", Out);
11463: if(Idx==1||Idx==0||type(Idx)==5){
11464: for(J=I; J<II; J++){
11465: if(type(Idx)!=4)
11466: str_tb("("+rtostr(J+Idx)+")",Out);
11467: else{
11468: JJ=length(Idx)-1;
11469: if(J<JJ) JJ=J;
11470: str_tb(my_tex_form(Idx[JJ]),Out);
11471: }
11472: if(J<II) str_tb(" & ",Out);
11473: }
11474: str_tb("\\\\\n ",Out);
11475: }
11476: }
11477: else str_tb("\\\\\n ",Out);
11478: for(J=0; J<S[1]; J++){
11479: if(J!=0) str_tb(" & ",Out);
11480: if(type(SS[I][J])==7) str_tb(SS[I][J],Out);
11481: }
11482: }
11483: Out=str_tb("\n\\end{", Out);
11484: if(II==S[0]) Out=str_tb((Lim==0&&F!=1)?MT[2]+Mat:Mat+"\\right"+MT[1],Out);
11485: else Out=str_tb(Mat+"\\right.",Out);
11486: }
11487: SS = str_tb(0,Out);
11488: if(FL!=1) return SS;
11489: if(F==1) LLL=idiv((LLL+S[1])*5+13,6);
11490: else LLL+=2*(1+S[1]);
11491: return [SS,LLL];
11492: }
11493:
11494: def sint(N,P)
11495: {
1.11 takayama 11496: if( type(N)==1 || N==0 ) {
1.6 takayama 11497: NT=ntype(N);
11498: if((type(Opt=getopt(str))==1 || Opt==0) && Opt>=0 && P>=0){
11499: if(Opt==2 || Opt==4 || Opt==0){
1.11 takayama 11500: if(N==0) return (Opt>0)?"0":0;
1.6 takayama 11501: Pw=0;
11502: if(NT==4){
11503: NN=abs(real(N));N1=abs(imag(N));
11504: if(NN<N1) NN=N1;
11505: }else NN=abs(N);
11506: while(NN<1 && NN>-1){
11507: Pw--;
11508: N*=10;NN*=10;
11509: }
11510: while(N>=10 || N<=-10){
11511: Pw++;
11512: N/=10;NN/=10;
11513: }
11514: if(Opt==0) return sint(N*10^Pw,P-Pw-1);
11515: S=(getopt(sqrt)==1)?sint(N,P|str=(Opt==4)?3:1,sqrt=1):sint(N,P|str=(Opt==4)?3:1);
11516: if(Pw==0) return S;
11517: if(NT==4)
11518: S="("+S+")";
11519: if(Pw==1){
11520: if(Opt==2)
11521: return S+"*10";
11522: else
11523: return S+"\\times10";
11524: }
11525: if(Opt==2)
11526: return S+"*10^("+rtostr(Pw)+")";
11527: else
11528: return S+"\\times10^{"+rtostr(Pw)+"}";
11529: }
11530: if(NT==4){
11531: NN=real(N);
11532: if(NN!=0){
11533: S=sint(NN,P|str=1);
11534: if(imag(N)>0) S=S+"+";
11535: }
11536: else S="";
11537: S=S+sint(imag(N),P|str=1)+((Opt==3)?((getopt(sqrt)==1)?"\\sqrt{-1}":"i"):"@i");
11538: return S;
11539: }
11540: if(N<0){
11541: N=-N;
11542: Neg="-";
11543: }else Neg="";
1.11 takayama 11544: N=rint(N*10^P)/10^P;
1.6 takayama 11545: NN=floor(N);
1.11 takayama 11546: NV=(N-NN+1)*10^P;
1.6 takayama 11547: NS=rtostr(NN);
11548: if(P<=0) return Neg+NS;
11549: if(NN==0 && getopt(zero)==0) NS="";
1.11 takayama 11550: return Neg+NS+"."+str_cut(rtostr(NV),1,P);
1.6 takayama 11551: }
11552: if(NT==4)
11553: return sint(real(N),P)+sint(imag(N),P)*@i;
11554: X = rint( N*10^P );
1.11 takayama 11555: return deval(X/10^P);
1.6 takayama 11556: }
11557: if( (type(N)==2) || (type(N)==3) ){
11558: NN = eval(N);
11559: if( type(NN)==1 )
11560: return sint(NN,P|option_list=getopt());
11561: else return N;
11562: }
1.8 takayama 11563: if( type(N)>3 && type(N) < 7)
1.6 takayama 11564: #ifdef USEMODULE
11565: return mtransbys(os_md.sint,N,[P]|option_list=getopt());
11566: #else
11567: return mtransbys(sint,N,[P]|option_list=getopt()));
11568: #endif
1.8 takayama 11569: return N;
1.6 takayama 11570: }
11571:
11572: def frac2n(N)
11573: {
11574: if((T=type(N))<0) return N;
11575: E=(getopt(big)==1)?eval(@e):0.1;
11576: if(T==1){
1.15 takayama 11577: if(ntype(N)==0) return (E*N)/E;
1.6 takayama 11578: else if(ntype(N)!=4) return N;
1.15 takayama 11579: else return (E*(1+@i)*N)/(E*(1+@i));
1.6 takayama 11580: }
11581: if(T==3||T==2){
11582: N=red(N);
11583: Nm=nm(N);Var=vars(Nm);V=car(Var);K=length(Var);
11584: for(S=0,I=mydeg(Nm,V);I>=0;I--) S+=frac2n(mycoef(Nm,I,V))*V^I;
11585: return S/dn(N);
11586: }
1.15 takayama 11587: if(T<4) return (E*N)/E;
1.6 takayama 11588: #ifdef USEMODULE
11589: return mtransbys(os_md.frac2n,N,[]|option_list=getopt());
11590: #else
11591: return mtransbys(frac2n,N,[]|option_list=getopt());
11592: #endif
11593: }
11594:
11595: def xyproc(F)
11596: {
11597: if(type(Opt=getopt(opt))!=7) Opt="";
11598: if(type(Env=getopt(env))!=7)
11599: Env=(!TikZ)?"xy":"tikzpicture";
11600: if(F==1)
11601: return(Opt=="")?"\\begin{"+Env+"}\n":"\\begin{"+Env+"}["+Opt+"]\n";
11602: if(F==0) return "\\end{"+Env+"}\n";
11603: if(type(F)==7){
11604: F=xyproc(1|opt=Opt,env=Env)+F+xyproc(0|env=Env);
11605: if(getopt(dviout)==1) dviout(F);
11606: else return F;
11607: }
11608: }
11609:
11610: def xypos(P)
11611: {
11612: if(type(P[0])==7){
11613: if(P[0]=="") S="";
11614: else S=(!TikZ)?"\""+P[0]+"\"":"("+P[0]+")";
11615: }
11616: else{
11617: if(TikZ==0 && XYcm==1){
11618: X=sint(P[0]*10,XYPrec); Y=sint(P[1]*10,XYPrec);
11619: }else{
11620: X=sint(P[0],XYPrec); Y=sint(P[1],XYPrec);
11621: }
11622: S="("+rtostr(X)+","+rtostr(Y)+")";
11623: }
11624: if(!TikZ){
11625: if(length(P)>2 && (PP=P[2])!=""){
11626: S=S+" *";
11627: if(type(PP)==4 && length(PP)==2 && type(PP[0])==7){
11628: S=S+PP[0];
11629: PP=PP[1];
11630: }
11631: if(type(PP)==7){
11632: L=str_len(PP);
11633: if(str_chr(PP,0,"$")==0 && str_chr(PP,L-1,"$")==L-1){
11634: PP=str_cut(PP,1,L-2);
11635: }else S+="\\txt";
11636: }
11637: else PP=my_tex_form(PP);
11638: S=S+"{"+PP+"}";
11639: }
11640: if(length(P)>3){
11641: if(type(P[3])==7 && P[3]!="") S=S+"=\""+P[3]+"\"";
11642: if(length(P)>4 && type(P[4])==7) S=S+P[4];
11643: }
11644: }else{
11645: T="";
11646: if(length(P)>2 && (PP=P[2])!=""){
11647: F=1;
11648: if(type(PP)==4){
11649: if(length(PP)==2 && type(PP[0])==7){
11650: T="["+PP[0]+"]";
11651: PP=PP[1];
11652: }
11653: }
11654: if(type(PP)!=7) PP="$"+my_tex_form(PP)+"$";
11655: S=S+"{"+PP+"}";
11656: }else F=0;
11657: if(length(P)>3){
11658: if(type(P[3])==7 && P[3]!="") T=T+"("+P[3]+")";
11659: else if(P[3]==1) T=T+"(_)";
11660: if(length(P)>4 && type(P[4])==7) S=S+P[4];
11661: }
11662: if(length(P)>2){
11663: if(F) S="node"+T+" at"+S;
11664: else S="coordinate"+T+" at"+S;
11665: }
11666: }
11667: return S;
11668: }
11669:
11670: def xyput(P)
11671: {
11672: if((type(Sc=getopt(scale))==1 && Sc!=1) || type(Sc)==4){
11673: if(type(Sc)==1) Sc=[Sc,Sc];
11674: Sx=Sc[0];Sy=Sc[1];
11675: if(length(P)>2)
11676: P1=cons(Sy*P[1],cdr(cdr(P)));
11677: else P1=[Sy*P[1]];
11678: P=cons((type(P[0])==7)?P[0]:(Sx*P[0]),P1);
11679: }
11680: if(!TikZ) return "{"+xypos(P)+"};\n";
11681: return "\\"+xypos(P)+";\n";
11682: }
11683:
11684: def xyline(P,Q)
11685: {
11686: if(!TikZ) return "{"+xypos(P)+" \\ar@{-} "+xypos(Q)+"};\n";
11687: if(type(T=getopt(opt))!=7) T="";
11688: else T="["+T+"]";
11689: if(length(P)<3 && length(Q)<3)
11690: return "\\draw"+T+xypos(P)+"--"+xypos(Q)+";\n";
11691: if(length(P)==2) P=[P[0],P[1],"","_0"];
11692: else if(length(P)==3 || (length(P)==4 && P[3]==""))
11693: P=[P[0],P[1],P[2],"_0"];
11694: else if(length(P)>4 && P[3]=="")
11695: P=[P[0],P[1],P[2],"_0",P[4]];
11696: if(length(Q)==2) Q=[Q[0],Q[1],"","_1"];
11697: else if(length(Q)==3 || (length(Q)==4 && Q[3]==""))
11698: Q=[Q[0],Q[1],Q[2],"_1"];
11699: else if(length(Q)>4 && Q[3]=="")
11700: Q=[Q[0],Q[1],Q[2],"_1",Q[4]];
11701: return "\\draw "+T+xypos(P)+" "+xypos(Q)+"("+P[3]+")--("+Q[3]+");\n";
11702: }
11703:
11704: def xylines(P)
11705: {
11706: Lf=getopt(curve);
11707: if(type(Lf)!=1) Lf=0;
11708: SS=getopt(opt);
11709: SF=(SS==0)?1:0;
11710: if((Proc=getopt(proc))==1||Proc==2||Proc==3){
11711: OL=cons(["opt",0],delopt(getopt(),["opt","proc"]));
11712: R=xylines(P|option_list=OL);
11713: OP=(type(SS)<0)?[]:((type(SS)==4)?[["opt",SS[0]],["cmd",SS[1]]]:[["opt",SS]]);
11714: return [1,OP,R];
11715: }
11716: if(type(SS)!=7 && type(SS)!=4){
11717: if(Lf==0 && !TikZ) SS="@{-}";
11718: else SS="";
11719: }
11720: if(type(Sc=getopt(scale))==1 || type(Sc)==4){
11721: if(type(Sc)==1) Sc=[Sc,Sc];
11722: Sx=Sc[0];Sy=Sc[1];
11723: if(Sx!=1 || Sy!=1){
11724: for(PP=[], P0=P; P0!=[]; P0=cdr(P0)){
11725: PT=car(P0);
11726: if((type(PT)!=4 && type(PT)!=5) || (type(PT[0])!=1 && PT[0]!=0))
11727: PP=cons(PT,PP);
11728: else{
11729: if(length(PT)>2 && type(PT)==4)
11730: P1=cons(Sy*PT[1],cdr(cdr(PT)));
11731: else P1=[Sy*PT[1]];
11732: PP=cons(cons(Sx*PT[0],P1),PP);
11733: }
11734: }
11735: P=reverse(PP);
11736: }
11737: }
11738: if(type(Cl=CL0=getopt(close))!=1) Cl=0;
11739: if((Vb=getopt(verb))!=1&&type(Vb)!=4) Vb=0;
11740: if(type(Lf)!=1 || Lf==0){ /* lines */
11741: if(TikZ||SF){
11742: for(L=[],F=0,PT=P;PT!=[];PT=cdr(PT)){
11743: if(type(car(PT))<4){
11744: L=cons(car(PT),L);
11745: F=0;
11746: }else{
11747: if(F++>1) L=cons(1,L);
11748: L=cons(car(PT),L);
11749: }
11750: }
11751: if(Cl==1){
11752: L=cons(1,L);L=cons(-1,L);
11753: }
11754: if(L) L=reverse(L);
11755: if(SF) return L;
11756: if(type(SS)!=4) S=xybezier(L|opt=SS);
11757: else S=xybezier(L|opt=SS[0],cmd=SS[1]);
11758:
11759: }else{
11760: Out = str_tb(0,0);
11761: for(PT=P; PT!=[]; ){
11762: PS1=car(PT);
11763: PT=cdr(PT);
11764: if(PT==[]){
11765: if(Cl==1) PS2=car(P);
11766: else PS2=0;
11767: }else PS2=car(PT);
11768: str_tb(xyarrow(PS1,PS2|opt=SS),Out);
11769: }
11770: S=str_tb(0,Out);
11771: }
11772: }else if(Lf==2){ /* B-spline */
11773: if(SF) return P;
11774: if(!TikZ){
11775: Out = str_tb("{\\curve{",0);
11776: for(PT=P;PT!=[];PT=cdr(PT)){
11777: if(car(PT)==0){
11778: str_tb("}};\n{\\curve{",Out);
11779: continue;
11780: }
11781: if(PT!=P) str_tb("&",Out);
11782: str_tb(xypos([car(PT)[0],car(PT)[1]]),Out);
11783: }
11784: str_tb("}};\n",Out);
11785: S=str_tb(0,Out);
11786: }else Out=str_tb(xybezier(P|opt=SS),0);
11787: for(I=0;I<2;I++){
11788: Q=car(P);
11789: if(length(Q)>2)
11790: str_tb(xyput(Q),Out);
11791: P=reverse(P);
11792: }
11793: S=str_tb(0,Out);
11794: }else{ /* extended Bezier */
11795: RTo=getopt(ratio);
11796: if(type(Acc=getopt(Acc))!=1) Acc=0;
11797: if(type(RTo)!=1 || RTo>1.5 || RTo<0.001) RTo=0;
11798: if(Cl==1){
11799: PR=reverse(P);
11800: PT=car(PR);
11801: PR=cons(P[0],PR);
11802: PR=cons(P[1],PR);
11803: P=cons(PT,reverse(PR));
11804: }else if(Cl==-1) Cl=1;
11805: for(L=P2=P3=0,PT=P;;){
11806: P1=P2;P2=P3;P3=P4;
11807: P4=(PT==[])?0:car(PT);
11808: if(PT==[] && (Cl==1 || P3==0)) break;
11809: PT=cdr(PT);
11810: if(P3==0) str_tb("%\n", Out);
11811: if(P2==0 || P3==0 || (Cl==1 && P1==0)) continue;
11812: if(L!=0){
11813: if(car(L)==P2)
11814: L=cons(1,L);
11815: else{
11816: L=cons(0,L); L=cons(P2,L);
11817: }
11818: }else L=[P2];
11819: X=P3[0]-P2[0];Y=P3[1]-P2[1];
11820: DL1=DL2=0;DL=Acc?sqrt(X^2+Y^2):dsqrt(X^2+Y^2);
11821: if(P4!=0){
11822: XD1=P4[0]-P2[0];YD1=P4[1]-P2[1];DL1=Acc?sqrt(XD1^2+YD1^2):dsqrt(XD1^2+YD1^2);
11823: }
11824: if(P1!=0){
11825: XD2=P3[0]-P1[0];YD2=P3[1]-P1[1];DL2=Acc?sqrt(XD2^2+YD2^2):dsqrt(XD2^2+YD2^2);
11826: }
11827: if(RTo!=0)
11828: R=RTo;
11829: else if(DL1>0 && DL2>0){
11830: Cos=(XD1*XD2+YD1*YD2)/(DL1*DL2);
11831: RT=4/(3*(Acc?sqrt((1+Cos)/2):dsqrt((1+Cos)/2))+3);
11832: R=DL*RT/(DL1+DL2);
11833: }else if(DL1!=0)
11834: R=DL/(2*DL1);
11835: else if(DL2!=0)
11836: R=DL/(2*DL2);
11837: if(DL2!=0) L=cons([P2[0]+R*XD2,P2[1]+R*YD2],L);
11838: if(DL1!=0) L=cons([P3[0]-R*XD1,P3[1]-R*YD1],L);
11839: L=cons([P3[0],P3[1]],L);
11840: }
11841: if(CL0==1) L=cons(-1,cdr(L));
11842: if(L!=0) L=reverse(L);
11843: if(SF) return L;
11844: if(type(SS)==4)
11845: S=xybezier(L|opt=SS[0],cmd=SS[1],verb=Vb);
11846: else
11847: S=xybezier(L|opt=SS,verb=Vb);
11848: }
11849: if(getopt(dviout)!=1) return S;
11850: xyproc(S|dviout=1);
11851: }
11852:
11853: def saveproc(S,Out)
11854: {
11855: if(type(Out)==4){
11856: Out=cons(S,Out);
11857: return Out;
11858: }else{
11859: str_tb(S,Out);
11860: return Out;
11861: }
11862: }
11863:
1.18 takayama 11864: def xygrid(X,Y)
11865: {
11866: for(RR=[],I=0,Z=X;I<2;I++){
1.19 takayama 11867: U=Z[2];L=LL=[];M=Z[3];
11868: if(Z[1]==1||Z[1]==-1){
1.18 takayama 11869: if(type(M)==4) L=M;
11870: else{
1.19 takayama 11871: if(U*(-dlog(1-1/20)/dlog(10))>=M){
1.18 takayama 11872: L=cons([1,2,1/10],L);
1.19 takayama 11873: LL=cons([1,2,1/2],LL);
11874: }else if(U*(-dlog(1-1/10)/dlog(10))>=M)
1.18 takayama 11875: L=cons([1,2,1/5],L);
11876: else if(U*(-dlog(1-1/4)/dlog(10))>=M)
11877: L=cons([1,2,1/2],L);
1.19 takayama 11878: if(U*(-dlog(1-1/50)/dlog(10))>=M){
1.18 takayama 11879: L=cons([2,5,1/10],L);
1.19 takayama 11880: LL=cons([2,5,1/2],LL);
11881: }else if(U*(-dlog(1-1/25)/dlog(10))>=M)
1.18 takayama 11882: L=cons([2,5,1/5],L);
11883: else if(U*(-dlog(1-1/10)/dlog(10))>=M)
11884: L=cons([2,5,1/2],L);
1.19 takayama 11885: if(U*(-dlog(1-1/100)/dlog(10))>=M){
1.18 takayama 11886: L=cons([5,10,1/10],L);
1.19 takayama 11887: LL=cons([5,10,1/2],LL);
11888: }
1.18 takayama 11889: else if(U*(-dlog(1-1/50)/dlog(10))>=M)
11890: L=cons([5,10,1/5],L);
11891: else if(U*(-dlog(1-1/20)/dlog(10))>=M)
11892: L=cons([5,10,1/2],L);
1.19 takayama 11893: L=cons(L,cons(LL,[[[1,10,1]]]));
1.18 takayama 11894: }
11895: R=scale(L|scale=U);
1.19 takayama 11896: if(Z[1]==-1){
11897: for(LL=[];R!=[];R=cdr(R)){
11898: for(L=[],T=car(R);T!=[];T=cdr(T)) L=cons(U-car(T),L);
11899: LL=cons(reverse(L),LL);
11900: }
11901: R=reverse(LL);
11902: }
1.18 takayama 11903: }else if(Z[1]==0){
11904: if(type(M)==4){
11905: R=scale(M|f=x,scale=U);
11906: }else{
11907: V=0;
11908: if(U/10>=M) V=1/10;
11909: else if(U/5>=M) V=1/5;
11910: else if(U/2>=M) V=1/2;
11911: R=[];
11912: if(V>0){
11913: UU=U*V;
11914: for(R=[],J=UU;J<U;J+=UU) R=cons(J,R);
11915: }
1.19 takayama 11916: if(V==1/10) L=[U/2];
11917: else L=[];
11918: R=cons(R,cons(L,[[0,U]]));
1.18 takayama 11919: }
11920: }else if(type(Z[1])==4){
11921: R=Z[1];
1.19 takayama 11922: if(length(R)==0||type(R[0])!=4) R=[[],[],R];
1.18 takayama 11923: }else return 0;
1.19 takayama 11924: K=length(R);
11925: S=newvect(K);
11926: for(J=0;J<K;J++){
11927: for(S[J]=[],JJ=0;JJ<=Z[0];JJ+=U){
11928: for(P=R[J];P!=[];P=cdr(P))
11929: if(car(P)+JJ<=Z[0]) S[J]=cons(car(P)+JJ,S[J]);
11930: }
11931: }
11932: for(J=0;J<K;J++) S[J]=lsort(S[J],[],1);
11933: for(U=[],J=K-1;J>0;J--){
11934: U=lsort(S[J],U,0);S[J-1]=lsort(S[J-1],U,1);
1.18 takayama 11935: }
1.19 takayama 11936: RR=cons(vtol(S),RR);
1.18 takayama 11937: Z=Y;
11938: }
11939: if((Raw=getopt(raw))==1) return RR;
11940: SS=[];
11941: if(type(Sf=getopt(shift))==7){
11942: Sx=Sf[0];Sy=Sf[1];
11943: }else Sx=Sy=0;
11944: for(I=0;I<2;I++){
11945: for(S0=[],L=RR[I];L!=[];L=cdr(L)){
11946: for(S=[],T=car(L);T!=[];T=cdr(T)){
11947: if(S!=[]) S=cons(0,S);
11948: if(I==0){
11949: S=cons([X[0]+Sx,car(T)+Sy],S);
11950: S=cons([Sx,car(T)+Sy],S);
11951: }else{
11952: S=cons([car(T)+Sx,Y[0]+Sy],S);
11953: S=cons([car(T)+Sx,Sy],S);
11954: }
11955: }
11956: S0=cons(S,S0);
11957: }
11958: SS=cons(reverse(S0),SS);
11959: }
11960: SS=reverse(SS);
11961: if(Raw==2) return SS;
11962: if(length(Y)<5) T=[["",""]];
11963: else if(type(Y[4])==4) T=[Y[4]];
11964: else T=[Y[4],Y[4]];
11965: if(length(X[4])==4) T=cons([""],T);
11966: else if(type(X[4])==4) T=cons(X[4],T);
11967: else T=cons([X[4]],T);
11968: for(Sx=Sy=[],I=0;I<2;I++){
11969: TT=T[I];
11970: for(V=SS[I];V!=[];V=cdr(V)){
11971: Op=car(TT);
11972: if(length(TT)>1) TT=cdr(TT);
11973: if(car(V)==[]) continue;
11974: if(Op=="") S=xylines(car(V));
11975: else S=xylines(car(V)|opt=Op);
11976: if(I==0) Sx=cons(S,Sx);
11977: else Sy=cons(S,Sy);
11978: }
11979: }
11980: for(S="",Sx=reverse(Sx), Sy=reverse(Sy);Sx!=[]&&Sy!=[];){
11981: if(Sx!=[]){
11982: S+=car(Sx);Sx=cdr(Sx);
11983: }
11984: if(Sy!=[]){
11985: S+=car(Sy);Sy=cdr(Sy);
11986: }
11987: }
11988: return S;
11989: }
11990:
11991:
1.22 takayama 11992: def addIL(I,L)
1.18 takayama 11993: {
1.22 takayama 11994: if(I==0){
11995: for(R=[];L!=[];L=cdr(L)) R=addIL(car(L),R);
11996: return reverse(R);
1.18 takayama 11997: }
1.22 takayama 11998: if(type(In=getopt(in))==1){
11999: if(In==-1){
12000: J=JJ=I[1];I=I[0];
12001: for(R=[];L!=[];L=cdr(L)){
12002: J=lmin([car(L)[0],JJ]);
12003: if(J>I) R=cons([I,J],R);
12004: I=lmax([car(L)[1],I]);
12005: }
12006: if(I<JJ) R=cons([I,JJ],R);
12007: return reverse(R);
12008: }else{
12009: for(;L!=[];L=cdr(L)){
12010: if(car(L)[0]>I) return 0;
12011: if(car(L)[1]>=I){
12012: if(In==3) return car(L);
12013: if(In==1||(I!=car(L)[0]&&I!=car(L)[1])) return 1;
12014: return 2;
12015: }
12016: }
12017: return 0;
12018: }
12019: }
12020: I0=car(I);I1=I[1];
12021: for(F=0,R=[];L!=[];L=cdr(L)){
12022: if(I0>car(L)[1]){
12023: R=cons(car(L),R);
12024: continue;
12025: }
12026: if(I0<=car(L)[1]){
12027: I0=lmin([I0,car(L)[0]]);
12028: if(I1<car(L)[0]){
12029: R=cons([I0,I1],R);
12030: for( ;L!=[];L=cdr(L)) R=cons(car(L),R);
12031: F=1;
12032: break;
12033: }
12034: I1=lmax([I1,car(L)[1]]);
12035: }
12036: }
12037: if(!F) R=cons([I0,I1],R);
12038: return reverse(R);
1.18 takayama 12039: }
12040:
12041: def xy2curve(F,N,Lx,Ly,Lz,A,B)
12042: {
1.22 takayama 12043: Raw=getopt(raw);
12044: if(type(Gap=getopt(gap))==4){
12045: MG=Gap[1];Gap=car(Gap);
12046: }else MG=3;
12047: if(type(Gap)!=1 && Gap!=0) Gap=0.7;
12048: if(type(Dvi=getopt(dviout))<1) Dvi=0;
12049: OL=[["dviout",Dvi]];
12050: if(type(Opt=getopt(opt))<1) Opt=0;
12051: else OL=cons(["opt",Opt],OL);
12052: if(type(Sc=getopt(scale))!=1 && type(Sc)!=4) Sc=[1,1,1];
12053: else if(type(Sc)!=4) Sc=[Sc,Sc,Sc];
12054: else if(length(Sc)!=3) Sc=[Sc[0],Sc[1],Sc[1]];
12055: M=diagm(3,Sc);
12056: if(A!=0||B!=0){
12057: if(type(A)==6) M=A;
12058: else M=mrot([0,-B,-A]|deg=1)*M;
12059: V=M*newvect(3,[x,y,z]);
12060: Fx=compdf(V[0],[x,y,z],F);Fy=compdf(V[1],[x,y,z],F);Fz=compdf(V[2],[x,y,z],F);
12061: }else{
12062: for(I=0;I<3;I++){
12063: if(type(T=F[I])!=4) T=f2df(T);
12064: if(type(T)==4) T=cons(car(T)*Sc[I],cdr(T));
12065: else T*=Sc[I];
12066: if(I==0) Fx=T;
12067: else if(I==1) Fy=T;
12068: else Fz=T;
12069: }
12070: }
12071: if(Raw==5||!Gap)
12072: return (Dvi||!Gap)? xygraph([Fy,Fz],N,Lx,Ly,Lz|option_list=OL):[Fx,Fy,Fz];
1.18 takayama 12073: R=xygraph([Fy,Fz],N,Lx,Ly,Lz|raw=2);
1.22 takayama 12074: R0=cdr(car(R));R1=R[1];
12075: for(LT=[];R0!=[];R0=cdr(R0),R1=cdr(R1))
12076: if(car(R0)!=0) LT=cons([R1[0],R1[1]],LT);
12077: LT=reverse(LT);
1.19 takayama 12078: if(N<0){
12079: Be=xylines(car(R)|curve=1,proc=3,close=-1);
12080: LT=reverse(cdr(LT));
12081: LT=reverse(cdr(LT));
12082: }
12083: else Be=xylines(car(R)|curve=1,proc=3);
1.18 takayama 12084: Be=cdr(cdr(Be));
1.22 takayama 12085: Be=lbezier(car(Be));
12086: if(Raw==4) return [Be,LT,Lx];
12087: X=ptcombz(Be,0,0);
12088: Var=(length(Lx)==3)?car(Lx):x;
12089: if(type(Eq=getopt(eq))!=1) Eq=0.01;
12090: if(TikZ==1){
12091: Gap/=10;Eq/=10;
1.18 takayama 12092: }
12093: for(R=[],XT=X;XT!=[];XT=cdr(XT)){
12094: V=car(XT);
1.22 takayama 12095: U=LT[V[0][0]];
12096: T=U[0]*V[1][0]+U[1]*(1-V[1][0]);
12097: VV=myfdeval(Fx,[Var,T]);
12098: U=LT[V[0][1]];
1.18 takayama 12099: T=U[0]*V[1][1]+U[1]*(1-V[1][1]);
1.22 takayama 12100: VV-=myfdeval(Fx,[Var,T]);
12101: if(abs(VV)<Eq) continue;
12102: I=(VV<0)?0:1;
12103: R=cons([V[0][I],V[1][I],V[0][1-I],V[1][1-I]],R);
1.18 takayama 12104: }
12105: R=qsort(R);
1.22 takayama 12106: if(Raw==3) return [Be,R];
12107: Db=newvect(L=length(Be));
12108: for(I=0;I<L;I++) Db[I]=[];
12109: for(TR=R;TR!=[];TR=cdr(TR)){
12110: V1=ptbezier(Be,[I=car(TR)[0],P=car(TR)[1]])[1];
12111: V2=ptbezier(Be,[car(TR)[2],car(TR)[3]])[1];
12112: T=dsqrt(1-dvangle(V1,V2)^2);
12113: if(T<1/MG) T=MG;
12114: GP=Gap/T;
12115: W=GP/dnorm(V1);
12116: Db[I]=addIL([P-W,P+W],Db[I]);
12117: if(P-W<0 && I>0) Db[I-1]=addIL([P-W+1,1],Db[I-1]);
12118: if(P+W>1 && I+1<L) Db[I+1]=addIL([0,P+W-1],Db[I+1]);
12119: }
12120: Db=vtol(Db);
12121: for(Bf=[];Be!=[];Be=cdr(Be),Db=cdr(Db)){
12122: if(car(Db)==[]) Bf=cons(car(Be),Bf);
12123: else{
12124: D=addIL([0,1],car(Db)|in=-1);
12125: for(;D!=[];D=cdr(D))
12126: Bf=cons(tobezier(car(Be)|inv=car(D)),Bf);
12127: }
12128: }
12129: Bf=reverse(Bf);
12130: if(Raw==2) return Bf;
12131: OL=[];
12132: if(Opt){
12133: if(type(Opt)==4&&length(Opt)>1) OL=[["opt",Opt[0]],["cmd",Opt[1]]];
12134: else OL=[["opt",Opt]];
12135: }else OL=[];
12136: S=xybezier(lbezier(Bf|inv=1)|option_list=OL);
12137: if(Raw==1||!Dvi) return S;
12138: return xyproc(S|dviout=Dvi);
12139: }
12140:
12141: def rungeKutta(F,N,Lx,Y,IY)
12142: {
12143: if((Pr=getopt(prec))==1){
12144: One=eval(exp(0));
12145: }else{
12146: One=1;Pr=0;
12147: }
12148: if((FL=getopt(last))!=1) FL=0;
12149: if(length(Lx)>2){
12150: V=car(Lx);Lx=cdr(Lx);
12151: }else V=x;
12152: if(Pr==0) Lx=[deval(Lx[0]),deval(Lx[1])];
12153: else Lx=[eval(Lx[0]),eval(Lx[1])];
12154: if(type(Y)==4){
12155: if((Sing=getopt(single))==1||type(F)!=4)
12156: F=append(cdr(Y),[F]);
12157: L=length(Y);
12158: for(TF=[];F!=[];F=cdr(F))
12159: TF=cons(f2df(car(F)),TF);
12160: F=reverse(TF);
12161: }else{
12162: L=1;
12163: F=f2df(F);
12164: }
12165: if(getopt(val)==1) V1=1;
12166: else V1=0;
12167: H=(Lx[1]-Lx[0])/N;H2=H/2;
12168: FV=findin(V,vars(F));
12169: K=newvect(4);
12170: if(L==1){
12171: R=[[T=Lx[0],S=IY]];
12172: if(!H) return R;
12173: for(;;){
12174: for(I=0;I<4;I++){
12175: if(I==0) W=[[V,T],[Y,S]];
12176: else if(I==3) W=[[V,T+H],[Y,S+H*K[2]]];
12177: else W=[[V,T+H2],[Y,S+H2*K[I-1]]];
12178: if(FV<0) W=cdr(W);
12179: K[I]=Pr?myfeval(F,W)*One:myfdeval(F,W);
12180: }
12181: S+=(K[0]+2*K[1]+2*K[2]+K[3])*H/6;T+=H;
12182: if(!FL) R=cons([deval(T),S],R);
12183: if((T+H-Lx[1])*H>0) break;
12184: }
12185: }else{
12186: T=Lx[0];
12187: R=[cons(T,V1?[car(IY)]:IY)];
12188: S=ltov(IY);
12189: if(!H) return R;
12190: for(;;){
12191: for(I=0;I<4;I++){
12192: if(I==0) W=cons([V,T ],lpair(Y,vtol(S)));
12193: else if(I==3) W=cons([V,T+H ],lpair(Y,vtol(S+H*K[2])));
12194: else W=cons([V,T+H2],lpair(Y,vtol(S+H2*K[I-1])));
12195: if(FV<0) W=cdr(W);
12196: for(TK=[],TF=F;TF!=[];TF=cdr(TF)){
12197: TK=cons(Pr?myfeval(car(TF),W)*One:myfdeval(car(TF),W),TK);
12198: }
12199: K[I]=ltov(reverse(TK));
12200: }
12201: S+=(K[0]+2*K[1]+2*K[2]+K[3])*H/6;T+=H;
12202: TS=vtol(S);
12203: if(V1) TS=[car(TS)];
12204: if(!FL) R=cons(cons(deval(T),TS),R);
12205: if((T+H-Lx[1])*H>0) break;
12206: }
12207: }
12208: return FL?(V1?S[0]:S):reverse(R);
1.18 takayama 12209: }
12210:
1.6 takayama 12211: def xy2graph(F0,N,Lx,Ly,Lz,A,B)
12212: {
1.18 takayama 12213: /* (x,y,z) -> (z sin B + x cos A cos B + y sin A cos B,
12214: -x sin A + y cos A, z cos B - x cos A sin B - y sin A sin B) */
1.6 takayama 12215: if((Proc=getopt(proc))==1||Proc==2){
12216: OPT0=[["proc",3]];
12217: }else{
12218: Proc=0;OPT0=[];
12219: }
12220: if(type(DV=getopt(dviout))==4){
12221: S=["ext","shift","cl","dviout"];
12222: OL=delopt(getopt(),S);
12223: OL=cons(["proc",1],OL);
12224: R=xy2graph(F0,N,Lx,Ly,Lz,A,B|option_list=OL);
12225: OL=delopt(getopt(),S|inv=1);
12226: return execdraw(R,DV|optilon_list=OL);
12227: }
12228: if(N==0 || N>100 || N<-100) N=-16;
12229: if(N<0){
12230: N=-N;N1=-1;N2=NN+1;
12231: }else{
12232: N1=0;N2=NN=N;
12233: }
12234:
12235: Ratio=Ratio2=1;
12236: if(type(Sc=Sc0=getopt(scale))!=1 && type(Sc)!=4) Sc=1;
12237: if(type(Sc)==4){
12238: Ratio=Sc[1]/Sc[0];
12239: if(length(Sc)>2) Ratio2=Sc[2]/Sc[0];
12240: Sc=Sc[0];
12241: }
12242: if(type(Vw=getopt(view))!=1) Vw=0;
12243: if(type(Raw=getopt(raw))!=1) Raw=0;
12244: if(type(M1=getopt(dev))==1) M2=M1;
12245: else if(type(M1)==4){
12246: M2=M1[1];M1=M1[0];
12247: }else M1=0;
12248: if(type(M3=getopt(acc))!=1 || (M3<0.5 && M3>100)) M3=1;
12249: if(M1<=0) M1=16;
12250: if(M2<=0) M2=16;
12251: OL=[["para",1],["scale",Sc]];
12252: if(Raw==1) OL=cons(["raw",1],OL);
12253: if(type(Prec=getopt(prec))>=0) OL=cons(["prec",Prec],OL);
12254: L=newvect(4,[[Lx[1],Ly[0]],[Lx[1],Ly[1]],[Lx[0],Ly[1]],[Lx[0],Ly[0]]]);
12255: Lx=[deval(Lx[0]),deval(Lx[1])];
12256: Ly=[deval(Ly[0]),deval(Ly[1])];
12257: Lz=[deval(Lz[0]),deval(Lz[1])];
12258: A=(A0=A)%360;
12259: F00=F0;
12260: if(type(F0)<4){
12261: FC=f2df(F0);
12262: if(findin(z,Vars=vars(FC))>=0 && findin(x,Vars)<0 && findin(y,Vars)<0)
12263: F0=[w,[z,0,x+y*@i],[w,os_md.abs,FC]];
12264: }
12265: if(type(Org=getopt(org))==4){ /* shift origin */
12266: Lx=[Lx[0]-Org[0],Lx[1]-Org[0]];
12267: Ly=[Ly[0]-Org[1],Ly[1]-Org[1]];
12268: Lz=[Lz[0]-Org[2],Lz[1]-Org[2]];
12269: F0=mysubst(F0,[[x,x+Org[0]],[y,y+Org[1]]]);
12270: if(type(F0)==4){
12271: F0=cons(F0[0]-Org[2],cdr(F0));
12272: }
12273: else F0-=Org[2];
12274: }else Org=[0,0,0];
12275: Cpx=getopt(cpx);
12276: if(type(Cpx)<0){
12277: if(str_str(rtostr(F0),"@i")>=0) Cpx=1;
12278: else Cpx=0;
12279: }
12280: if(A<0) A+=360;
12281: if(A<90){
12282: Sh=1;F1=F0;Cx=x-Org[0];Cy=y-Org[1];
12283: }else if(A<180){ /* x -> y, y -> -x */
12284: Sh=2;A-=90; F1=mulsubst(F0,[[x,-y],[y,x]]);
12285: LL=Ly;Ly=[-Lx[1],-Lx[0]];Lx=LL;Cx=y-Org[1];Cy=-x+Org[0];
12286: }else if(A<270){
12287: Sh=3;A-=180; F1=subst(F0,[[x,-x],[y,-y]]);
12288: Lx=[-Lx[1],-Lx[0]];Ly=[-Ly[1],-Ly[0]];Cx=-x+Org[0];Cy=-y+Org[1];
12289: }else{
12290: Sh=4;A-=270;F1=mulsubst(F0,[[x,y],[y,-x]]);
12291: LL=Lx;Lx=[-Ly[1],-Ly[0]];Ly=LL;Cx=-y+Org[1];Cy=x-Org[0];
12292: }
12293: A=@pi*A/180; B=@pi*B/180;
12294: if(A==0) A=@pi/3;
12295: if(B==0) B=@pi/12;
12296: NN=N*M2;
12297: Ac=dcos(deval(A)); As=dsin(deval(A));
12298: if(Ac<=0.087 || As<=0.087){
12299: mycat(["Unsuitable angle",A0,"(6-th argument)!"]);
12300: return -1;
12301: }
12302: Bc=Ratio*dcos(deval(B)); Bs=dsin(deval(B));
12303: if(Bc<0){
12304: mycat("Unsuitable angle (7-th argument)!");
12305: return -1;
12306: }
12307: /*
12308: z = f(x,y) => X=-As*x+Ac*y, Y= Bc*f(x,y)-Bsc*x-Bss*y
12309: Out X-coord is in [X0,X1], dvided by Dev segments
12310: J-th segment of Y-coord : ZF[J]==1 => [Z0[0],Z1[J]]
12311: */
12312: Bsc=Bs*Ac;Bss=Bs*As;
12313: if(Ratio2!=1){
12314: if(Sh%2==1){
12315: Ac*=Ratio2;Bss*=Ratio2;
12316: }else{
12317: As*=Ratio2;Bsc*=Ratio2;
12318: }
12319: }
12320: CX=-As*Cx+Ac*Cy;CY=Bc*(z-Org[2])-Bsc*Cx-Bss*Cy;
12321: if(type(Dvi=getopt(dviout))!=1 && getopt(trans)==1) return [CX*Sc,CY*Sc];
12322: if(type(N1=getopt(inf))==1){
12323: if(Proc) Dvi=N1;
12324: else if(Dvi<=0) Dvi=-N1;
12325: }
12326: X0=-As*Lx[1]+Ac*Ly[0];X1=-As*Lx[0]+Ac*Ly[1];
12327: F1=mysubst(F1,[@pi,deval(@pi)]);
12328: Tf=type(F1=f2df(F1|opt=0));
12329: if(Tf!=4) F=Bc*F1-Bsc*x-Bss*y;
12330: else F=append([Bc*F1[0]-Bsc*x-Bss*y],cdr(F1));
12331: Dx=(Lx[1]-Lx[0])/NN; Dy=(Ly[1]-Ly[0])/NN;
12332: if(type(Err=getopt(err))==1)
12333: F=mysubst(F,[[x,x+Err*Dx/1011.23],[y,y+Err*Dy/1101.34]]);
12334: Out=(Proc)?[]:str_tb(0,0);
12335: Dev=N*M1;
12336: XD=(X1-X0)/Dev;
12337: OLV=newvect(2,[OL,OL]);
12338: if(type(Ura=getopt(opt))==4 || type(Ura)==7){
12339: if(type(Ura)==7) Ura=[Ura,Ura];
12340: else{
12341: OLV[0]=cons(["opt",Ura[0]],OL);
12342: OLV[1]=cons(["opt",Ura[1]],OL);
12343: }
12344: }
12345: for(KC=0; KC<=1; KC++){ /* draw curves */
12346: Z0=newvect(Dev+1); Z1=newvect(Dev+1); ZF=newvect(Dev+1);
12347: for(I=0; I<=NN; I++){
12348: FV=I%M2;
12349: if(KC==0){
12350: X=x; Y=Ly[1]-I*Dy; LX=Lx; DD=Dx; G=mysubst(F,[y,Y]);
12351: if(!FV){
12352: if(!Proc) str_tb(["%y=",rtostr(Y),"\n"],Out);
12353: else Out=cons([-2,"y="+rtostr(Y)],Out);
12354: }
12355: }else{
12356: X=Lx[1]-I*Dx; Y=x; LX=Ly; DD=Dy; G=mysubst(F,[[x,X],[y,Y]]);
12357: if(!FV){
12358: if(!Proc) str_tb(["%x=",rtostr(X),"\n"],Out);
12359: else Out=cons([-2,"x="+rtostr(X)],Out);
12360: }
12361: }
12362: XX=-As*X+Ac*Y; A1=coef(XX,1,x); A0=coef(XX,0,x); /* XX = A1*x + A0, x = (XX-A0)/A1 */
12363: if(!FV && Vw==1){
12364: if(Proc) Out=cons(xygraph([XX,G],N,LX,[X0,X1],Lz|scale=Sc,para=1,proc=3),Out);
12365: else str_tb(xygraph([XX,G],N,LX,[X0,X1],Lz|scale=Sc,para=1),Out);
12366: continue;
12367: }
12368: V=VT=LX[1];
12369: J0=(subst(XX,x,LX[0])-X0)/XD; J1=(subst(XX,x,LX[1])-X0)/XD;
12370: if(J0<J1){
12371: J0=ceil(J0); J1=floor(J1); JD=1; /* fixed x: y: dec => (x,z):(dec,inc) */
12372: }else{
12373: J0=floor(J0); J1=ceil(J1); JD=-1; /* fixed y: x: dec => (x,z):(inc,inc) */
12374: }
12375: for(FF=1,J=J1;;J-=JD){
12376: V1=VT;
12377: VT=(X0+J*XD-A0)/A1;GG=mysubst(G,[x,VT]);
12378: if(Cpx>=1) VV=myeval(GG);
12379: else VV=(Tf==4)? mydeval(GG):deval(GG); /* J -> V */
12380: if(ZF[J]==0 || VV<=Z0[J] || VV>=Z1[J]){ /* visible */
12381: if(FF==0){
12382: V0=(VT+V1)/2;
12383: if(!FV && Vw==-1 && Raw!=1){ /* draw doted line */
12384: K=ceil(M3*(V-V0)/(M2*DD));
12385: if(N1<0) K=-K;
12386: OPT=append(OPT0,[["opt",(TikZ)?"dotted":"~*=<3pt>{.}"],["scale",Sc],["para",1]]);
12387: Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz|
12388: option_list=OPT),Out);
12389: }
12390: V=V0;
12391: }
12392: if(ZF[J]==0){
12393: ZF[J]=1; Z0[J]=Z1[J]=VV;
12394: }else if(VV<=Z0[J]) Z0[J]=VV;
12395: else Z1[J]=VV;
12396:
12397: if(VV>=Z1[J]) FF=1;
12398: else if(VV<=Z0[J]) FF=-1;
12399: }else{
12400: if(FF!=0){
12401: V0=(VT+V1)/2;
12402: K=ceil(M3*(V-V0)/(M2*DD));
12403: if(N1<0) K=-K;
12404: if(!FV){
12405: OPT=append(OPT0,OLV[(1-FF)/2]);
12406: Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz|option_list=OPT),Out);
12407: }
12408: V=V0;
12409: }
12410: FF=0;
12411: }
12412: if(J==J0) break;
12413: }
12414: if(FV) continue;
12415: V0=LX[0];K=ceil(M3*(V-V0)/(M2*DD));
12416: if(N1<0) K=-K;
12417: if(FF!=0){
12418: if(Raw!=1){
12419: OPT=append(OPT0,OLV[(1-FF)/2]);
12420: Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz|option_list=OPT),Out);
12421: }else if(Vw==-1 && Raw!=1){
12422: OPT=append(OPT0,[["opt",(TikZ)?"dotted":"~*=<3pt>{.}"]]);
12423: Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz|option_list=OPT),Out);
12424: }
12425: }
12426: }
12427: }
12428: OptSc=(Sc==1)?[]:[["scale",Sc]];
12429: if(type(LZ=getopt(ax))==4){ /* draw box */
12430: FC=0;
12431: if(length(LZ)==3) FC=LZ[2];
12432: P0=newvect(2,[-As*Lx[1]+Ac*Ly[1],Bc*(LZ[0]-Org[0])-Bsc*Lx[1]-Bss*Ly[1]]);
12433: Vx=newvect(2,[As*(Lx[1]-Lx[0]),Bsc*(Lx[1]-Lx[0])]);
12434: Vy=newvect(2,[Ac*(Ly[0]-Ly[1]),Bss*(Ly[1]-Ly[0])]);
12435: Vz=newvect(2,[0,Bc*(LZ[1]-LZ[0])]);
12436: OL=OL0=append(OPT0,OL);
12437: if(TikZ && type(Ura)==4 && length(Ura)>2) OL0=cons(["opt",Ura[2]],OL);
12438: LL=[[P0+Vz,P0+Vx+Vz],[P0,P0+Vx]];
12439: if(Bs>0){
12440: LL=cons([P0+Vy+Vz,Pz=P0+Vx+Vy+Vz],LL);
12441: LL=cons([P0+Vx+Vz,Pz],LL);
12442: PP=Pz-Vz;
12443: }
12444: else{
12445: LL=cons([P0+Vy,Pz=P0+Vx+Vy+Vz],LL);
12446: LL=cons([P0+Vx,Pz],LL);
12447: PP=Pz+Vz;
12448: }
12449: J=ceil((PP[0]-X0)/XD+0.5);
12450: LL=append([[P0+Vy,P0+Vy+Vz],[P0+Vy,P0+Vy+Vz],[P0+Vx,P0+Vx+Vz],[P0,P0+Vz],
12451: [P0+Vz,P0+Vy+Vz],[P0,P0+Vy]],LL);
12452: for(LL=reverse(LL);LL!=[];LL=cdr(LL)) Out=saveproc(xylines(car(LL)|option_list=OL0),Out);
12453: if(Dev>4) Dev2=ceil(Dev/2);
12454: if(FC<0 && Raw!=1){
12455: if(TikZ){
12456: if(type(Ura)==4 && length(Ura)>2)
12457: OL1=cons(["opt",Ura[2]+",dotted"],OL);
12458: else OL1=cons(["opt","dotted"],OL);
12459: }else OL1=cons(["opt","@{.}"],OL);
12460: if(FC==-8) FC=0;
12461: }
12462: for(I=0;I<3;I++){ /* box with hidden part */
12463: if(I==1) Pz=PP-Vx;
12464: else if(I==2) Pz=PP-Vy;
12465: LP=Pz-PP;
12466: for(FV=-1,K=0;K<=Dev2; K++){
12467: PPx=PP[0]+(K/Dev2)*LP[0]; PPy=PP[1]+(K/Dev2)*LP[1];
12468: J=ceil((PPx-X0)/XD);
12469: if(K!=Dev2 && (J<0||J>Dev)) continue;
12470: if(K!=Dev2 && (ZF[J]==0 || PPy<Z0[J] || PPy>Z1[J])){ /* visible */
12471: if(FV!=1){
12472: FV=1;
12473: PPP=[PPx,PPy];
12474: }
12475: }else{
12476: if(FV!=0){
12477: if(FV==1) Out=saveproc(xylines([PPP,[PPx,PPy]]|option_list=OL1),Out);
12478: FV=0;
12479: }
12480: }
12481: }
12482: }
12483: if(FC!=0 && Raw!=1){ /* show coordinate*/
12484: if(iand(FC,4)){
12485: Sub=1;
12486: if(TikZ){
12487: S0="\\scriptsize";S1="";
12488: }else{
12489: S0="{}_{"; S1="}";
12490: }
12491: }else Sub=0;
12492: if(iand(FC,2))
12493: LLL=[[1,0,P0+Vx,(TikZ)?"right":"+!L"],[3,0,P0+Vy,(TikZ)?"left":"+!R"]];
12494: else LL=[];
12495: if(Bs>0){
12496: LLL=cons([0,0,P0,(TikZ)?"below":"+!U"],LLL);
12497: LLL=cons([2,1,P0+Vx+Vy+Vz,(TikZ)?"above":"+!D"],LLL);
12498: }else{
12499: LLL=cons([2,0,P0+Vx+Vy,(TikZ)?"below":"+!U"],LLL);
12500: LLL=cons([0,1,P0+Vz,(TikZ)?"above":"+!D"],LLL);
12501: }
12502: for(TLL=LLL;TLL!=[];TLL=cdr(TLL)){
12503: TL=car(TLL);LL=L[(Sh+TL[0])%4];
12504: if(Cpx==0 || Cpx==3){
12505: S=ltotex([LL[0],LL[1],LZ[TL[1]]]|opt="coord");
12506: SS="("+rtostr(LL[0]) +","+rtostr(LL[1])+","+rtostr(LZ[TL[1]])+")";
12507: }else{
12508: S=ltotex([LL[0]+LL[1]*@i,LZ[TL[1]]]|opt="coord",cpx=Cpx);
12509: SS="("+rtostr(LL[0])+"+"+rtostr(LL[1])+"i,"+ rtostr(LZ[TL[1]])+")";
12510: }
12511: if(TikZ) S="$"+S+"$";
12512: if(Sub) S=S0+S+S1;
12513: if(!TikZ) S="$"+S+"$";
12514: if(Proc) Out=cons([2,OptSc,[TL[2][0],TL[2][1]],[[TL[3],S]],SS],Out);
12515: else str_tb(xyput([TL[2][0],TL[2][1],[TL[3],S]]|option_list=OptSc),Out);
12516: }
12517: }
12518: }
12519: if(type(Pt=getopt(pt))==4){ /* option pt=[] */
12520: if(type(Pt[0])<4) Pt=[[Pt]];
12521: if(length(Pt)>1&&type(Pt[1])!=4) Pt=[Pt];
12522: for(PT=Pt;PT!=[];PT=cdr(PT)){
12523: PP=car(PT);
12524: if(type(PP)==4 && length(PP)==3 && type(PP[0])<2 && type(PP[2])<2) PP=[PP];
12525: P=car(PP);
12526: if(type(P)==7) Q=[P,0];
12527: else if(P==1) Q=["_",0];
12528: else Q=mysubst([CX,CY],[[x,deval(P[0])],[y,deval(P[1])],[z,deval(P[2])]]);
12529: if(length(PP)>1 && type(PP[1])==4 && length(PP[1])==3){ /* draw line */
12530: PP=cdr(PP);P=car(PP);
12531: if(type(P)==7) Q1=P;
12532: else if(P==1) Q="_";
12533: else Q1=mysubst([CX,CY],[[x,deval(P[0])],[y,deval(P[1])],[z,deval(P[2])]]);
12534: if(length(PP)<2 || PP[1]==0 || iand(PP[1],1)) OL2="";
12535: else OL2=(TikZ)?"dotted":"@{.}";
12536: if(length(PP)>2 && type(PP[2])==7){
12537: if(OL2=="") OL2=PP[2];
12538: else{
12539: if(TikZ) OL2=OL2+",";
12540: OL2=OL2+PP[2];
12541: }
12542: }
12543: OL1=OL;
12544: if(OL2!="") OL1=cons(["opt",OL2],OL1);
12545: if(length(PP)<2 || PP[1]>=0)
12546: Out=saveproc(xylines([Q,Q1]|option_list=OL1),Out);
12547: else{
12548: LP0=Q1[0]-Q[0];LP1=Q1[1]-Q[1];
12549: for(FV=-1,K=0;K<=Dev2; K++){
12550: PPx=Q[0]+(K/Dev2)*LP0; PPy=Q[1]+(K/Dev2)*LP1;
12551: J=ceil((PPx-X0)/XD);
12552: if(K!=Dev2 && (J<0 || J>Dev || ZF[J]==0 || PPy<Z0[J] || PPy>Z1[J])){
12553: /* visible */
12554: if(FV!=1){
12555: FV=1;
12556: PPP=[PPx,PPy];
12557: }
12558: }else{
12559: if(FV!=0){
12560: if(FV==1) Out=saveproc(xylines([PPP,[PPx,PPy]]|option_list=OL1),Out);
12561: FV=0;
12562: }
12563: }
12564: }
12565: }
12566: continue;
12567: }
12568: if(length(PP)==1) S="$\\bullet$";
12569: else if(type(PP[1])==7) S=PP[1];
12570: else if(type(PP[1])==4){
12571: if(length(PP[1])>1 && type(PP[1][1])!=7)
12572: S=cons(car(PP),cons("$\\bullet$",cdr(cdr(PP))));
12573: else S=PP[1];
12574: }else S="$\\bullet$";
12575: if(length(PP)<=2){
12576: if(Proc) Out=cons([2,OptSc,[Q[0],Q[1]],[S]],Out);
12577: else str_tb(xyput([Q[0],Q[1],S]|option_list=OptSc),Out);
12578: }else if(!TikZ){
12579: if(Proc) Out=cons([2,OptSc,[Q[0],Q[1]],[S,"",PP[2]]],Out);
12580: else str_tb(xyput([Q[0],Q[1],S,"",PP[2]]|option_list=OptSc),Out);
12581: }else{
12582: if(Proc) Out=cons([2,OptSc,[Q[0],Q[1]],cons(S,cdr(cdr(PP)))],Out);
12583: else str_tb(xyput(append([Q[0],Q[1],S],cdr(cdr(PP)))|option_list=OptSc),Out);
12584: }
12585: }
12586: }
12587: if(Proc){
12588: S=reverse(Out);
12589: if(Proc==1||Proc==3){
12590: for(W=[],I=0;I<2;I++) for(J=0;J<2;J++) for(K=0;K<2;K++)
12591: W=cons(mysubst([CX*Sc,CY*Sc],[[x,Lx[I]],[y,Ly[J]],[z,Lz[K]]]),W);
12592: W=ptbbox(W);
12593: S=cons([0,W[0],W[1],(TikZ)?1:1/10],S);
12594: }
12595: }else S=str_tb(0,Out);
12596: if(type(Dvi)!=1||(Proc&&abs(Dvi)<2)) return S;
12597: Lout=[];
12598: if(abs(Dvi)>=2){
12599: /* show title */
12600: L0=[];
12601: Title=getopt(title);
12602: if(type(Title)!=7)
12603: Title=(type(F00)==4)?("\\texttt{"+verb_tex_form(F00)+"}"):my_tex_form(F00);
12604: if(type(Title)==7){
12605: T=my_tex_form(L[3][0])+"\\le x\\le "+my_tex_form(L[1][0])+",\\,"+
12606: my_tex_form(L[3][1])+"\\le y\\le "+my_tex_form(L[1][1])+")";
12607: if(Proc){
12608: if(Cpx>=1) L0=[[5,[["eq",1]],"|"+Title+"|\\quad(z=x+yi,\\ "+T]];
12609: else L0=[[5,[["eq",1]],"z="+Title+"\\ \\ ("+T]];
12610: }else{
12611: if(Cpx>=1) dviout("|"+Title+"|\\quad(z=x+yi,\\ "+T|eq=1,keep=1);
12612: else dviout("z="+Title+"\\ \\ ("+T|eq=1,keep=1);
12613: }
12614: }
12615: A=rint(deval(180*A/@pi))+90*(Sh-1);
12616: if(A>=180) A-=180;
12617: B=rint(deval(180*B/@pi));
12618: if(abs(Dvi)>=3){
12619: T="\\text{angle } ("+my_tex_form(A)+"^\\circ,"+my_tex_form(B)+"^\\circ)";
12620: if(Ratio!=1 || Ratio2!=1) T=T+"\\quad\\text{ratio }1:"
12621: +my_tex_form(sint(Ratio2,2))+":"+my_tex_form(sint(Ratio,2));
12622: if(Proc) L0=cons([5,[["eq",1]],T],L0);
12623: else dviout(T|eq=1,keep=1);
12624: }
12625: SS="% range "+rtostr([L[3][0],L[1][0]])+"x"+rtostr([L[3][1],L[1][1]])+
12626: " angle ("+ rtostr(A) +","+ rtostr(B)+") dev=";
12627: if(M1==M2) SS=SS+rtostr(M1);
12628: else SS=SS+rtostr([M1,M2]);
12629: if(M3!=1) SS=SS+" acc="+rtostr(M3);
12630: if(type(Sc0)>=0) SS=SS+" scale="+rtostr(Sc0);
12631: if(Proc){
12632: S=cons([5,[],SS],S);
12633: for(;L0!=[];L0=cdr(L0)) S=cons(car(L0),S);
12634: return S;
12635: }
12636: if(Dvi>0){
12637: dviout(SS|keep=1);
12638: dviout(xyproc(S)|eq=8);
12639: }else Lout=[SS,S];
12640: }else{
12641: if(Dvi>0) dviout(xyproc(S));
12642: else Lout=[S];
12643: }
12644: if(getopt(trans)==1) return cons([CX*Sc,CY*Sc],Lout);
12645: if(Dvi<0) return Lout;
12646: }
12647:
1.20 takayama 12648: def orthpoly(N)
12649: {
12650: F=0;
12651: if(type(P=getopt(pol))==7){
12652: for(L=["Le","Ge","Tc","2T","Ja","He","La","Se"];L!=[];L=cdr(L),F++)
12653: if(str_str(P,car(L)|end=2)==0) break;
12654: }else P=0;
12655: if(type(D=N)==4) D=N[0];
12656: if(!isint(D)||D<0) return 0;
12657: if(F==0) return seriesHG([-D,D+1],[1],(1-x)/2,D);
12658: if(F==1) return red(seriesHG([-D,D+2*N[1]],[N[1]+1/2],(1-x)/2,D)*binom(D+2*N[1]-1,D));
12659: if(F==2) return seriesHG([-D,D],[1/2],(1-x)/2,D);
12660: if(F==3){
12661: if(D==0) return 0;
12662: return orthpoly([D-1,1]|pol="Ge");
12663: }
12664: if(F==4) return red(seriesHG([-D,D+N[1]],[N[2]],x,D));
12665: if(F==5){
12666: for(S=I=1;I<=D;I+=2) S*=I;
12667: if(iand(D,1)) return seriesHG([-(D-1)/2],[3/2],x^2/2,D-1)*x*S*(-1)^((D-1)/2);
12668: else return seriesHG([-D/2],[1/2],x^2/2,D)*S*(-1)^(D/2);
12669: }
12670: if(F==6){
12671: NN=(type(N)==4)?N[1]:0;
12672: return red(seriesHG([-D],[NN+1],x,D)*binom(D+NN,D));
12673: }
12674: if(F==7){
12675: NN=N[1];
12676: for(S=1,I=1;I<=D;I++) S+=(-1)^I*binom(D,I)*binom(D+I,I)*sftpow(x,I)/sftpow(NN,I);
12677: return S;
12678: }
12679: return 0;
12680: }
12681:
12682: def schurpoly(L)
12683: {
12684: N=length(L);
12685: for(R=[],I=1;L!=[];L=cdr(L),I++) R=cons(car(L)+N-I,R);
12686: L=reverse(R);
12687: if(type(X=getopt(var))!=4){
12688: V=(type(X)>1)?X:"x";
12689: for(X=[],I=0;I<N;I++) X=cons(makev([V,N-I]),X);
12690: }
12691: M=newmat(N,N);
12692: for(I=0;I<N;I++)
12693: for(J=0;J<N;J++) M[I][J]=X[I]^L[J];
12694: P=det(M);
12695: for(I=0;I<N;I++)
12696: for(J=I+1;J<N;J++) P=sdiv(P,X[I]-X[J]);
12697: return P;
12698: }
12699:
1.6 takayama 12700: def fouriers(A,B,X)
12701: {
1.20 takayama 12702: if((Y=getopt(y))==0||type(Y)>0) Y=deval(Y);
12703: else Y=0;
12704: if((V=getopt(const))==0||type(V)>0){
12705: V=myfeval(V,Y);
12706: K=1;
12707: }else K=0;
1.6 takayama 12708: if(A!=[]&&type(car(A))>1){
1.20 takayama 12709: for(C=[],I=A[1];I>=K;I--) C=cons(myf2eval(car(A),I,Y),C);
12710: if(K) C=cons(0,C);
1.6 takayama 12711: A=C;
12712: }
1.20 takayama 12713: if(K){
12714: if(A!=[]) A=cdr(A);
12715: A=cons(V,A);
12716: }
1.6 takayama 12717: if(B!=[]&&type(car(B))>1){
1.20 takayama 12718: for(C=[],I=B[1];I>0;I--) C=cons(myf2eval(car(B),I,Y),C);
1.6 takayama 12719: B=C;
12720: }
1.20 takayama 12721: L=length(B)+1;
12722: if(length(A)>=L) L=length(A)+1;
12723: if(type(Sum=getopt(sum))>0){
12724: if(Sum==1) Sum=1-x;
12725: else if(Sum==2) Sum=[(z__)/(3.1416*x),[z__,os_md.mysin,3.1416*x]];
12726: else Sum=f2df(Sum);
12727: C=[];
12728: if(A!=[]){
12729: C=cons(car(A),C);
12730: A=cdr(A);
12731: }
12732: for(I=1;A!=[];A=cdr(A),I++) C=cons(car(A)*myf2eval(Sum,I/L,L),C);
12733: A=reverse(C);
12734: for(C=[],I=1;B!=[];B=cdr(B),I++) C=cons(car(B)*myf2eval(Sum,I/L,L),C);
12735: B=reverse(C);
12736: }
1.6 takayama 12737: if(getopt(cpx)==1){
1.20 takayama 12738: if(type(X=eval(X))>1) return todf([os_md.fouriers,[["cpx",1]]],[[A],[B],[X]]);
1.6 takayama 12739: V=dexp(@i*X);
12740: for(C=A,P=1,I=0;C!=[];C=cdr(C),I++){
1.20 takayama 12741: R+=S*car(C)*P;
1.6 takayama 12742: P*=V;
12743: }
12744: V=dexp(-@i*X);
12745: for(C=B,P=1,I=0;C!=[];C=cdr(C),I++){
12746: P*=V;
12747: R+=car(C)*P;
12748: }
12749: return R;
12750: }
12751: if(type(X=eval(X))>1) return todf(os_md.fouriers,[[A],[B],[X]]);
12752: for(C=A,I=0;C!=[];C=cdr(C),I++)
12753: R+=car(C)*mycos(I*X);
12754: for(C=B,I=1;C!=[];C=cdr(C),I++)
12755: R+=car(C)*mysin(I*X);
12756: return R;
12757: }
12758:
12759:
12760: def myexp(Z)
12761: {
12762: if(type(Z=eval(Z))>1) return todf(os_md.myexp,[Z]);
12763: if((Im=imag(Z))==0) return dexp(Z);
12764: return dexp(real(Z))*(dcos(Im)+@i*dsin(Im));
12765: }
12766:
12767: def mycos(Z)
12768: {
12769: if(type(Z=eval(Z))>1) return todf(os_md.mycos,[Z]);
12770: if((Im=imag(Z))==0) return dcos(Z);
12771: V=myexp(Z*@i);
12772: return (V+1/V)/2;
12773: }
12774:
12775: def mysin(Z)
12776: {
12777: if(type(Z=eval(Z))>1) return todf(os_md.mysin,[Z]);
12778: if((Im=imag(Z))==0) return dsin(Z);
12779: V=myexp(Z*@i);
12780: return (1/V-V)*@i/2;
12781: }
12782:
12783: def mytan(Z)
12784: {
12785: if(type(Z=eval(Z))>1) return todf(os_md.mytan,[Z]);
1.17 takayama 12786: if((Im=imag(Z))==0) return dtan(Z);
1.6 takayama 12787: V=myexp(2*Z*@i);
12788: return @i*(1-V)/(1+V);
12789: }
12790:
12791: def mylog(Z)
12792: {
12793: if(type(Z=eval(Z))>1) return todf(os_md.mylog,[Z]);
12794: if((Im=imag(Z))==0) return dlog(Z);
12795: return dlog(dabs(Z))+@i*myarg(Z);
12796: }
12797:
12798: def mypow(Z,R)
12799: {
12800: if(type(Z=eval(Z))>1||type(R=eval(R))>1) return todf(os_md.mypow,[Z,R]);
12801: if(Z==0) return 0;
12802: if(isint(2*R)){
12803: if(R==0) return 1;
12804: if(isint(R)) return Z^R;
12805: V=dsqrt(Z);
12806: if(R==1/2) return V;
12807: return Z^(R-1/2)*V;
12808: }
12809: return myexp(R*mylog(Z));
12810: }
12811:
12812: def myarg(Z)
12813: {
12814: if(type(Z=map(eval,Z))==4){
12815: if(length(Z)!=2) return todf(os_md.myarg,[Z]);
12816: Re=Z[0];Im=Z[1];
12817: }else if(type(Z)>1){
12818: return todf(os_md.myarg,[Z]);
12819: }else {
12820: Im=imag(Z);Re=real(Z);
12821: }
12822: if(Re==0) return (Im<0)?-deval(@pi)/2:deval(@pi)/2;
12823: V=datan(Im/Re);
12824: if(Re>0) return V;
12825: return (V>0)?(V-deval(@pi)):(V+deval(@pi));
12826: }
12827:
12828: def myatan(Z)
12829: {
12830: if(type(Z=eval(Z))>1) return todf(os_md.myatan,[Z]);
12831: if((Im=imag(Z))==0) return datan(Z);
12832: mylog((1-Z*@i)/(1+Z*@i))*@i/2;
12833: }
12834:
12835: def myasin(Z)
12836: {
12837: if(type(Z=eval(Z))>1) return todf(os_md.myasin,[Z]);
12838: return deval(@pi/2)-myacos(Z);
12839: }
12840:
12841: def frac(X)
12842: {
12843: if(type(X=eval(X))>1) return todf(os_md.frac,[X]);
12844: return (ntype(X)==3)? pari(frac,X):(X-floor(X));
12845: }
12846:
12847: def myacos(Z)
12848: {
12849: if(type(Z=eval(Z))>1) return todf(os_md.myacos,[Z]);
12850: if(imag(Z)==0 && Z<=1 && Z>=-1) return dacos(Z);
12851: return mylog(Z-dsqrt(Z^2-1))*@i;
12852: }
12853:
12854: def arg(Z)
12855: {
12856: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.arg,[Z]);
12857: return (type(Z)==4)?pari(arg,Z[0],Z[1]):arg(sqrt,Z);
12858: }
12859:
12860: def sqrt(Z){
12861: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.sqrt,[Z]);
12862: R=(type(Z)==4)?Z[1]:Z;
12863: if(ntype(R)==0){
12864: if(R==0) return 0;
12865: if(R>0){
12866: if(pari(issquare,R)) return pari(isqrt,nm(R))/pari(isqrt,dn(R));
12867: }else{
12868: R=-R;
12869: if(pari(issquare,R)) return pari(isqrt,nm(R))/pari(isqrt,dn(R))*@i;
12870: }
12871: }
12872: return (type(Z)==4)?pari(sqrt,Z[0],Z[1]):pari(sqrt,Z);
12873: }
12874:
12875: def gamma(Z)
12876: {
12877: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.gamma,[Z]);
12878: return (type(Z)==4)?pari(gamma,Z[0],Z[1]):pari(gamma,Z);
12879: }
12880:
12881: def lngamma(Z)
12882: {
12883: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.lngamma,[Z]);
12884: return (type(Z)==4)?pari(lngamma,Z[0],Z[1]):pari(lngamma,Z);
12885: }
12886:
12887: def digamma(Z)
12888: {
12889: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.digamma,[Z]);
12890: return (type(Z)==4)?pari(digamma,Z[0],Z[1]):pari(digamma,Z);
12891: }
12892:
12893: def dilog(Z)
12894: {
12895: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.dilog,[Z]);
12896: return (type(Z)==4)?pari(dilog,Z[0],Z[1]):pari(dilog,Z);
12897: }
12898:
12899: def erfc(Z)
12900: {
12901: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.erfc,[Z]);
12902: return (type(Z)==4)?pari(erfc,Z[0],Z[1]):pari(erfc,Z);
12903: }
12904:
12905: def zeta(Z)
12906: {
12907: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.zeta,[Z]);
12908: return (type(Z)==4)?pari(zeta,Z[0],Z[1]):pari(zeta,Z);
12909: }
12910:
12911: def eta(Z)
12912: {
12913: if(vars(Z=map(eval,Z))!=[]) return todf(os_md.eta,[Z]);
12914: return (type(Z)==4)?pari(eta,Z[0],Z[1]):pari(eta,Z);
12915: }
12916:
12917: def jell(Z)
12918: {
12919: if(vars(Z=map(eval,V))>1) return todf(os_md.jell,[Z]);
12920: return (type(Z)==4)?pari(jell,Z[0],Z[1]):jell(jell,Z);
12921: }
12922:
12923: def evals(F)
12924: {
12925: if(type(F)==7){
12926: if(type(Del=getopt(del))!= 7) return eval_str(F);
12927: S=strtoascii(Del);K=length(S);
12928: if(K==0) return [eval_str(F)];
12929: Raw=getopt(raw);
12930: F=strtoascii(F);L=[];T1=0;
12931: do{
12932: T2=str_str(F,S|top=T1);
12933: if(T2<0) T2=10000;
12934: FT=str_cut(F,T1,T2-1);
12935: L=cons((Raw==1)?FT:evals(FT),L);
12936: T1=T2+K;
12937: }while(T2!=10000);
12938: return reverse(L);
12939: }
12940: if(type(F)==4){
12941: if(type(S=car(F))==7){
12942: S+="(";
12943: for(I=0,FT=cdr(F); FT!=[]; I++,FT=cdr(FT)){
12944: if(type(ST=car(FT))!=7) ST=rtostr(ST);
12945: if(I>0) S=S+","+ST;
12946: else S=S+ST;
12947: }
12948: S=S+")";
12949: return eval_str(S);
12950: }else return call(S,cdr(F));
12951: }
12952: return F;
12953: }
12954:
12955: def myval(F)
12956: {
12957: if(type(F)!=4){
12958: F=f2df(sqrt2rat(F));
12959: if(type(F)!=4) return F;
12960: };
12961: if(length(F)==1) V=car(F);
12962: else for(V=car(F),F=cdr(F); F!=[];){
12963: FT=car(F);
12964: if(type(G=FT[1])==2){
12965: if(length(FT)>2){
12966: FT2=myval(FT[2]);
12967: if(length(FT)>3) FT3=myval(FT[3]);
12968: };
12969: X=red(FT2/@pi);Vi=-red(FT2*@i/@pi);W=red(FT2/@e);
12970: if(G==os_md.mypow && FT3==1/2){
12971: G=os_md.sqrt;
12972: FT=[FT[0],G,FT[2]];
12973: }
12974: if((T=findin(G,
12975: [sin,os_md.mysin,cos,os_md.mycos,tan,os_md.mytan]))>=0
12976: &&(isint(6*X)||isint(4*X))){
12977: if(T==2||T==3){
12978: T=0;X=1/2-X;
12979: }
12980: X=X-floor(X/2)*2;
12981: if(T==0||T==1){
12982: if(X>1){
12983: S=-1;X-=1;
12984: }else S=1;
12985: if(X>1/2) X=1-X;
12986: if(X==0) R=0;
12987: else if(X==1/6) R=1/2;
12988: else if(X==1/4) R=2^(1/2)/2;
12989: else if(X==1/3) R=3^(1/2)/2;
12990: else R=1;
12991: R*=S;
12992: }else{
12993: if(X>1) X-=1;
12994: if(X>1/2){
12995: S=-1;V=1-X;
12996: }else S=1;
12997: if(X==0) R=0;
12998: else if(X==1/6) R=3^(1/2)/3;
12999: else if(X==1/4) R=1;
13000: else if(X==1/3) R=3^(1/2);
13001: else R=2^512;
13002: R*=S;
13003: }
13004: }else if((G==exp||G==os_md.myexp)&&(isint(FT2)||isint(6*Vi)||isint(4*Vi))){
13005: if(isint(FT2)) R=@e^FT2;
13006: else R=myval([z+w*@i,[z,cos,Vi*@pi],[w,sin,Vi*@pi]]);
13007: }else if((G==pow||G==os_md.mypow) && (isint(FT3)||FT2==1||FT2==0)){
13008: if(FT2==0) R=0;
13009: else if(FT2==1) R=1;
13010: else R=FT2^FT3;
13011: }else if(G==os_md.abs&&ntype(P=eval(FT2))<4){
13012: R=FT2;
13013: if(P<0) R=-R;
13014: }else if((G==os_md.sqrt||G==dsqrt)&&type(FT2)<2&&ntype(FT2)==0)
13015: R=sqrtrat(FT2);
13016: else if((G==os_md.mylog||G==dlog)&&(FT2==@e||FT2==1))
13017: R=(FT2==1)?0:1;
13018: else if(length(FT)==3) R=eval((*G)(myeval(FT2)));
13019: #ifdef USEMODULE
13020: else R=call(G,map(os_md.myeval,cdr(cdr(FT))));
13021: #else
13022: else R=call(G,map(myeval,cdr(cdr(FT))));
13023: #endif
13024: }
13025: else if(G==0) R=FT[2];
13026: #ifdef USEMODULE
13027: else R=eval(call(G[0],map(os_md.myeval,cdr(cdr(FT)))|option_list=G[1]));
13028: #else
13029: else R=eval(call(G[0],map(myeval,cdr(cdr(FT)))|option_list=G[1]));
13030: #endif
13031: V=mysubst(V,[FT[0],R]);
13032: F=mysubst(cdr(F),[FT[0],R]);
13033: }
13034: if(type(V)<4 && !iscoef(V,os_md.iscrat)) V=eval(V);
13035: #if 0
13036: return (type(V)<4)?myeval(V):mtransbys(os_md.myeval,V,[]);
13037: #else
13038: return V;
13039: #endif
13040: }
13041:
13042: /* -1:空 0:整数 1:有理数 2:Gauss整数 3:Gauss有理数 4:それ以外の複素数 */
13043: /* def vntype(F)
13044: {
13045: if((T=type(F))<2){
13046: if(T<0) return -1;
13047: if((Tn=ntype(F))==0){
13048: return (isint(F))?0:1;
13049: }
13050: if(Tn==4){
13051: if(ntype(real(F))==0&&ntype(real(F))==0)
13052: return (isint(F)&&isint(F))?2:3;
13053: return 4;
13054: }
13055: }
13056: if(T==2){
13057: V=vars(F);
13058: if((VV=lsort(V,[@e,@pi],1))==[]){
13059: FT=mycoef(
13060: }else{
13061: if(length(VV)==1){
13062: }else
13063: }
13064: }else if(T==3){
13065:
13066: }
13067: }
13068: */
13069:
13070:
13071: def myeval(F)
13072: {
13073: if(type(F)!=4) V=F;
13074: else if(length(F)==1) V=car(F);
13075: else for(V=car(F),F=cdr(F); F!=[];){
13076: FT=car(F);
13077: if(type(G=FT[1])==2){
13078: if(length(FT)==3) R=(*G)(myeval(FT[2]));
13079: #ifdef USEMODULE
13080: else R=call(G,map(os_md.myeval,cdr(cdr(FT))));
13081: #else
13082: else R=call(G,map(myeval,cdr(cdr(FT))));
13083: #endif
13084: }
13085: else if(G==0) R=myeval(FT[2]);
13086: #ifdef USEMODULE
13087: else R=call(G[0],map(os_md.myeval,cdr(cdr(FT)))|option_list=G[1]);
13088: #else
13089: else R=call(G[0],map(myeval,cdr(cdr(FT)))|option_list=G[1]);
13090: #endif
13091: V=mysubst(V,[FT[0],R]);
13092: F=mysubst(cdr(F),[FT[0],R]);
13093: }
13094: return (type(V)<4)?eval(V):mtransbys(eval,V,[]);
13095: }
13096:
13097: def mydeval(F)
13098: {
13099: if(type(F)!=4) V=F;
13100: else if(length(F)==1) V=car(F);
13101: else for(V=car(F),F=cdr(F); F!=[]; ){
13102: FT=car(F);
13103: if(type(G=FT[1])==2){
13104: if(length(FT)==3) R=(*G)(myeval(FT[2]));
13105: #ifdef USEMODULE
13106: else R=call(G,map(os_md.mydeval,cdr(cdr(FT))));
13107: #else
13108: else R=call(G,map(mydeval,cdr(cdr(FT))));
13109: #endif
13110: }
13111: else if(G==0) R=mydeval(FT[2]);
13112: #ifdef USEMODULE
13113: else R=call(G[0],map(os_md.mydeval,cdr(cdr(FT)))|option_list=G[1]);
13114: #else
13115: else R=call(G[0],map(mydeval,cdr(cdr(FT)))|option_list=G[1]);
13116: #endif
13117: V=mysubst(V,[FT[0],R]);
13118: F=mysubst(cdr(F),[FT[0],R]);
13119: }
13120: return (type(V)<4)?deval(V):mtransbys(deval,V,[]);
13121: }
13122:
13123: def myfeval(F,X)
13124: {
13125: if(type(X)==4){
13126: if(isvar(X[0])&&length(X)==2)
13127: return mydeval(mysubst(F,[X[0],X[1]]));
13128: if(type(X[0])==4&&isvar(X[0][0])&&length(X[0])==2){
13129: for(Y=X;Y!=[];Y=cdr(Y))
13130: F=mysubst(F,[car(Y)[0],car(Y)[1]]);
13131: return myeval(F);
13132: }
13133: }
13134: return myeval(mysubst(F,[x,X]));
13135: }
13136:
13137: def myf2eval(F,X,Y)
13138: {
13139: return myeval(mysubst(F,[[x,X],[y,Y]]));
13140: }
13141:
13142: def myf3eval(F,X,Y,Z)
13143: {
13144: return myeval(mysubst(F,[[x,X],[y,Y],[z,Z]]));
13145: }
13146:
13147: def myfdeval(F,X)
13148: {
13149: if(type(X)==4){
13150: if(isvar(X[0])&&length(X)==2)
13151: return mydeval(mysubst(F,[X[0],X[1]]));
13152: if(type(X[0])==4&&isvar(X[0][0])&&length(X[0])==2){
13153: for(Y=X;Y!=[];Y=cdr(Y))
13154: F=mysubst(F,[car(Y)[0],car(Y)[1]]);
13155: return mydeval(F);
13156: }
13157: }
13158: return mydeval(mysubst(F,[x,X]));
13159: }
13160:
13161: def myf2deval(F,X,Y)
13162: {
13163: return mydeval(mysubst(F,[[x,X],[y,Y]]));
13164: }
13165:
13166: def myf3deval(F,X,Y,Z)
13167: {
13168: return mydeval(mysubst(F,[[x,X],[y,Y],[z,Z]]));
13169: }
13170:
13171: def df2big(F)
13172: {
13173: AG=[[os_md.mysin,sin],[os_md.mycos,cos],[os_md.mytan,tan],[os_md.myasin,asin],
13174: [os_md.acos,acos],[os_md,atan,atan],[os_md.myexp,exp],[os_md.mylog,log],[os_md.mypow,pow]];
13175: if(getopt(inv)!=1) return mysubst(F,AG);
13176: else return mysubst(F,AG|inv=1);
13177:
13178: }
13179:
13180: def f2df(F)
13181: {
13182: if(type(Opt=getopt(opt))!=1) Opt=0;
13183: if(iand(Opt,1)){
13184: if(Opt>0) F=map(eval,F);
13185: else F=map(deval,F);
13186: }
13187: Cpx=getopt(cpx);
13188: if(type(F)==4 && iand(Opt,2)==0) return F;
13189: K=getopt(level);
13190: if(type(K)!=1) K=0;
13191: AG=[sin,cos,tan,asin,acos,atan,exp,sinh,cosh,tanh,log,pow];
13192: AGd=[os_md.mysin,os_md.mycos,os_md.mytan,os_md.myasin,os_md.myacos,
13193: os_md.myatan,os_md.myexp,os_md.myexp,os_md.myexp,os_md.myexp,
13194: os_md.mylog,os_md.sqrt,os_md.myexp];
13195: for(R=[],I=0,Arg=vars(F);Arg!=[];Arg=cdr(Arg)){
13196: Fn=functor(car(Arg));
13197: if(vtype(Fn)!=3) continue;
13198: V=args(car(Arg));
13199: for(PAG=AG,PAGd=AGd;PAG!=[];PAG=cdr(PAG),PAGd=cdr(PAGd)){
13200: if(Fn==car(PAG)){
13201: if(K==0) L="z__";
13202: else L="z"+rtostr(K)+"__";
13203: if(I==0) VC=makev([L]);
13204: else VC=makev([L,I]);
13205: I++;
13206: VC0=VC;
13207: if(Fn==sinh || Fn==cosh || Fn==tanh){
13208: VC=makev([L,I++]);
13209: if(Fn==sinh)
13210: R=cons([VC0,0,(VC^2-1)/(2*VC)],R);
13211: else if(Fn==cosh)
13212: R=cons([VC0,0,(VC^2+1)/(2*VC)],R);
13213: else
13214: R=cons([VC0,0,(VC^2-1)/(VC^2+1)],R);
13215: }
13216: if(Fn==pow && (V[1]!=1/2||Cpx==1)){
13217: #if 0
13218: R0=f2df(V[1]*((type(V[0])==1)?dlog(V[0]):log(V[0]))|level=K+1);
13219: PAGd=cdr(PAGd);
13220: #else
13221: R=cons([VC,os_md.mypow,V[0],V[1]],R);
13222: F=mysubst(F,[car(Arg),VC0]);
13223: Arg=cons(0,vars(F));
13224: break;
13225: #endif
13226: }else R0=f2df(V[0]|level=K+1);
13227: R=cons([VC,car(PAGd),R0],R);
13228: F=mysubst(F,[car(Arg),VC0]);
13229: Arg=cons(0,vars(F));
13230: break;
13231: }
13232: }
13233: }
13234: if(R==[]) return F;
13235: if(Cpx==1){
13236: for(PAG=P,PAGd=AGd;PAG!=[];PAG=cdr(PAG),PAGd=cdr(PAGd))
13237: R=mysubst(R,[car(PADd),car(PAG)]);
13238: }
13239: return cons(F,reverse(R));
13240: }
13241:
13242: def todf(F,V)
13243: {
13244: if(type(V)!=4) V=[V];
13245: for(R=[];V!=[];V=cdr(V)){
13246: R=cons(f2df(car(V)),R);
13247: }
13248: V=reverse(R);
13249: Z=makenewv([F,V]);
13250: return [Z,cons(Z,cons(F,V))];
13251: }
13252:
13253: def compdf(F,V,G)
13254: {
13255: FL=["abs","floor","rint","zeta","gamma","arg","real","imag","conj"];
13256: FS=[os_md.abs,floor,rint,os_md.zeta,os_md.gamma,os_md.myarg,real,imag,conj];
13257: if(type(F)==7){
13258: if(str_str(F,"|")==0){
13259: F="abs("+str_cut(F,1,str_len(F)-2)+")";
13260: }else if(str_str(F,"[")==0){
13261: F="floor("+str_cut(F,1,str_len(F)-2)+")";
13262: }
13263: I=str_str(F,"(");
13264: Var=x;
13265: if(I>0){
13266: J=str_pair(F,I+1,"(",")");
13267: if(J<0) return 0;
13268: Var=eval_str(str_cut(F,I+1,J-1));
13269: Var=f2df(Var);
13270: F0=str_cut(F,0,I-1);
13271: }
13272: if((I=findin(F0,FL))<0&&(I=findin(F,FL))<0) F=f2df(eval_str(F));
13273: else F=[z__,[z__,FS[I],Var]];
13274: }
13275: if(type(F)!=4) F=f2df(F);
13276: if(type(G)!=4) G=f2df(G);
1.20 takayama 13277: if(V==G) return F; /* subst(F(V),V,G) */
1.6 takayama 13278: VF=vars(F);VG=vars(G);
1.20 takayama 13279: if(type(V)==4){
13280: for(VT=[],VV=V;VV!=[];VV=cdr(VV)){
13281: if(findin(car(VV),VF)>=0){
13282: X=makenewv(append(VF,VG));
13283: VF=cons(X,VF);
13284: F=mysubst(F,[car(VV),X]);
13285: VT=cons(X,VT);
13286: }else VT=cons(car(VV),VT);
13287: }
13288: for(V=reverse(VT);V!=[];V=cdr(V),G=cdr(G)) F=compdf(F,car(V),car(G));
13289: return F;
13290: }
1.6 takayama 13291: for(E=I=0;I<30;I++){
13292: for(J=0;J<30;J++){
13293: X=makev(["z__",I,J]);
13294: if(findin(X,VF)<0 && findin(X,VG)<0){
13295: E=1;break;
13296: }
13297: }
13298: if(E) break;
13299: }
13300: if(!E) return 0;
13301: if(type(G)<4) return mysubst(F,[V,G]);
13302: if(type(F)<4) F=[F]; /* return compdf([X,[X,0,F]],V,G); */
13303: F=mysubst(F,[V,X]);
13304: if(isvar(G[0])){
13305: G=mysubst(G,[G[0],X]);
13306: if(length(G)==2&&type(G[1])==4&&G[1][0]==X) G=G[1];
13307: G=cons(G,cdr(F));
13308: }
13309: else G=cons([X,0,G],cdr(F));
13310: return cons(car(F),G);
13311: }
13312:
13313: def fzero(F,LX)
13314: {
13315: if(length(LX)==3){
13316: V=LX[0];LX=cdr(LX);
13317: }else V=x;
13318: LX1=eval(LX[0]);LX2=eval(LX[1]);
13319: if(getopt(zero)==1){
13320: if(getopt(cont)==1) CT=1;
13321: else CT=0;
13322: if(getopt(trans)!=1 && type(F)<4) F=f2df(F);
13323: F=mysubst(F,[[@pi,deval(@pi)],[@e,deval(@e)]]);
13324: if(type(Dev=getopt(dev))!=1 || Dev<2) Dev=16;
13325: V1=myeval(mysubst(F,[V,X1=LX1]));
13326: V2=myeval(mysubst(F,[V,X2=LX2]));
13327: if(V1>0){
13328: V0=V1;V1=V2;V2=V0;
13329: X0=X1;X1=X2;X2=X0;
13330: }
13331: if(V1<0 && V2>0){
13332: D=(V2-V1)*1024;
13333: for(I=0; I<Dev; I++){
13334: /* mycat([D,X1,V1,X2,V2]) ; */
13335: if(iand(I,1)) X0=(X1+X2)/2;
13336: else X0=(V2*X1-V1*X2)/(V2-V1);
13337: V0=myeval(mysubst(F,[V,X0]));
13338: if(V0==0||V0==V1||V0==V2) return [X0,V0];
13339: if(V0<0){
13340: if(!CT && V0+D<0) return [];
13341: V1=V0;X1=X0;
13342: }else{
13343: if(!CT && V0>D) return [];
13344: V2=V0;X2=X0;
13345: }
13346: }
13347: X0=(V2*X1-V1*X2)/(V2-V1);
13348: return [X0,myeval(mysubst(F,[V,X0]))];
13349: }
13350: if(V0==0) return [X0,V0];
13351: if(V1==0) return [X1,V1];
13352: return [];
13353: }
13354: if(type(F)<4) F=f2df(F);
13355: F=mysubst(F,[[@pi,deval(@pi)],[@e,deval(@e)]]);
13356: L=[];
13357: if(type(F)<4){
13358: if(type(F)==3) F=nm(red(F));
13359: if((Deg=deg(F,V))<=2){
13360: if(Deg==2){
13361: D=(C1=coef(F,1,V))^2-4*(C2=coef(F,2,V))*coef(F,0,V);
13362: if(D>=0){
13363: R=dsqrt(D);
13364: if((S=(-C1+R)/(2*C2))>=LX1&&S<=LX2) L=[[S,mysubst(F,[V,S])]];
13365: if(D!=0 && (S=(-C1-R)/(2*C2))>=LX1&&S<=LX2) L=cons([S,mysubst(F,[V,S])],L);
13366: }
13367: L=qsort(L);
13368: }else if(Deg==1&&(S=-coef(F,0,V)/coef(F,1,V))>=LX1&&S<=LX2)
13369: L=[[S,mysubst(F,[V,S])]];
13370: return L;
13371: }
13372: for(L=[];S!=[];S=cdr(S))
13373: if(car(S)>=LX1&&car(S)<=LX2) L=cons([car(S),mysubst(F,[V,car(S)])],L);
13374: return qsort(L);
13375: }
13376: if(type(Div=getopt(mesh))!=1 || Div<=0)
13377: Div = 2^(10);
13378: W=(LX2-LX1)/Div;
13379: for(I=V2=0;I<=Div;I++){
13380: X1=X2;X2=LX1+I*W;V1=V2;
13381: if((V2=myeval(mysubst(F,[V,X2])))==0)
13382: L=cons([X2,V2],L);
13383: if(V1*V2<0){
13384: L0=fzero(F,[V,X1,X2]|zero=1,trans=1);
13385: if(L0!=[]) L=cons(L0,L);
13386: }
13387: }
13388: return reverse(L);
13389: }
13390:
13391: def fmmx(F,LX)
13392: {
13393: if(length(LX)==3){
13394: V=LX[0];LX=cdr(LX);
13395: }else V=x;
13396: LX1=eval(LX[0]);LX2=eval(LX[1]);
13397: FT=F;
13398: if(getopt(trans)!=1 && type(F)<4) FT=f2df(FT);
13399: FT=mysubst(FT,[[@pi,eval(@pi)],[@e,eval(@e)]]);
13400: if(type(G=getopt(dif))>=1){
13401: if(G==1) G=os_md.mydiff(F,V);
13402: L=fzero(G,[V,LX1,LX2]|option_list=getopt());
13403: R=[[LX1,myeval(mysubst(FT,[V,LX1]))]];
13404: for(I=0;L!=[];L=cdr(L),I++){
13405: X=car(L)[0];
13406: if(X==LX1) continue;
13407: R=cons([X,myeval(mysubst(FT,[V,X]))],R);
13408: }
13409: if(X!=LX2) R=cons([LX2,myeval(mysubst(FT,[V,LX2]))],R);
13410: if(getopt(mmx)!=1) return reverse(R);
13411: for(Mi=Ma=car(R);R!=[];R=cdr(R)){
13412: if(car(R)[1]>Ma[1]) Ma=car(R);
13413: else if(car(R)[1]<Mi[1]) Mi=car(R);
13414: }
13415: return [Mi,Ma];
13416: }
13417: if(type(Div=getopt(mesh))!=1 || Div<=0)
13418: Div = 2^(10);
13419: if(type(Dev=getopt(dev))!=1 || Dev<2) Dev=16;
13420: W=(LX2-LX1)/Div;
13421: for(I=V2=V3=0;I<=Div;I++){
13422: X1=X2;X2=X3;X3=LX1+I*W;V1=V2;V2=V3;
13423: V3=myeval(mysubst(FT,[V,X3]));
13424: if(I==0) L=[[X3,V3]];
13425: if(I<2) continue;
13426: if((V1-V2)*(V2-V3)<0){
13427: X02=X2;V02=V2;X03=X3;V03=V3;
13428: for(J=0; J<Dev && X1!=X3; J++){
13429: X12=(X1+X2)/2;V12=myeval(mysubst(FT,[V,X12]));
13430: if((V1-V12)*(V12-V2)<=0){
13431: X3=X2;V3=V2;X2=X12;V2=V12;continue;
13432: }
13433: X23=(X2+X3)/2;V23=myeval(mysubst(FT,[V,X23]));
13434: if((V12-V2)*(V2-V23)<=0){
13435: X1=X12;V1=V12;X3=X23;V3=V23;continue;
13436: }
13437: if((V2-V23)*(V23-V3)<=0){
13438: X1=X2;V1=V2;X2=X23;V2=V23;continue;
13439: }
13440: }
13441: L=cons([X2,V2],L);
13442: X2=X02;V2=V02;X3=X03;V3=V03;
13443: }
13444: }
13445: L=cons([LX2,myeval(mysubst(FT,[V,LX2]))],L);
13446: if(getopt(mmx)!=1) return L;
13447: for(Mi=Ma=car(L);L!=[];L=cdr(L)){
13448: if(car(L)[1]>Ma[1]) Ma=car(L);
13449: else if(car(L)[1]<Mi[1]) Mi=car(L);
13450: }
13451: return [Mi,Ma];
13452: }
13453:
13454: def flim(F,L)
13455: {
13456: FD=f2df(F);
13457: Lim0=4;Lim=12;FS=1;
13458: if(type(Pc=getopt(prec))==1){
13459: if((Pc>1&&Pc<31)||Pc>-5) Lim+=Pc;
13460: }
13461: if(type(Pc=getopt(init))==1 && Pc>0) FS*=Pc;
13462: if(type(L)==7) L=[L];
13463: else if(type(L)<2){
13464: K=flim(F,["+",L]|option_list=getopt());
13465: if(K=="") return K;
13466: K1=flim(F,["-",L]|option_list=getopt());
13467: if(K1=="") return K1;
13468: if(type(K)==7||type(K1)==7){
13469: if(K!=K1) return "";
13470: return K;
13471: }
13472: if(abs(K)<10^(-5)){
13473: if(abs(K1)<10^(-5)) return (K1+K)/2;
13474: else return "";
13475: }
13476: if(abs((K1-K)/K)<10^(-4)) return (K1+K)/2;
13477: return "";
13478: }
13479: if(type(L)!=4||type(L[0])!=7) return "";
13480: if(L[0]=="-"||L[0]=="-infty"){
13481: FS=-FS;
13482: }else if(L[0]!="+"&&L[0]!="infty") return "";
13483: FI=(length(L)==1)?1:0;
13484: for(Inf=0,I=Lim0;I<Lim;I++){
13485: D1=FS*8^I;D2=8*D1;
13486: if(FI==0){
13487: D1=1/D1;D2=1/D2;
13488: }
13489: if(D1>D2){
13490: D=D1;D1=D2;D1=D;
13491: X1=D1;X2=D2;
13492: }
13493: if(FI==0){
13494: D1+=L[1];D2+=L[1];
13495: }
13496: K=fmmx(FD,[D1,D2]|mmx=1,mesh=16,dev=4);
13497: if(I>Lim0){
13498: if(DF<K[1][1]-K[0][1]&&DF>10^(-8)&&DF<10^7){
13499: if(I>Lim0+1){
13500: if(Inf==0) return "";
13501: }else Inf=1;
13502: }else if(Inf==1) return "";
13503: }
13504: DF=K[1][1]-K[0][1];
13505: }
13506: if(Inf==1){
13507: if(K[0][1]>10^8) return "+";
13508: else if(K[1][1]<-10^8) return "-";
13509: return "";
13510: }
13511: V=(myfeval(FD,D1)+1.0)-1.0;
13512: if(V!=0 && abs(V)<10^(-9)) return 0;
13513: return V;
13514: }
13515:
13516: def fcont(F,LX)
13517: {
13518: if(length(LX)==3){
13519: V=LX[0];LX=cdr(LX);
13520: }else V=x;
13521: LX1=eval(LX[0]);LX2=eval(LX[1]);
13522: if(getopt(trans)!=1 && type(F)<4) FT=f2df(F);
13523: if(type(Div=getopt(mesh))!=1 || Div<=0)
13524: Div = 2^(10);
13525: if(type(Dev=getopt(dev))!=1 || Dev<2) Dev=16;
13526: W=(LX2-LX1)/Div;
13527: if((Df=getopt(dif))!=1){
13528: Df=0;
13529: }else{
13530: if(Dev==16) Dev=6;
13531: WD=W/2^(Dev+1);
13532: }
13533: F=FT;
13534: C=2;
13535: for(I=V2=V3=0;I<=Div;I++){
13536: X1=X2;X2=X3;X3=LX1+I*W;V1=V2;V2=V3;
13537: V3=myeval(mysubst(F,[V,X3]));
13538: if(Df){
13539: if(I==Div) break;
13540: V3=(myeval(mysubst(F,[V,X3+WD]))-V3)/WD;
13541: }
13542: if(I==0) L=[[X3,V3]];
13543: if(I<2) continue;
13544: if(C*dabs(2*V2-V1-V3) > dabs(V1-V3)){
13545: X01=X1;V01=V1;X02=X2;V02=V2;X03=X3;V03=V3;
13546: for(J=0; X01!=X03; J++){
13547: if(dabs(V01-V02)>dabs(V02-V03)){
13548: X03=X02;V03=V02;
13549: }else{
13550: X01=X02;V01=V02;
13551: }
13552: if(J==Dev) break;
13553: X02=(X01+X02)/2;
13554: V02=myeval(mysubst(F,[V,X02]));
13555: if(Df) V02=(myeval(mysubst(F,[V,WD]))-V02)/WD;
13556: if(C*dabs(2*V02-V01-V03) < dabs(V01-V03)) break;
13557: }
13558: if(J==Dev||X01==X03) L=cons([X01,X03,V03-V01],L);
13559: }
13560: }
13561: return reverse(L);
13562: }
13563:
13564: def xygraph(F,N,LT,LX,LY)
13565: {
13566: if((Proc=getopt(proc))!=1&&Proc!=2&&Proc!=3) Proc=0;
13567: if(type(DV=getopt(dviout))==4){
13568: OL=delopt(getopt(),["dviout","shift","ext","cl"]);
13569: OL=cons(["proc",1],OL);
13570: R=xygraph(F,N,LT,LX,LY|option_list=OL);
13571: OL=delopt(getopt(),["shift","ext","cl"]|inv=1);
13572: return execdraw(R,DV|optilon_list=OL);
13573: }
13574: if(N==0) N=32;
13575: if(N<0){
13576: N=-N;
13577: N1=-1; N2=N+1;
13578: }else{
13579: N1=0; N2=N;
13580: }
13581: if(length(LT)==3 && isvar(LT[0])==1){
13582: TT=LT[0]; LT=cdr(LT);
13583: F=mysubst(F,[TT,x]);
13584: }
13585: if(LX==0) LX=LT;
13586: if((Acc=getopt(Acc))!=1) Acc=0;
13587: if(Acc){
13588: LX=[eval(LX[0]),eval(LX[1])];
13589: LY=[eval(LY[0]),eval(LY[1])];
13590: LT=[eval(LT[0]),eval(LT[1])];
13591: }else{
13592: LX=[deval(LX[0]),deval(LX[1])];
13593: LY=[deval(LY[0]),deval(LY[1])];
13594: LT=[deval(LT[0]),deval(LT[1])];
13595: }
13596: TD=(LT[1]-LT[0])/N;
13597: if(type(Mul=getopt(scale))!=1){
13598: if(type(Mul)==4){
13599: MulX=Mul[0]; MulY=Mul[1];
13600: }else MulX=MulY=1;
13601: }else MulX=MulY=Mul;
13602: if(type(Org=getopt(org))==4){
13603: Orgx=Org[0];Orgy=Org[1];
13604: }else Orgx=Orgy=0;
13605: if(type(F)!=4 || (getopt(para)!=1 && length(F)>1 && type(F[0])<4 && type(F[1])==4)) {
13606: if(getopt(rev)!=1){
13607: F1=x; /* LX[0]+(LX[1]-LX[0])*(x-LT[0])/(TD*N); */
13608: F2=F;
13609: }else{
13610: F1=F;
13611: F2=x; /* LY[0]+(LY[1]-LY[0])*(x-LT[0])/(TD*N); */
13612: }
13613: }else{
13614: F1=F[0]; F2=F[1];
13615: }
13616: if(F1==0 || F2==0) LT=[];
13617: if(length(LT)==2){
13618: if(Acc){
13619: for(LTT=[],I=N2;I>=N1;I--)
13620: LTT=cons(eval(LT[0]+I*(LT[1]-LT[0])/N),LTT);
13621: }else{
13622: for(LTT=[],I=N2;I>=N1;I--)
13623: LTT=cons(deval(LT[0]+I*(LT[1]-LT[0])/N),LTT);
13624: }
13625: LT=LTT;
13626: }
13627: Cpx=getopt(cpx);
13628: if(Cpx!=1 && (str_str(rtostr(F1),"@i")>=0 || str_str(rtostr(F2),"@i")>=0))
13629: Cpx=1;
13630: if(type(Cpx)<0) Cpx=0;
13631: if(!Acc){
13632: if(type(F1)<4) F1=f2df(F1);
13633: if(type(F2)<4) F2=f2df(F2);
13634: }
13635: if(type(Err=getopt(err))==1){
13636: F1=mysubst(F1,[x,x+Err*TD/1001.23]);
13637: F2=mysubst(F2,[x,x+Err*TD/1001.23]);
13638: }
13639: if(type(F1)==4 || type(F2)==4){
13640: Dn=1;
13641: }else Dn=dn(F1)*dn(F2);
13642: for(V=[],PT=LT;PT!=[]; PT=cdr(PT)){
13643: T=car(PT);
13644: if(myfeval(Dn,T)==0){
13645: V=cons(0,V); continue;
13646: }
13647: if(Cpx>0||Acc){
13648: X=myfeval(F1,T);Y=myfeval(F2,T);
13649: }else{
13650: X=myfdeval(F1,T);Y=myfdeval(F2,T);
13651: }
13652: if((N1==0||(PT!=LT&&length(PT)!=1)) && (X<LX[0]||X>LX[1]||Y<LY[0]||Y>LY[1]))
13653: V=cons(0,V);
13654: else
13655: V=cons([MulX*(X-Orgx),MulY*(Y-Orgy)],V);
13656: }
13657: V=reverse(V);
13658: Gap0=Gap=Arg=0;
13659: if(type(Prec=getopt(prec))<0)
13660: Level=0;
13661: else if(Prec==0) Level=4;
13662: else if(type(Prec)==1){
13663: Level=Prec;
13664: if(Level<0){
13665: Level=-Level;
13666: Gap0=1;
13667: }
13668: }else if(type(Prec)==4){
13669: Level=Prec[0];
13670: if(length(Prec)>1) Arg=Prec[1];
13671: if(length(Prec)>2) Gap0=Prec[2];
13672: }
13673: if(Level>0){
13674: if(Level>16) Level=16;
13675: if(Arg<=0) Arg=30;
13676: else if(Arg>120) Arg=120;
13677: Arg=Acc?eval(@pi*Arg/180):deval(@pi*Arg/180);
13678: SL=dcos(Arg);
13679: }
13680: if(Gap0>0){
13681: if(Gap0<2) Gap0=16;
13682: else if(Gap0>512) Gap0=512;
13683: Gap=((MulX*(LX[1]-LX[0]))^2+(MulY*(LY[1]-LY[0]))^2)/(Gap0^2);
13684: }
13685: for(I=0;I<Level;I++){
13686: for(F=K=G=0,NV=NLT=[],PLT=LT,PV=V;PLT!=[];K++,PLT=cdr(PLT),PV=cdr(PV)){
13687: TG=0;D0=D1;CLT0=CLT;CV0=CV;CV=car(PV);CLT=car(PLT);
13688: if(length(PV)>1){
13689: if((CV1=car(cdr(PV)))!=0 && CV!=0)
13690: D1=[CV[0]-CV1[0],CV[1]-CV1[1]];
13691: else D1=0;
13692: }else K=-1; /* ? */
13693: if(K>0 &&(((D1==0||D0==0)&&(CV0!=0||CV!=0||CV1!=0)) || dvangle(D0,D1)<SL ||
13694: (Gap>0 && type(D0)==4 && (TG=(D0[0]^2+D0[1]^2-Gap)>0)))){
13695: G++;T1=(CLT0+CLT)/2;
13696: if(F==0 && (CV0!=0 || CV!=0)){
13697: if(myfdeval(Dn,T1)==0){
13698: NV=cons(0,NV); NLT=cons(T1,NLT);
13699: }
13700: if(Cpx>0||Acc){
13701: X=myfeval(F1,T1);Y=myfeval(F2,T1);
13702: }else{
13703: X=myfdeval(F1,T1);Y=myfdeval(F2,T1);
13704: }
13705: if(K==1 && N1<0){
13706: NV=[];NLT=[];
13707: }
13708: if((K>1||N1==0)&&(X<LX[0]||X>LX[1]||Y<LY[0]||Y>LY[1])){
13709: NV=cons(0,NV);NLT=cons(T1,NLT);F=0;
13710: }else{
13711: NV=cons([MulX*(X-Orgx),MulY*(Y-Orgy)],NV);NLT=cons(T1,NLT);
13712: }
13713: }
13714: NV=cons(CV,NV);NLT=cons(CLT,NLT);
13715: if(!TG&&(CV0!=0||CV1!=0)){
13716: T2=(car(cdr(PLT))+CLT)/2;
13717: if(myfdeval(Dn,T2)==0){
13718: NV=cons(0,NV); NLT=cons(CLT,NLT);
13719: }
13720: if(Cpx>0||Acc){
13721: X=myfeval(F1,T2);Y=myfeval(F2,T2);
13722: }else{
13723: X=myfdeval(F1,T2);Y=myfdeval(F2,T2);
13724: }
13725: if((N1==0||length(PV)!=2)&&(X<LX[0]||X>LX[1]||Y<LY[0]||Y>LY[1])){
13726: NV=cons(0,NV);NLT=cons(T1,NLT);
13727: }else{
13728: NV=cons([MulX*(X-Orgx),MulY*(Y-Orgy)],NV);NLT=cons(T2,NLT);
13729: }
13730: }
13731: if(length(PV)==2 && N1==-1) break;
13732: F=1;
13733: }else{
13734: F=0;NV=cons(CV,NV);NLT=cons(CLT,NLT);
13735: }
13736: }
13737: V=reverse(NV);LT=reverse(NLT);
13738: if(G==0) break;
13739: }
13740: if(Gap>0){
13741: for(NV=[],PV=V;PV!=[];PV=cdr(PV)){
13742: NV=cons(P0=car(PV),NV);
13743: if(length(PV)>1 && P0!=0 && PV[1]!=0
13744: && (P0[0]-PV[1][0])^2+(P0[1]-PV[1][1])^2>Gap) NV=cons(0,NV);
13745: }
13746: V=reverse(NV);
13747: }
1.18 takayama 13748: if((Raw=getopt(raw))==1) return V;
13749: if(Raw==2) return [V,LT];
1.6 takayama 13750: OL=[["curve",1]];OLP=[];
13751: if(type(C=getopt(ratio))==1){
13752: OL=cons(["ratio",C],OL);OLP=cons(["ratio",C],OLP);
13753: }
13754: if(Acc==1) OL=cons(["Acc",1],OL);
13755: if(N1<0) OL=cons(["close",-1],OL);
13756: if(type(Opt=getopt(opt))!=7 && type(Opt)!=4){
13757: if(Opt==0) return xylines(V|option_list=cons(["opt",0],OL));
13758: }
13759: OL=cons(["opt",(Proc)?0:Opt],OL);
13760: if(type(Opt)>=0) OLP=cons(["opt",Opt],OLP);
13761: if(type(Vb=getopt(verb))==1||type(Vb)==4){
13762: OL=cons(["verb",Vb],OL);OLP=cons(["verb",Vb],OL);
13763: }
13764: if(Proc){
13765: S=(Proc==1)?
13766: [[0,[MulX*(LX[0]-Orgx),MulX*(LX[1]-Orgx)],[MulY*(LY[0]-Orgy),MulY*(LY[1]-Orgy)],
13767: (TikZ)?1:1/10]]:[];
13768: S=cons([1,OLP,xylines(V|option_list=OL)],S);
13769: if(Proc==3) return car(S);
13770: }else S=xylines(V|option_list=OL);
13771: if(type(Pt=getopt(pt))==4){
13772: if(type(Pt[0])!=4) Pt=[Pt];
13773: if(length(Pt)>1 && type(Pt[1])!=4) Pt=[Pt];
13774: for(PT=Pt;PT!=[];PT=cdr(PT)){
13775: PP=car(PT);
13776: if(type(PP[0])!=4) PP=[PP];
13777: P=car(PP);PP=cdr(PP);
13778: Qx=MulX*(P[0]-Orgx);Qy=MulY*(P[1]-Orgy);
13779: if(length(PP)>0 && type(PP[0])==4){ /* draw line */
13780: P=car(PP);
13781: Q1x=MulX*(P[0]-Orgx);Q1y=MulY*(P[1]-Orgy);
13782: if(length(PP)<1 || car(PP)==0 || iand(car(PP),1))
13783: OL=["opt",(TikZ)?"-":"@{-}"];
13784: else OL=["opt",(TikZ)?".":"@{.}"];
13785: if(Proc) S=cons([1,OL,[[Qx,Qy],[Q1x,Q1y]]],S);
13786: else S=S+xylines([[Qx,Qy],[Q1x,Q1y]]|optilon_list=OL);
13787: continue;
13788: }
13789: if(length(PP)==0 || type(car(PP))!=7) SS="$\\bullet$";
13790: else SS=car(PP);
13791: if(length(PP)<=1){
13792: if(Proc) S=cons([2,[],[Qx,Qy],[SS]],S);
13793: else S=S+xyput([Qx,Qy,SS]);
13794: }else{
13795: if(Proc) S=cons([2,[],[Qx,Qy],[[SS],"",PP[1]]],S);
13796: S=S+xyput([Qx,Qy,SS,"",PP[1]]);
13797: }
13798: }
13799: }
13800: if(type(Ax=getopt(ax))==4){ /* draw axis */
13801: Adx0=Ady0=0; Adx1=Ady1=0.1;
13802: if(!TikZ){
13803: if(!XYcm) Adx1=Ady1=1;
13804: LOp="@{-}"; LxOp="+!U"; LyOp="+!R";
13805: }else{
13806: LOp="-"; LxOp="below"; LyOp="left";
13807: }
13808: LOp0=LOp1=LOp;
13809: LxOO=(Ax[1]==LY[0])?LxOp:(TikZ)?"below left":"+!UR";
13810: if(type(AxOp=getopt(axopt))>0){
13811: if(type(AxOp)==1){
13812: if(AxOp>0) Adx1=Ady1=AxOp;
13813: else if(AxOp<0){
13814: Adx1=Ady1=0; Adx0=Ady0=AxOp;
13815: }
13816: }else if(type(AxOp)==4){
13817: if(type(T=car(AxOp))==4 && length(AxOp)>1){
13818: if(type(T)==7){
13819: LxOp=T; LyOp=AxOp[1];
13820: }else if(type(T)==4){
13821: Ay0=T[0]; Ay1=T[1]; Ax0=AxOp[1][0]; Ax1=AxOp[1][1];
13822: if(length(T)>2) LxOp=T[2];
13823: if(length(AxOp[1])>2) LyOp=AxOp[1][2];
13824: }
13825: }
13826: if(length(AxOp)>2 && type(AxOp[2])==7) LxOO=AxOp[2];
13827: if(length(AxOp)>3 && type(AxOp[3])==7) LOp0=AxOp[3];
13828: if(length(AxOp)>4 && type(AxOp[4])==7) LOp1=AxOp[4];
13829: }
13830: if(type(AxOp)==7) LOp0=AxOp;
13831: }
13832: if(Ax[0]>=LX[0] && Ax[0]<=LX[1]){ /* draw marks on x-axis */
13833: if(Proc) S=cons([3,(type(LOp0)>=0)?[["opt",LOp0]]:[],
13834: [MulX*(Ax[0]-Orgx),MulY*(LY[0]-Orgy)],[MulX*(Ax[0]-Orgx),MulY*(LY[1]-Orgy)]],S);
13835: else S=S+xyarrow([MulX*(Ax[0]-Orgx),MulY*(LY[0]-Orgy)],
13836: [MulX*(Ax[0]-Orgx),MulY*(LY[1]-Orgy)]|opt=LOp0);
13837: if(length(Ax)>2){
13838: D=Ax[2];
13839: if(type(D)==1 && D>0){
13840: I0=ceil((LX[0]-Ax[0])/D); I1=floor((LX[1]-Ax[0])/D);
13841: for(DD=[],I=I0; I<=I1; I++){
13842: if(length(Ax)<5) DD=cons(I*D,DD);
13843: else if(Ax[4]==0) DD=cons([I*D,I*D+Ax[0]],DD);
13844: else if(Ax[4]==1) DD=cons([I*D,I*D],DD);
13845: else if(Ax[4]==2) DD=cons([I*D,I],DD);
13846: }
13847: D=DD;
13848: }
13849: if(type(D)==4){
13850: for(;D!=[]; D=cdr(D)){
13851: T=car(D);
13852: if(type(T)==4) T=car(T);
13853: X=MulX*(T+Ax[0]-Orgx); Y=MulY*(Ax[1]-Orgy);
13854: if(T!=0){
13855: if(Proc) S=cons([3,(type(LOp1)>=0)?[["opt",LOp1]]:[],[X,Y+Ady0],[X,Y+Ady1]],S);
13856: else S=S+xyarrow([X,Y+Ady0],[X,Y+Ady1]|opt=LOp1);
13857: }
13858: if(type(car(D))==4){
13859: Arg=[(T==0)?LxOO:LxOp,D[0][1]];
13860: if(Proc) S=cons([2,[],[X,Y+Ady0],[Arg]],S);
13861: else S=S+xyput([X,Y+Ady0,Arg]);
13862: }
13863: }
13864: }
13865: }
13866: }
13867: if(Ax[1]>=LY[0] && Ax[1]<=LY[1]){ /* draw marks on y-axis */
13868: if(Proc) S=cons([3,[["opt",LOp0]],
13869: [MulX*(LX[0]-Orgx),MulY*(Ax[1]-Orgy)],
13870: [MulX*(LX[1]-Orgx),MulY*(Ax[1]-Orgy)]],S);
13871: else S=S+xyarrow([MulX*(LX[0]-Orgx),MulY*(Ax[1]-Orgy)],
13872: [MulX*(LX[1]-Orgx),MulY*(Ax[1]-Orgy)]|opt=LOp0);
13873: if(length(Ax)>3){
13874: D=Ax[3];
13875: if(type(D)==1 && D>0){
13876: I0=ceil((LY[0]-Ax[1])/D); I1=floor((LY[1]-Ax[0])/D);
13877: for(DD=[],I=I0; I<=I1; I++){
13878: if(length(Ax)<5) DD=cons(I*D,DD);
13879: else if(I!=0){
13880: if(Ax[4]==0) DD=cons([I*D,I*D+Ax[1]],DD);
13881: if(Ax[4]==1) DD=cons([I*D,I*D],DD);
13882: if(Ax[4]==2) DD=cons([I*D,I],DD);
13883: }
13884: }
13885: D=DD;
13886: }
13887: if(type(D)==4){
13888: for(;type(D)==4&&D!=[]; D=cdr(D)){
13889: T=car(D);
13890: if(type(T)==4) T=car(T);
13891: X=MulX*(Ax[0]-Orgx); Y=MulY*(T+Ax[1]-Orgy);
13892: if(T!=0){
13893: if(Proc) S=cons([3,(type(LOp0)>=0)?[["opt",LOp1]]:[],
13894: [X+Adx0,Y],[X+Adx1,Y]],S);
13895: else S=S+xyarrow([X+Adx0,Y],[X+Adx1,Y]|opt=LOp1);
13896: }
13897: if(type(car(D))==4){
13898: if(Proc) S=cons([2,[],[X,Y+Ady0],[[LyOp,D[0][1]]]],S);
13899: else S=S+xyput([X,Y+Ady0,[LyOp,D[0][1]]]);
13900: }
13901: }
13902: }
13903: }
13904: }
13905: }
13906: if(Proc) return reverse(S);
13907: if(getopt(dviout)!=1) return S;
13908: xyproc(S|dviout=1);
13909: }
13910:
13911: def xyarrow(P,Q)
13912: {
13913: Cmd = ["fill","filldaw","shade","shadedraw","clip ","pattern","path ","node","coordinate"];
13914: if(type(P)<4) return "%\n";
13915: SS=getopt(opt);
13916: if(!TikZ){
13917: if(type(Q)<4) return "";
13918: S="{"+xypos(P)+" \\ar";
13919: if(type(SS)==7) S=S+SS;
13920: return S+" "+xypos(Q)+"};\n";
13921: }
13922: if(type(SS)==4 && length(SS)>1){
13923: if(length(SS)>2) SU=SS[2];
13924: ST=SS[1];
13925: SS=SS[0];
13926: }
13927: if(type(SS)!=7) SS="->";
13928: if(type(ST)!=7) ST=" -- ";
13929: if(type(SU)!=7) SU="";
13930: if(type(S=getopt(cmd))==7) S="\\"+S;
13931: else S="\\draw";
13932: if(type(Q)!=4){
13933: if(Q>0 && Q<=length(Cmd)) S="\\"+Cmd[Q-1]+"";
13934: if(SS!="-") S=S+"["+SS+"]";
13935: if(SU!="") SU="["+SU+"]";
13936: return S+xypos(P)+ST+SU+";\n";
13937: }
1.8 takayama 13938: if(SS!="-"&&SS!="") S=S+"["+SS+"]";
1.6 takayama 13939: if(length(P)<3 && length(Q)<3)
13940: return S+xypos(P)+ST+xypos(Q)+SU+";\n";
13941: if(length(P)==2) P=[P[0],P[1],"","_0"];
13942: else if(length(P)==3 || (length(P)==4 && P[3]==""))
13943: P=[P[0],P[1],P[2],"_0"];
13944: else if(P[3]=="")
13945: P=[P[0],P[1],P[2],"_0",P[4]];
13946: if(length(Q)==2) Q=[Q[0],Q[1],"","_1"];
13947: else if(length(Q)==3 || (length(Q)==4 && Q[3]==""))
13948: Q=[Q[0],Q[1],Q[2],"_1"];
13949: else if(Q[3]=="")
13950: Q=[Q[0],Q[1],Q[2],"_1",Q[4]];
13951: return S+xypos(P)+" "+xypos(Q)+"("+P[3]+")"+ST+"("+Q[3]+")"+SU+";\n";
13952: }
13953:
13954: def xyarrows(P,Q,R)
13955: {
13956: PQ=newvect(4);
13957: PQ[0]=(type(P[0])!=4)?f2df(P[0]):P[0];
13958: PQ[1]=(type(P[1])!=4)?f2df(P[1]):P[1];
13959: PQ[2]=(type(Q[0])!=4)?f2df(Q[0]):Q[0];
13960: PQ[3]=(type(Q[1])!=4)?f2df(Q[1]):Q[1];
13961: if(type(R[0])!=4) R=[R];
13962: TR=R[0];NX=TR[2];X=X0=TR[0];DX=(TR[1]-TR[0])/NX;
13963: if(length(R)==2){
13964: TR=R[1];NY=TR[2];Y=TR[0];DY=(TR[1]-TR[0])/NY;
13965: }else{
13966: NY=1;Y=DY=0;
13967: }
13968: if(type(L=getopt(abs))!=1) L=0;
13969: if(type(Sc=getopt(scale))!=1) Sc=0;
13970: OL=[];
13971: if(type(Opt=getopt(opt))==7) OL=cons(["opt",Opt],OL);
13972: Tb=str_tb(0,0);
13973: for(J=0;J<NY;Y+=DY,J++){
13974: for(I=0,X=X0;I<NX;I++,X+=DX){
13975: PX=myf2eval(PQ[0],X,Y);PY=myf2eval(PQ[1],X,Y);
13976: VX=myf2eval(PQ[2],X,Y);VY=myf2eval(PQ[3],X,Y);
13977: if(L>0){
13978: C=dnorm([VX,VY]);
13979: if(C!=0){
13980: VX*=L/C;VY*=L/C;
13981: }
13982: }
13983: if(Sc){
13984: VX*=Sc;VY*=Sc;
13985: }
13986: if(VX||VY) str_tb(xyarrow([PX,PY],[PX+VX,PY+VY]|optilon_list=OL),Tb);
13987: }
13988: }
13989: return str_tb(0,Tb);
13990: }
13991:
13992: def polroots(L,V)
13993: {
13994: INIT=1;
13995: if(type(CF=getopt(comp))!=1) CF=0;
13996: OL=getopt();
13997: if(CF>32){
13998: CF-=64;
13999: INIT=0;
14000: }else OL=cons(["comp",CF+64],delopt(OL,"comp"));
14001: if(type(V)==4&&length(V)==1){
14002: L=L[0];V=V[0];
14003: }
14004: Lim=Lim2=[];
14005: if(type(L)<4){
14006: if(type(Lim=getopt(lim))==4){
1.17 takayama 14007: if(type(Lim[0])!=4){
14008: if(!isvar(Lim[0])) Lim=cons(V,[Lim]);
14009: Lim=[Lim];
14010: }
14011: if(!isvar(Lim[0][0])) Lim=[cons(V,Lim)];
1.6 takayama 14012: Lim=delopt(Lim,V|inv=1);
14013: if(Lim!=[]){
14014: Lim=Lim[0];
14015: if(length(Lim)==3) Lim2=Lim[2];
14016: Lim=Lim[1];
14017: }
14018: }else{
14019: Lim=Lim2=[];
14020: }
14021: if((CF==-2||CF==-1||CF==2)&&iscoef(L,os_md.israt)){ /* Rat+Comp, Rat+Real or Rat */
14022: S=(CF==-1)?getroot(L,V|cpx=1):getroot(L,V);
14023: for(RR=[],F=x;S!=[];S=cdr(S)){
14024: if(findin(V,vars(C=car(S)))<0){ /* Rational solution */
14025: if(type(C)<2){
14026: if(Lim!=[]&&(real(C)<Lim[0]||real(C)>Lim[1])) continue;
14027: if(Lim2!=[]&&(imag(C)<Lim2[0]||imag(C)>Lim2[1])) continue;
14028: }
14029: if(F!=C) RR=cons(F=C,RR);
14030: }else if(CF<0){ /* Irrational solution */
14031: if((R=pari(roots,mysubst(C,[V,x])))!=0){
14032: for(R=vtol(R);R!=[];R=cdr(R))
14033: if((C=car(R))!=F && ntype(C)<CF+6){
14034: if(Lim!=[]&&(real(C)<Lim[0]||real(C)>Lim[1])) continue;
14035: if(Lim2!=[]&&(imag(C)<Lim2[0]||imag(C)>Lim2[1])) continue;
14036: RR=cons(F=C,RR);
14037: }
14038: }
14039: }
14040: }
14041: return qsort(RR);
14042: }
14043: R=pari(roots,subst(L,V,x));
14044: if(R==0){
14045: R=[0];
14046: if(CF==1){
14047: for(R=[0],I=mydeg(L,V);I>1; I--)
14048: R=cons(0,R);
14049: }
14050: return R;
14051: }
14052: if(CF==1){ /* Complex */
14053: if(Lim==[]&&Lim2==[]) return vtol(R);
14054: for(L=[],I=length(R)-1;I>=0;I--){
14055: C=R[I];
14056: if(Lim!=[]&&(real(C)<Lim[0]||real(C)>Lim[1])) continue;
14057: if(Lim2!=[]&&(imag(C)<Lim2[0]||imag(C)>Lim2[1])) continue;
14058: L=cons(C,L);
14059: }
14060: return L;
14061: }
14062: for(L=[],F=x,I=length(R)-1;I>=0;I--){ /* Real */
14063: if(ntype(R[I])<4 && F!=R[I]){
14064: if(Lim!=[] && (R[I]<Lim[0]||R[I]>Lim[1])) continue;
14065: L=cons(F=R[I],L);
14066: }
14067: }
14068: return qsort(L);
14069: }
14070: if(SS==0&&INIT==1){
14071: SS=polroots(L,V|option_list=OL);
14072: if(SS!=0) return SS;
1.18 takayama 14073: for(C=0;SS==0&&C<5;C++){
1.6 takayama 14074: I=(C==0)?1:(iand(random(),0xff)-0x80);
14075: for(LL=[],K=length(L)-1;K>=0;K--){
14076: for(Q=0,J=length(L)-1;J>=0;J--)
14077: Q+=L[J]*(I+K)^J;
14078: LL=cons(Q,LL);
14079: }
14080: SS=polroots(LL,V|option_list=OL);
14081: if(SS!=0) return SS;
14082: }
14083: return SS;
14084: }
14085: C=2^(-32);
14086: if(type(getopt(err))==1) C=err;
14087: if((N=length(V))!=length(L)) return [];
14088: if(N==1) return polroots(L[0],V[0]|option_list=OL);
14089: for(L1=[],I=1;I<N;I++){
14090: Res=res(V[0],L[I-1],L[I]);
14091: if(type(Res)<2) return Res;
14092: L1=cons(res(V[0],L[I-1],L[I]),L1);
14093: }
14094: R=polroots(L1,V1=cdr(V)|option_list=OL);
14095: if(type(R)<2) return R;
14096: for(SS=[];R!=[];R=cdr(R)){
14097: RS=(N==2)?[car(R)]:car(R);
14098: for(I=0,L0=L[0];I<N-1;I++) L0=mysubst(L0,[V1[I],RS[I]]);
1.17 takayama 14099: if(L0==0) return 0;
1.6 takayama 14100: S0=polroots(L0,V[0]|option_list=OL);
14101: if(type(S0)<2) return S0;
14102: for(S=S0;S!=[];S=cdr(S)){
14103: S0=cons(car(S),RS);
14104: for(LT=cdr(L);LT!=[];LT=cdr(LT)){
14105: for(I=0,TV=car(LT);I<N;I++) TV=mysubst(TV,[V[I],S0[I]]);
14106: if(abs(TV)>C) break;
14107: }
14108: if(LT==[]) SS=cons(S0,SS);
14109: }
14110: }
14111: return reverse(SS);
14112: }
14113:
14114: def ptcommon(X,Y)
14115: {
14116: if(length(X)!=2 || length(Y)!=2) return 0;
14117: if(type(X[1])==4){ /* X is a line */
14118: if((In=getopt(in))==-1||In==-2||In==-3){
14119: X0=(X[0][0]+X[1][0])/2;X1=(X[0][1]+X[1][1])/2;
14120: X=[[X0,X1],[X0+X[1][1]-X[0][1],X1-X[1][0]+X[0][0]]];
14121: if(In==-1&&type(Y[1])==4) return ptcommon(Y,X|in=-2);
14122: /* for the second line */
14123: if(In==-3) In=1;
14124: else In=0;
14125: }else if(In==2||In==3){
14126: X=(X[1][0]-X[0][0])+(X[1][1]-X[0][1])*@i;
14127: if(X==0) return 0;
14128: Y=(Y[1][0]-Y[0][0])+(Y[1][1]-Y[0][1])*@i;
14129: X=myarg(Y/X);
14130: return (In==2)?X:(X*180/deval(@pi));
14131: }else if(In!=1) In=0;
14132: if(type(Y[0])<=3){
14133: if(In==1){
14134: return [(Y[1]*X[0][0]+Y[0]*X[1][0])/(Y[0]+Y[1]),
14135: (Y[1]*X[0][1]+Y[0]*X[1][1])/(Y[0]+Y[1])];
14136: }
14137: XX=X[1][0]-X[0][0];YY=X[1][1]-X[0][1];
14138: Arg=(length(Y)<2)?0:Y[1];
14139: Arg=deval(Arg);
14140: if(Arg!=0){
14141: S=dcos(Arg)*XX-dsin(Arg)*YY;
14142: YY=dsin(Arg)*XX+dcos(Arg)*YY;
14143: XX=S;
14144: }
14145: S=dnorm([XX,YY]);
14146: if(S!=0){
14147: XX*=Y[0]/S;YY*=Y[0]/S;
14148: }
14149: return [X[1][0]+XX,X[1][1]+YY];
14150: }
14151: S=[X[0][0]+(X[1][0]-X[0][0])*x_,X[0][1]+(X[1][1]-X[0][1])*x_];
14152: if(type(Y[1])==4){ /* Y is a line */
14153: T=[Y[0][0]+(Y[1][0]-Y[0][0])*y_-S[0],
14154: Y[0][1]+(Y[1][1]-Y[0][1])*y_-S[1]];
14155: R=lsol(T,[x_,y_]);
14156: if(type(R[0])==4&&type(R[1])==4&&R[0][0]==x_&&R[1][0]==y_){
14157: if(!In || (R[0][1]>=0&&R[0][1]<=1&&R[1][1]>=0&&R[1][1]<=1) )
14158: return subst(S,x_,R[0][1],y_,R[1][1]);
14159: }
14160: if((type(R[0])>0&&type(R[0])<4)||(type(R[1])>0&&type(R[1])<4)) return 0;
14161: if(!In) return 1;
14162: I=(X[0][0]==X[1][0]&&Y[0][0]==Y[1][0]&&X[0][0]==Y[0][0])?1:0;
14163: if(X[0][I]<=X[1][I]){
14164: X0=X[0][I];X1=X[1][I];
14165: }else{
14166: X1=X[0][I];X0=X[1][I];
14167: }
14168: return ((Y[0][I]<X0 && Y[1][I]<X0)||(Y[0][I]>X1&&Y[1][I]>X1))?0:1;
14169: }else if(Y[1]==0){ /* orth */
14170: T=[Y[0][0]+(X[1][1]-X[0][1])*y_-S[0],
14171: Y[0][1]-(X[1][0]-X[0][0])*y_-S[1]];
14172: R=lsol(T,[x_,y_]);
14173: if(type(R[0])==4&&type(R[1])==4&&R[0][0]==x_&&R[1][0]==y_){
14174: if(!In||(R[0][1]>=0&&R[0][1]<=1))
14175: return subst(S,x_,R[0][1],y_,R[1][1]);
14176: }
14177: return (X[0]==X[1])?0:1;
14178: }else if(type(Y[1])==1 && Y[1]>0){ /* circle */
14179: T=(S[0]-Y[0][0])^2+(S[1]-Y[0][1])^2-Y[1]^2;
14180: D=mycoef(T,1,x_)^2-4*mycoef(T,0,x_)*mycoef(T,2,x_);
14181: if(D==0){
14182: V=mycoef(T,1,x_)/(2*mycoef(T,2,x_));
14183: if(!in||(V>=0&&V<=1)) return [subst(S,x_,V)];
14184: }
14185: else if((type(D)==1&&D>0)){
14186: D=dsqrt(D);
14187: V=-(mycoef(T,1,x_)+D)/(2*mycoef(T,2,x_));
14188: if(!In||(V>=0&&V<=1)) L=[subst(S,x_,V)];
14189: else L=[];
14190: V=(D-mycoef(T,1,x_))/(2*mycoef(T,2,x_));
14191: if(!In||(V>=0&&V<=1)) L=cons(subst(S,x_,V),L);
14192: if(length(L)>0) return L;
14193: }
14194: }
14195: return 0;
14196: }
14197: if(type(Y[1])==4 || X[1]==0) return ptcommon(Y,X);
14198: /* X is a circle */
14199: if(Y[1]==0){ /* tangent line */
14200: if(Y[0][0]==X[0][0]+X[1] || Y[0][0]==X[0][0]-X[1]) L=[[Y[0][0],X[0][1]]];
14201: else L=[];
14202: P=(Y[0][0]+x_-X[0][0])^2+(Y[0][1]+x_*y_-X[0][1])^2-X[1]^2;
14203: Q=mycoef(P,1,x_)^2-4*mycoef(P,2,x_)*mycoef(P,0,x_);
14204: for(R=polroots(Q,y_);R!=[];R=cdr(R)){
14205: X0=-subst(mycoef(P,1,x_)/(2*mycoef(P,2,x_)),y_,car(R));
14206: L=cons([Y[0][0]+X0,Y[0][1]+car(R)*X0],L);
14207: }
14208: }else{ /* Y is a circle */
14209: P=(x_-X[0][0])^2+(y_-X[0][1])^2-X[1]^2;
14210: Q=(x_-Y[0][0])^2+(y_-Y[0][1])^2-Y[1]^2;
14211: V=(X[0][0]!=Y[0][0])?[x_,y_]:[y_,x_];
14212: R=subst(P,V[0],T=lsol(P-Q,V[0]));
14213: if(type(T[0])<4) return (T[0]==0)?1:0;
14214: S=polroots(R,V[1]);
14215: for(L=[];S!=[];S=cdr(S)){
14216: R=subst(T,V[1],car(S));
14217: if(V[0]==x_) L=cons([R,car(S)],L);
14218: else L=cons([S,R],L);
14219: }
14220: }
14221: if(length(L)!=0) return L;
14222: return 0;
14223: }
14224:
14225: def tobezier(L)
14226: {
14227: if((Div=getopt(div))==1||Div==2){
14228: if(length(L)!=4) return [tobezier(L|inv=[0,1/2]),tobezier(L|inv=[1/2,1])];
14229: if(type(L)==4) L=ltov(L);
14230: if(type(L[0])==4)
14231: L=[ltov(L[0]),ltov(L[1]),ltov(L[2]),ltov(L[3])];
14232: S=[(L[0]+3*L[1]+3*L[2]+L[3])/8];
14233: T=[L[3]];
14234: S=cons((L[0]+2*L[1]+L[2])/4,S);
14235: T=cons((L[2]+L[3])/2,T);
14236: S=cons((L[0]+L[1])/2,S);
14237: T=cons((L[1]+2*L[2]+L[3])/4,T);
14238: S=cons(L[0],S);
14239: T=cons((L[0]+3*L[1]+3*L[2]+L[3])/8,T);
14240: return [S,T];
14241: }
14242: if(Div>2&&Div<257){
14243: L=tobezier(L);
14244: for(R=[],I=Div-1;I>=0;I--)
14245: R=cons(tobezier(L|inv=[I/Div,(I+1)/Div]),R);
14246: return R;
14247: }
14248: if((V=getopt(inv))==1 || type(V)>3){
14249: if(type(L[0])>3 && type(V)>3) L=tobezier(L);
14250: if(type(V)>3 && length(V)>2) V2=V[2];
14251: if(type(V2)!=2) V2=t;
14252: if(type(V)>3) L=subst(L,V2,(V[1]-V[0])*V2+V[0]);
14253: N=mydeg(L,V2);
14254: for(R=[],I=0;I<=N;I++){
14255: RT=mycoef(L,I,V2);
14256: R=cons(RT/binom(N,I),R);
14257: L-=RT*V2^I*(1-V2)^(N-I);
14258: }
14259: return reverse(R);
14260: };
14261: N=length(L)-1;
14262: V=newvect(2);
14263: for(I=0;I<=N;I++,L=cdr(L)){
14264: if(type(X=car(L))==4) X=ltov(X);
14265: V+=X*binom(N,I)*t^I*(1-t)^(N-I);
14266: }
14267: return V;
14268: }
14269:
14270: def cutf(F,X,VV)
14271: {
14272: if(type(car(V=VV))==2){
14273: Y=[car(V),X];
14274: V=cdr(V);
14275: }else Y=X;
14276: if(type(X)>1){
14277: Y=(type(Y)==4)?Y[0]:x;
14278: V1=makenewv(F);
14279: if(X==Y||Y==x){
14280: V2=makenewv([F,V1]);
14281: F=mysubst(F,[Y,V2]);
14282: V=cons(V2,V);
14283: }
14284: return [V1,[V1,os_md.cutf,[F],X,[V]]];
14285: }
14286: if(car(V)!=[] && X<car(V)[0]) return myfeval(car(V)[1],Y);
14287: for(V=cdr(V); ;V=R){
14288: if((R=cdr(V))==[]){
14289: if(car(V)!=[] && car(V)[0]<X) return myfeval(car(V)[1],Y);
14290: return myfeval(F,Y);
14291: }
1.20 takayama 14292: if(car(V)==[]||X>car(V)[0]) continue;
1.6 takayama 14293: if(X==car(V)[0]) return car(V)[1];
14294: return myfeval(F,Y);
14295: }
14296: }
14297:
1.12 takayama 14298: def fsum(F,L)
1.6 takayama 14299: {
1.12 takayama 14300: if(getopt(df)==1){
14301: F=f2df(F);
14302: }else Sub=getopt(subst);
1.6 takayama 14303: if(type(L[0])==2){
14304: X=L[0];
14305: L=cdr(L);
14306: }else X=0;
14307: V=(length(L)>2)?L[2]:1;
14308: for(R=0,I=L[0];;I+=V){
14309: if(V==0||(I-L[1])*V>0) return R;
1.12 takayama 14310: R+=(Sub==1)?subst(F,X?X:x,I):os_md.myfeval(F,X?[X,I]:I);
1.6 takayama 14311: }
14312: }
14313:
14314: def periodicf(F,L,X)
14315: {
14316: if(type(L)==4) L=[eval(L[0]),eval(L[1])];
14317: else L=eval(L);
14318: if(isvar(X)){
1.20 takayama 14319: Y=makenewv([X,F]);
14320: Z=makenewv([X,Y,F]);
1.16 takayama 14321: return [Z,[Z,os_md.periodicf,[mysubst(F,[x,Y])],(type(L)==4)?[L]:L,[[Y,X]]]];
14322: }
14323: if(type(X)==4){
14324: V=X[0];
14325: X=X[1];
14326: }else V=x;
14327: if(type(F)==5){
14328: X=eval(X);
14329: return myfeval(F[floor(X/L)%length(F)],[V,X-floor(X/L)*L]);
1.6 takayama 14330: }
14331: if(type(L)==4){
14332: X-=floor((X-L[0])/(L[1]-L[0]))*(L[1]-L[0]);
14333: return myfeval(F,[V,X]);
14334: }
14335: }
14336:
14337: def cmpf(X)
14338: {
14339: if(type(X)>3){
14340: if(type(L)==7) return [S_Fc,Dx,S_Ic,S_Ec,S_EC,S_Lc];
14341: S_Lc=0;
14342: if(type(S_Fc=X[0])!=4) S_Fc=f2df(S_Fc);
14343: S_Ic=X[1];
14344: if(length(S_Ic)>2){
14345: S_Fc=mysubst(S_Fc,[S_Ic[0],x]);
14346: S_Ic=cdr(S_Ic);
14347: }
14348: S_Dc=(type(S_Ic[0])==7)?1:0;
14349: if(type(S_Ic[1])==7) S_Dc=ior(S_Dc,2);
14350: if(type(S_Ec=getopt(exp))!=1) S_Ec=0;
14351: if(S_Ec<=0){
14352: S_EC=-S_Ec;
14353: if(S_EC==0) S_EC=1;
14354: if(S_Dc==3) S_EC*=2;
14355: else S_EC/=4;
14356: if(type(F=X[0])==3&&vars(F)==[x]&&(D=deg(nm(F),x))==deg(dn(F),x)-2){
14357: S_Lc=S_EC*coef(nm(F),D,x)/coef(dn(F),D+2,x);
14358: }
14359: }else{
14360: S_EC=S_Ec;
14361: if(S_Dc==3) S_EC*=12;
14362: else S_EC/=6;
14363: }
14364: if(type(S_Fc)==3) S_Fc=red(S_Fc);
14365: S_EC=1/S_EC;
14366: return [z_,[z_,os_md.cmpf,x]];
14367: }
14368: if(X<=0 && iand(S_Dc,1)) return S_Lc;
14369: if(X>=1 && iand(S_Dc,2)) return S_Lc;
14370: if(S_Dc==3){
14371: if(S_Ec>0){
14372: Y0=dexp(1/X)*S_EC;
14373: Y1=dexp(1/(1-X))*S_EC;
14374: return myfeval(S_Fc,Y1-Y0)*(Y0/X^2+Y1/(1-X)^2);
14375: }
14376: return myfeval(S_Fc,S_EC/(1-X)-S_EC/X)*(S_EC/(1-X)^2+S_EC/X^2);
14377: }
14378: if(S_Dc==1){
14379: if(S_Ec>0){
14380: Y=dexp(1-1/X);
14381: R=myfeval(S_Fc,S_EC*(Y-1)+I[1])*Y;
14382: }
14383: else R=myfeval(S_Fc,I[1]+(1-1/X)*S_EC);
14384: return R*S_EC/X^2;
14385: }
14386: if(S_Dc==2){
14387: if(S_Ec>0){
14388: Y=dexp(X/(1-X));
14389: R=myfeval(S_Fc,S_EC*(Y-1)+S_Ic[0])*Y;
14390: }else R=myfeval(S_Fc,S_EC*X/(1-X)+S_Ic[0]);
14391: return R*S_EC/(1-X)^2;
14392: }
14393: X=S_Ic[0]+(S_Ic[1]-S_Ic[0])*X;
14394: return myfeval(S_Fc,X)/(S_Ic[1]-Ic[0]);
14395: }
14396:
14397: def fresidue(P,Q)
14398: {
14399: if(iscoef(Q,os_md.israt)) S=fctr(Q);
14400: else S=[[Q,1]];
14401: for(R=[];S!=[];S=cdr(S)){
14402: T=car(S);
14403: if((D=mydeg(T[0],z))==0) continue;
14404: L=[];
14405: if(iscoef(T[0],os_md.iscrat)) L=getroot(T[0],z|cpx=2);
14406: if(findin(z,vars(L))>=0) L=[];
14407: if(L==[]) L=polroots(T[0],z|comp=-1);
14408: for(;L!=[];L=cdr(L)){
14409: QQ=Q;
14410: for(I=T[1]; I>1;I--) QQ=mydiff(QQ,z);
14411: for(U=0,W=I=T[1];I>0;I--,W++){
14412: QQ=diff(QQ,z);
14413: U+=subst(QQ,z,L[0])*(z-L[0])^(W-T[1])/fac(W);
14414: }
14415: UD=mydiff(U,z);
14416: for(I=T[1],K=1,PP=P; I>1;I--,K++)
14417: PP=diff(PP,z)*U-K*PP*UD;
14418: QQ=subst(PP,z,L[0])/subst(U,z,L[0])^K;
14419: /* if(D==2) QQ=sqrt2rat(QQ); */
14420: R=cons([L[0],sqrt2rat(QQ)],R);
14421: }
14422: }
14423: if(type(L=getopt(cond))==4){
14424: for(S=[];R!=[];R=cdr(R)){
14425: Z=car(R);
14426: for(LL=L;LL!=[];LL=cdr(LL)){
14427: X=real(car(Z));Y=imag(car(Z));
14428: if(myf3eval(car(LL),X,Y,car(Z))<=0) break;
14429: }
14430: if(LL==[]) S=cons(Z,S);
14431: }
14432: R=reverse(S);
14433: }
14434: if((Sum=getopt(sum))==1||Sum==2){
14435: for(S=0;R!=[];R=cdr(R)) S+=car(R)[1];
14436: if(Sum==2) S*=2*@pi*@i;
14437: return sqrt2rat(S);
14438: }
14439: return R;
14440: }
14441:
14442: def fint(F,D,V)
14443: {
14444: if(((L=length(V))==2 || (L==3&&isvar(V[0])<3))
14445: && (type(V[L-1])==7||(type(V[L-1])<3&&type(eval(V[L-1]))<2)))
14446: /* real integral */
14447: return areabezier([F,D,V]|option_list=getopt());
14448: /* complex integral */
14449: if(L>1&&type(V[1])==4&&type(V[1][1])<4){
14450: if(type(V[0])==4&&type(V[0][0])<2){
14451: for(R=[],VT=car(V),VV=cdr(V);VV!=[];VV=cdr(VV),VT=VU){
14452: if((VU=car(VV))==-1) VU=car(V);
14453: R=cons([ptcommon([VT,VU],[t,1-t]|in=1),[0,1]],R);
14454: }
14455: V=reverse(R);
14456: }
14457: else if(L==2) V=[V];
14458: }
14459: Opt=cons(["cpx",1],getopt());
14460: for(R=0;V!=[];V=cdr(V)){
14461: VT=car(V);
14462: X=car(VT)[0];XD=red(diff(X,t));
14463: Y=car(VT)[1];YD=red(diff(Y,t));
14464: F=mysubst(F,[[x,X],[y,Y],[z,X+@i*Y]]);
14465: if(type(F)==4)
14466: FF=cons(F[0]*(XD+@i*YD),cdr(F));
14467: else FF=red(F*(XD+@i*YD));
14468: R+=areabezier([FF,D,cons(t,VT[1])]|option_list=Opt);
14469: }
14470: return R;
14471: }
14472:
14473: def areabezier(V)
14474: {
14475: if(getopt(cpx)==1){
14476: Opt=delopt(getopt(),"cpx");
14477: F=V[0];
14478: if(!isvar(Var=V[2][0])) Var=x;
14479: if(type(F)==3 && vars(F)==[Var] && imag(dn(F))!=0){
14480: F=(nm(F)*conj(dn(F)))/(dn(F)*conj(dn(F)));
14481: V0=red(real(nm(F))/dn(F));
14482: R=areabezier([V0,V[1],V[2]]|option_list=Opt);
14483: V0=red(imag(nm(F))/dn(F));
14484: return R+@i*areabezier([V0,V[1],V[2]]|option_list=Opt);
14485: }
14486: if(getopt(Acc)!=1) F=f2df(F);
14487: V0=compdf([o,[o,real,o_]],o_,F);
14488: R=areabezier([V0,V[1],V[2]]|option_list=Opt);
14489: V0=compdf([o,[o,imag,o_]],o_,F);
14490: return R+@i*areabezier([V0,V[1],V[2]]|option_list=Opt);
14491: }
14492: if(type(V[0])!=4 || vars(V[0][0])!=0){
14493: Mx=[-2.0^(512),2.0^(512)];
14494: I=length(V[2]);
14495: if(type(V[2][I-1])==7||type(V[2][I-2])==7){ /* infinite interval */
14496: if(type(Ec=getopt(exp))==1) R=cmpf([V[0],V[2]]|exp=Ec);
14497: else R=cmpf([V[0],V[2]]);
14498: V=[R,V[1],[0,1]];
14499: }
14500: if(type((Int=getopt(int)))==1 && type(V[0])<4 && (V1=V[1])>=0){
14501: if(Int==2&&iand(V1,1)) V1++;
14502: if(!V1) V1=32;
14503: Opt=cons(["raw",1],getopt());
14504: W=xygraph(V[0],V[1],V[2],Mx,Mx|option_list=Opt);
14505: SS=W[0][1];
14506: for(S0=S1=0,I=0,L=W;L!=[] && I<=V1;I++, L=cdr(L)){
14507: if(iand(I,1)) S1+=car(L)[1];
14508: else S0+=car(L)[1];
14509: if (I==V1) SS+=car(L)[1];
14510: }
14511: VV=deval(V[2][1]-V[2][0]);
14512: if(Int==2)
14513: return (2*S0+4*S1-SS)*VV/(3*V1);
14514: else
14515: return (2*S0+2*S1-SS)*VV/(2*V1);
14516: }
14517: Opt=cons(["opt",0],getopt());
14518: V=xygraph(V[0],V[1],V[2],Mx,Mx|option_list=Opt);
14519: }
14520: if(type(V[0][0])!=4) V=os_md.lbezier(V);
14521: for(S=0; V!=[]; V=cdr(V)){
14522: B=tobezier(car(V));
14523: P=intpoly(B[1]*diff(B[0],t),t);
14524: S+=mysubst(P,[t,1]);
14525: }
14526: return S;
14527: }
14528:
14529: def velbezier(V,L)
14530: {
14531: if(L==0) L=[t,0,1];
14532: else L=[(length(L)==3)?L[2]:t,L[0],L[1]];
14533: for(R=[],II=length(V)-1;II>=0;II--){
14534: S=fmmx(diff(V[II],L[0]|dif=1),L|dif=1);
14535: for(U=0;S!=[];S=cdr(S)) if((T=abs(car(S)[1]))>U) U=T;
14536: R=cons(U,R);
14537: }
14538: return R;
14539: }
14540:
14541: def ptbezier(V,L)
14542: {
14543: if(type(V[0])==4&&type(V[0][0])!=4) V=lbezier(V);
14544: K=length(V);
14545: if(type(L)<2){
14546: if(L<0) return K;
14547: if(L>=K-1) L=[K-1,1];
14548: else{
14549: L0=floor(L);
14550: if(L0>=K-1) L0=K-1;
14551: L=[L0,L-L0];
14552: }
14553: }
14554: if(L[0]>=0) B=V[L[0]];
14555: else B=V[K+L[0]];
14556: B=tobezier(B);
14557: BB=[diff(B[0],t),diff(B[1],t)];
14558: return [subst(B,t,L[1]),subst(BB,t,L[1])];
14559: }
14560:
14561: def ptcombezier(P,Q,T)
14562: {
14563: if(type(T)<2){
14564: if(T<2) T=20; /* default */
14565: return ptcombezier(P,Q,[0,0,1,T]);
14566: }
14567: V=T[2]/2;;
14568: PB=tobezier(P|div=1);
14569: PP=[ptbbox(PB[0]),ptbbox(PB[1])];
14570: QB=tobezier(Q|div=1);
14571: QQ=[ptbbox(QB[0]),ptbbox(QB[1])];
14572: for(L=[],I=0;I<2;I++){
14573: for(J=0;J<2;J++){
14574: if(!iscombox(PP[I],QQ[J])) continue;
14575: if(T[3]<=1) return
14576: [[T[0]+(I+0.5)*V,T[1]+(J+0.5)*V,
14577: [(PP[I][0][0]+PP[I][0][1])/2,(PP[I][1][0]+PP[I][1][1])/2]]];
14578: else{
14579: #if 0
14580: U=PB[I][0];V=PB[I][length(PB[I])-1];
14581: if(abs(A=(U[0]-V[0]))>abs(B=(U[1]-V[I])))
14582: M=mat([1,0],[-B/A,1]);
14583: else if(U!=V)
14584: M=mat([1,-A/B],[0,1]);
14585: else continue;
14586: if(!iscombox(ptbox(ptaffine(M,PB[I])),ptbox(ptaffine(M,QB[J])))) continue;
14587: #endif
14588:
14589: LN=ptcombezier(PB[I],QB[J],[T[0]+I*V,T[1]+J*V,V,T[3]-1]);
14590: #if 0
14591: L=append(LN,L);
14592: #else
14593: if(LN!=[]){
14594: if(L==[]) L=LN;
14595: else for(VV=3*V/2^T[3];LN!=[];LN=cdr(LN)){
14596: for(LT=L;LT!=[];LT=cdr(LT)){
14597: if(abs(car(LN)[0]-car(LT)[0])<VV&&abs(car(LN)[1]-car(LT)[1])<VV) break;
14598: }
14599: }
14600: }
14601: if(length(L)>32){ /* Too many points */
14602: I=J=2;
14603: }
14604: #endif
14605: }
14606: }
14607: }
14608: return L;
14609: }
14610:
14611:
14612: def ptcombz(P,Q,T)
14613: {
14614: if(P==Q) Q=0;
14615: if(type(P[0][0])!=4) P=P0=lbezier(P);
14616: if(Q==0){
14617: Q=P;F=1;
14618: }
14619: else if(type(Q[0][0])!=4) Q=lbezier(Q);
14620: for(R=[],I=0,Q0=Q;P!=[];P=cdr(P),I++){
14621: for(J=0,Q=Q0;Q!=[];Q=cdr(Q),J++){
14622: if(F==1&&I<J+2) break;
14623: if((RT=ptcombezier(car(P),car(Q),T))!=[]){
14624: RT=cons([I,J],RT);
14625: R=cons(RT,R);
14626: }
14627: }
14628: }
14629: if((Red=getopt(red))==1||Red==2){
14630: if(type(M=getopt(prec))!=1) M=12;
14631: for(F=0,T=P0;T!=[];T=cdr(T)){
14632: for(S=car(T);S!=[];S=cdr(S)){
14633: if(type(ST=car(S))==4 && type(ST[0])<2){
14634: if(F++==0){
14635: X0=X1=ST[0];Y0=Y1=ST[1];
14636: }else{
14637: if(ST[0]<X0) X0=ST[0];
14638: if(ST[0]>X1) X1=ST[0];
14639: if(ST[1]<Y0) Y0=ST[1];
14640: if(ST[1]>Y1) Y1=ST[1];
14641: }
14642: }
14643: }
14644: }
14645: V0=(X1-X0)/2^M;V1=(Y1-Y2)/2^M;
14646: for(RR=[],RT=R;RT!=[];RT=cdr(RT))
14647: for(S=cdr(car(RT));S!=[];S=cdr(S)) RR=cons(car(S)[2],RR);
14648: RR=ltov(RR);L=length(RR);
14649: for(I=0;I<L;I++)
14650: for(K=1,J=I+1;K!=0&&J<L;J++)
14651: if(abs(RR[I][0]-RR[J][0])<V0 && abs(RR[I][1]-RR[J][1])<V1) RR[I]=K=0;
14652: R0=[];
14653: I=L-1;
14654: if(Red==2){
14655: for(;I>=0;I--) if(RR[I]!=0) R0=cons(RR[I],R0);
14656: }else{
14657: for(RT=R;RT!=[];RT=cdr(RT)){
14658: R00=[car(RT)[0]];
14659: for(S=cdr(car(RT));S!=[];S=cdr(S),I--)
14660: if(RR[L-I-1]!=0) R00=cons(car(S),R00);
14661: if(length(R00)>1) R0=cons(reverse(R00),R0);
14662: }
14663: }
14664: return R0;
14665: }
14666: return reverse(R);
14667: }
14668:
14669: def draw_bezier(ID,IDX,B)
14670: {
14671: if(getopt(init)==1){
14672: S_FDot=0;
14673: return;
14674: }
14675: if(type(Col=getopt(col))!=1&&Col!=0) Col=0;
14676: Dot=0;
14677: if(type(Opt=getopt(opt))==7){
14678: if(!Col){
14679: Col=drawopt(Opt,0);
14680: if(Col==-1) Col=0;
14681: }
14682: T=drawopt(Opt,3);
14683: if(iand(T,2)){
14684: M=iand(T,1)?1/8:1/4;
14685: for(C=Col,Col=I=0;I<20;I+=8)
14686: Col+=ishift(0xff-(floor((0xff-iand(0xff,ishift(C,I)))*M)),-I);
14687: }
14688: if(iand(T,4)) Dot=2; /* 2 or 3 or 4 or 6 */
14689: else if(iand(T,8)) Dot=4;
14690: }
14691: if(type(B)==4 && (type(B[0])==4||type(B[0])==5) && type(B[0][0])<2) B=lbezier(B);
14692: else if(type(B)==5) B=[vtol(B)];
14693: for(;B!=[];B=cdr(B)){
14694: if(vars(F=car(B))==[]){
14695: #if 1
14696: if(length(F)<3&&!Dot){ /* line or point */
14697: if(length(F)>0){
14698: G=[rint(F[0][0]),rint(F[0][1])];
14699: if(length(F)==1) draw_obj(ID,IDX,G,Col);
14700: else{
14701: G=[G[0],G[1],rint(F[1][0]),rint(F[1][1])];
14702: draw_obj(ID,IDX,G,Col);
14703: }
14704: }
14705: continue;
14706: }
14707: #endif
14708: if(length(F)<2) continue;
14709: F=tobezier(F);
14710: }
14711: N=velbezier(F,0);
14712: N=(N[0]>N[1])?N[0]:N[1];
14713: if(!N) N=1;
14714: for(I=0;I<=N;I++,S_FDot++){
14715: if(Dot!=iand(S_FDot,Dot)) continue;
14716: G=subst(F,t,I/N);
14717: G=[rint(G[0]),rint(G[1])];
14718: if(G!=G0){
14719: draw_obj(ID,IDX,G,Col);
14720: G0=G;
14721: }
14722: }
14723: }
14724: if(S_FDot-->=2^32) S_FDot=0;
14725: return 0;
14726: }
14727:
1.29 takayama 14728:
14729: /*
14730: def redbezier(L)
14731: {
14732: V=newvect(4);ST=0;
14733: for(R=[],I=0,T=L;T=[];T=cdr(T){
14734: if(type(car(T))<4){
14735: F=0;
14736: if(I==3)
14737: if(car(T)==0){
14738: }else if(car(T)==1){
14739: }else if(car(T)==-1){
14740: if(I<3) V[I++]=ST;
14741: }
14742: }else if(I==3){
14743: if(R==[] || car(R)!=1){
14744: R=cons(V[0],R);
14745: if(ST==0) ST=V[0];
14746: }
14747: for(J=1;J<3;J++) R=cons(V[J],R);
14748: while((T=cdr(T))!=[]){
14749: R=cons(car(T),R);
14750: if(type(car(R))<4)
14751: }
14752: }else{
14753: if(ST==0) ST=car(T);
14754: V[I++]= car(T);
14755: }
14756: }
14757: }
14758: */
14759:
1.6 takayama 14760: def lbezier(L)
14761: {
14762: if((In=getopt(inv))==1||In==2||In==3){
14763: for(F=0,R=[];L!=[];L=cdr(L)){
14764: LT=car(L);
14765: if(F==car(LT)) R=cons(1,R);
14766: else{
14767: if(R!=[]&&F!=0) R=cons(0,R);
14768: R=cons(G=car(LT),R);
14769: if(In==3) In==2;
14770: }
14771: for(LT=cdr(LT);LT!=[];LT=cdr(LT))
14772: R=cons(car(LT),R);
14773: if((F=car(R))==G&&In==1){
14774: R=cons(-1,cdr(R));
14775: F=0;
14776: }
14777: }
14778: if(In==3 && car(R)==G) R=cons(-1,cdr(R));
14779: return reverse(R);
14780: }
14781: for(F=0,RT=R=[];L!=[];L=cdr(L)){
14782: if(type(T=car(L))==4||type(T)==5){
14783: if(F==0){
14784: FT=T;F=1;
14785: }
14786: RT=cons(T,RT);
14787: }else if(T==0){
14788: if(RT==[]) R=cons(reverse(RT),R);
14789: RT=[];F=0;
14790: }else if(T==1){
14791: if(RT!=[]){
14792: R=cons(reverse(RT),R);
14793: RT=[car(RT)];
14794: }else{
14795: RT=[];F=0;
14796: }
14797: }else if(T==-1){
14798: RT=cons(FT,RT);
14799: R=cons(reverse(RT),R);
14800: RT=[];F=0;
14801: }
14802: }
14803: if(RT!=[]) R=cons(reverse(RT),R);
14804: return reverse(R);
14805: }
14806:
14807:
14808: def xybezier(L)
14809: {
14810: if(L==0 || (LS=length(L))==0) return "";
14811: Out=str_tb(0,0);
14812: if(type(VF=getopt(verb))==4){
14813: if(type(car(VF))>3){
14814: VFS=VF;VF=1;
14815: }else{
14816: VFS=cdr(VF);VF=car(VF);
14817: }
14818: }else VFS=["$\\bullet$","$\\times$"];
14819: if(VF!=1 && VF!=2) VF=0;
14820: if(!TikZ){
14821: if(VF) Ob=str_tb(0,0);
14822: T="\n**\\crv{";
14823: if(type(Opt=getopt(opt))==7 && Opt!="") T=T+Opt;
14824: L00=Q=L[I0=0];S=S1="";
14825: for(F=0,I=1;I<=LS;I++){
14826: P=Q;Q=(I==LS)?0:L[I];
14827: if(type(Q)==4){
14828: if(F==0){
14829: S1="";L0=P;F=1;
14830: continue;
14831: }else if(F==1)
14832: F=2;
14833: else if(F==2){
14834: S1=S1+"&";
14835: }
14836: S1=S1+xypos(P);
14837: if(VF&&length(VFS)>1) str_tb(xyput([P[0],P[1],VFS[1]]),Ob);
14838: }else{
14839: if(Q==0){
14840: if(F>0){
14841: str_tb("{"+xypos(L0)+";"+xypos(P)+T+S1+"}};\n",Out);
14842: if(VF){
14843: str_tb(xyput([L[0][0],L[0][1],VFS[0]]),Ob);
14844: if(VF==1) str_tb(xyput([P[0],P[1],VFS[0]]),Ob);
14845: }
14846: F=0;
14847: }
14848: }else if(Q==1){
14849: str_tb("{"+xypos(L0)+";"+xypos(P)+T+S1+"}};\n",Out);
14850: if(VF){
14851: str_tb(xyput([L[0][0],L[0][1],VFS[0]]),Ob);
14852: if(VF==1) str_tb(xyput([P[0],P[1],VFS[0]]),Ob);
14853: }
14854: F=1;
14855: }else if(Q==-1){
14856: if(F==2)
14857: S1=S1+"&";
14858: str_tb("{"+xypos(L0)+";"+xypos(L00)+T+S1+xypos(P)+"}};\n",Out);
14859: if(VF) str_tb(xyput([L[0][0],L[0][1],VFS[0]]),Ob);
14860: F=0;
14861: }
14862: if(F==1){
14863: if(I<LS-1 && type(L[I+1])<2){
14864: if(L[I+1]==-1){
14865: str_tb("{"+xypos(P)+";"+xypos(L00)+T+"}};\n",Out);
14866: }
14867: if(VF) str_tb(xyput([P[0][0],P[0][1],VFS[0]]),Ob);
14868: F=0;
14869: }
14870: }
14871: while(++I<LS && type(L[I])<2);
14872: if(I>=LS) break;
14873: if(F==1){
14874: Q=P;I--;F=0;
14875: }else L00=Q=L[I];
14876: }
14877: }
14878: }else{
14879: if(type(T=getopt(cmd))==7){
14880: if(T!="") T="\\"+T;
14881: }else T="\\draw";
14882: if((Rel=getopt(relative))==1) VF=0;
14883: if(VF) Ob=str_tb(0,0);
14884: if(type(Opt=getopt(opt))==7 && Opt!="") T=T+"["+Opt+"]";
14885: Out=str_tb(T,0);
14886: Q=L[0];
14887: for(F=M=0,I=1;I<=LS;I++){
14888: P=Q; Q=(I==LS)?0:L[I];
14889: if(++M>XYLim){
14890: str_tb("\n",Out);M=1;
14891: }
14892: if(type(Q)==4 || type(Q)==5 || type(Q)==7){
14893: if(F==0){
14894: str_tb(" ",Out);
14895: F=1;
14896: }else if(F==1){
14897: str_tb(" .. controls ",Out);
14898: F=2;
14899: }else if(F==2){
14900: str_tb(" and ",Out);
14901: F=2;
14902: }
14903: PP=xypos(P);
14904: if(Rel==1 && F==2) PP="+"+PP;
14905: str_tb(PP,Out);
14906: if(VF&&((F<2)||length(VFS)>1))
14907: str_tb(xyput([P[0],P[1],(F<2)?VFS[0]:VFS[1]]),Ob);
14908: }else{
14909: /* if(I<LS-1) VF=0; */
14910: if(Q==0||Q==1){
14911: PP=xypos(P);
14912: if(Rel==1) PP="+"+PP;
14913: str_tb(((F==0)?" ":((F==1)?" -- ":" .. "))+PP,Out);
14914: if(VF) str_tb(xyput([P[0],P[1],VFS[0]]),Ob);
14915: F=Q;
14916: }else if(Q==-1){
14917: PP=xypos(P);
14918: if(Rel==1) PP="+"+PP;
14919: if(F==1)
14920: str_tb("..controls "+PP+" .. cycle",Out);
14921: else if(F==2)
14922: str_tb(" and "+PP+" .. cycle",Out);
14923: if(VF&&length(VFS)>1) str_tb(xyput([P[0],P[1],VFS[1]]),Ob);
14924: F=0;
14925: }
14926: if(F==1){
14927: if(I<LS-1){
14928: if(L[I+1]==-1){
14929: str_tb(" -- cycle",Out);
14930: I=I+1;
14931: F=0;
14932: }
14933: else if(type(L[I+1])<2) F=0;
14934: }
14935: }
14936: while(++I<LS && type(L[I])<2);
14937: if(I>=LS) break;
14938: Q=L[I];
14939: }
14940: }
14941: str_tb(";\n",Out);
14942: }
14943: if(VF) str_tb(str_tb(0,Ob),Out);
14944: return str_tb(0,Out);
14945: }
14946:
14947: def xybox(L)
14948: {
14949: K=length(L);
14950: P=L[0];Q=L[1];
14951: if(K==2)
14952: LL=[ P, [P[0],Q[1]], Q, [Q[0],P[1]] ];
14953: else{
14954: R=L[2];
14955: LL=[ P, R, Q, [P[0]+Q[0]-R[0],P[1]+Q[1]-R[1]] ];
14956: }
14957: Opt=getopt();
14958: SS=getopt(opt);
1.8 takayama 14959: FL=getopt(color);
14960: if(TikZ&&type(SS)<1&&K==2){
14961: if(type(FL)==4){
14962: F=FL[0];
14963: if(length(FL)>1) CMD=FL[1];
14964: }else if(type(FL)==7) F=FL;
14965: else F="";
14966: F=cons(F,["rectangle"]);
14967: if(CMD) return xyarrow(P,Q|opt=F,cmd=CMD);
14968: else return xyarrow(P,Q|opt=F);
14969: }
1.6 takayama 14970: if(type(SS)!=7&&!TikZ) Opt=cons(["opt","@{-}"],Opt);
14971: Opt=cons(["close",1],Opt);
14972: return xylines(LL|option_list=Opt);
14973: }
14974:
14975: def xyang(S,P,Q,R)
14976: {
14977: Opt=getopt();
14978: if(type(Prec=getopt(prec))!=1) Prec=0;
14979: if(type(Q)>2){
14980: if(R==1||R==-1){ /* 直角 */
14981: P1=ptcommon([Q,P],[-S,0]);
14982: S*=R;
14983: P2=ptcommon([P,P1],[S,@pi/2]);
14984: P3=ptcommon([P1,P2],[S,@pi/2]);
14985: return xylines([P1,P2,P3]|option_list=Opt);
14986: }else if((AR=abs(R))==0||AR==2||AR==3||AR==4){ /* 矢印 */
14987: Ang=myarg([Q[0]-P[0],Q[1]-P[1]]);
14988: if(R<0) Ang+=3.14159;
14989: ANG=[0.7854,0.5236,1.0472];
14990: X=(AR==0)?1.5708:ANG[AR-2];
14991: U=[P[0]+S*dcos(Ang+X),P[1]+S*dsin(Ang+X)];
14992: V=[P[0]+S*dcos(Ang-X),P[1]+S*dsin(Ang-X)]; /* 矢先 */
14993: V=(X==0)?[U,V]:[U,P,V];
14994: if(getopt(ar)==1) V=append([Q,P,0],V); /* 心棒 */
14995: return xylines(V|option_list=Opt);
14996: }else if(AR>4&&AR<9){
14997: Ang=myarg([Q[0]-P[0],Q[1]-P[1]]);
14998: ANG=[0.7854,0.5236,0.3927,0.2618];
14999: X=ANG[AR-5];
15000: U=[P[0]+S*dcos(Ang+X),P[1]+S*dsin(Ang+X)];
15001: V=[P[0]+S*dcos(Ang-X),P[1]+S*dsin(Ang-X)];
15002: W=ptcommon([P,U],[P,Q]|in=-2);
15003: W1=[(U[0]+P[0]+W[0])/3,(U[1]+P[1]+W[1])/3];
15004: W2=[(V[0]+P[0]+W[0])/3,(V[1]+P[1]+W[1])/3];
15005: L=[U,W1,P,1,W2,V];
15006: if(getopt(ar)==1) L=append([Q,P,0],L);
15007: if(type(Sc=getopt(scale))>0){
15008: if(type(Sc)==1) Sc=[Sc,Sc];
15009: L=ptaffine(diagm(2,Sc),L);
15010: }
15011: Opt=getopt(opt);
15012: if(type(Opt)>0) OL=[["opt",Opt]];
15013: else OL=[];
15014: if(getopt(proc)==1) return append([2,OL],L);
15015: S=xybezier(L|optilon_list=OL);
15016: if(getopt(dviout)!=1) return S;
15017: dviout(S);
15018: return 1;
15019: }
15020: }
15021: if(type(Q)<3){
15022: X=deval(Q); Y=deval(R);
15023: }else{
15024: X=myarg([Q[0]-P[0],Q[1]-P[1]]);
15025: Y=myarg([R[0]-P[0],R[1]-P[1]]);
15026: }
15027: if(Prec>2) N=8;
15028: else if(Prec==2) N=6;
15029: else if(Prec==1) N=4;
15030: else N=3;
15031: U=deval(@pi)*2/N;
15032: if(X==Y||Y-X>6.28318){
15033: for(L=[],I=N-1;I>=0;I--) L=cons([P[0]+S*dcos(I*U),P[1]+S*dsin(I*U)],L);
15034: return xylines(L|option_list=append([["curve",1],["close",1]],Opt));
15035: }
15036: for(M=1;(Y-X)/M>U;M++);
15037: for(L=[],I=M+1;I>-2;I--){
15038: Ang=X+(Y-X)*I/M;
15039: L=cons([P[0]+S*dcos(Ang),P[1]+S*dsin(Ang)],L);
15040: }
15041: if(getopt(ar)!=1) return xylines(L|option_list=append([["curve",1],["close",-1]],Opt));
15042: OL=delopt(Opt,["dviout","opt","proc"]);
15043: S=xylines(L|option_list=append([["curve",1],["close",-1],["opt",0]],OL));
15044: T=xylines([P,L[1]]|option_list=cons(["opt",0],OL));
15045: S=ptaffine("close",[S,T]); /* connect curves */
15046: if(getopt(opt)==0) return S;
15047: OL=(type(SS=getopt(opt))>1)?[["opt",SS]]:[];
15048: if(type(T=getopt(proc))==1 && T>=1 && T<=3) return [1,OL,S];
15049: if(OL==[]) S=xybezier(S);
15050: else S=(type(SS)==7)? xybezier(S|opt=SS):xybezier(S|opt=SS[0],cmd=SS[1]);
15051: if(getopt(dviout)==1) return xyproc(S|dviout=1);
15052: return S;
15053: }
15054:
15055: def xyoval(P,L,R)
15056: {
15057: if(type(Arg=getopt(arg))!=4 && type(Arg=getopt(deg))==4){
15058: if(length(Arg)>2)
15059: Arg=[@pi*Arg[0]/180,@pi*Arg[1]/180,@pi*Arg[2]/180];
15060: else
15061: Arg=[@pi*Arg[0]/180,@pi*Arg[1]/180];
15062: }
15063: if(type(Arg)==4){
15064: Arg0=deval(Arg[0]); Arg1=deval(Arg[1]);
15065: if(length(Arg)>2) Arg2=deval(Arg[2]);
15066: if(Arg1<Arg0 || Arg0<-7) return 0;
15067: }
15068: if(type(Prec=getopt(prec))!=0) Prec=0;
15069: if((Ar=getopt(ar))!=1) Ar=0;
15070: L=xyang(L,[0,0],Arg0,Arg1|prec=Prec,opt=0,ar=Ar);
15071: Sc=getopt(scale);
15072: if(type(Sc=getopt(scale))<1) Sc=[1,1];
15073: else if(type(Sc)==1) Sc=[Sc,Sc];
15074: M=mat([1,0],[0,R]);
15075: L=ptaffine(M,L|shift=P);
15076: M=mat([Sc[0],0],[0,Sc[1]]);
15077: L=ptaffine(M,L|arg=Arg2);
15078: if((Opt=getopt(opt))==0) return L;
15079: Opt=(type(Opt)>1)? [["opt2",Opt]]:[];
15080: if(getopt(proc)==1) return [1,Opt,L];
15081: S=xybezier(L|option_list=getopt());
15082: if(getopt(dviout)==1){
15083: xyproc(S|dviout=1);
15084: return 1;
15085: }
15086: return S;
15087: }
15088:
15089: def xycirc(P,R)
15090: {
15091: ST=getopt(opt);
15092: if(type(ST)<0) ST="";
15093: if(type(Arg=getopt(arg))!=4 && type(Arg=getopt(deg))==4){
15094: Arg=[@pi*Arg[0]/180,@pi*Arg[1]/180];
15095: }
15096: /* Is it OK?
15097: if(TikZ==0 && XYcm==1){
15098: R*=10; P=[P[0]*10,P[1]*10];
15099: }
15100: */
15101: if(type(Arg)==4){
15102: Arg0=deval(Arg[0]); Arg1=deval(Arg[1]);
15103: if(Arg1<=Arg0 || Arg0<-7 || Arg1-Arg0>7) return 0;
15104: if(type(ST)==7)
15105: S=xygraph([R*cos(x)+P[0],R*sin(x)+P[1]],-4,[Arg0,Arg1],[P[0]-R-1,P[0]+R+1],
15106: [P[1]-R-1,P[1]+R+1]|opt=ST);
15107: else
15108: S=xygraph([R*cos(x)+P[0],R*sin(x)+P[1]],-4,[Arg0,Arg1],[P[0]-R-1,P[0]+R+1],
15109: [P[1]-R-1,P[1]+R+1]);
15110: if(getopt(close)==1){
15111: S=S+xyline([0,0],
15112: [deval(subst(R*cos(x)+P[0],x,Arg0)),deval(subst(R*sin(x)+P[0],x,Arg0))]);
15113: S=S+xyline([0,0],
15114: [deval(subst(R*cos(x)+P[0],x,Arg1)),deval(subst(R*sin(x)+P[0],x,Arg1))]);
15115: }
15116: return S;
15117: }
15118: if(TikZ){
15119: SP="";
15120: if(length(P)>2) SP=P[2];
15121: if(type(SP)!=7) SP="$"+my_tex_form(SP)+"$";
15122: if(R==0){
15123: if(ST!="") ST=ST+",";
15124: return "\\node ["+ST+"circle,draw]"+xypos([P[0],P[1]])+ "{"+SP+"};\n";
15125: }
1.8 takayama 15126: if(type(R)!=7) R=rtostr(deval(R));
1.6 takayama 15127: if(ST!="") ST="["+ST+"]";
15128: S="\\draw "+ST+xypos([P[0],P[1]])+" circle [radius="+R+"]";
15129: if(SP!="") S=S+" node at"+xypos([P[0],P[1]])+" {"+SP+"}";
15130: return S+";\n";
15131: }
15132: S="{"+xypos([P[0],P[1]]);
15133: if(length(P)>2){
15134: SP=P[2];
15135: if(type(P)!=7) SP=my_tex_form(SP);
15136: S=S+" *+{"+SP+"}";
15137: }
15138: S =S+" *\\cir";
15139: if(R!=0){
1.8 takayama 15140: R=deval(R);
1.6 takayama 15141: S=S+"<"+rtostr(R)+((XYcm)?"cm>":"mm>");
15142: }
15143: S = S+"{";
15144: if(type(ST)==7) S=S+ST;
15145: return S+"}};\n";
15146: }
15147:
1.33 takayama 15148: def xypoch(W,H,R1,R2)
15149: {
15150: if(H>R1||2*H>R2){
15151: errno(0);
15152: return;
15153: }
15154: if(type(Ar=getopt(ar))!=1) Ar=TikZ?0.25:2.5;
15155: T1=dasin(H/R1);S1=R1*dcos(T1);
15156: T2=dasin(H/R2);S2=R2*dcos(T2);
15157: T3=dasin(2*H/R2);S3=R2*dcos(T3);
15158: S=xyline([R1,0],[W-R1,0]);
15159: S+=xyang(R1,[W,0],-@pi,@pi-T1);
15160: S+=xyline([S2,H],[W-S1,H]);
15161: S+=xyang(R2,[0,0],T2,2*@pi-T3);
15162: S+=xylines([[S3,-2*H],[W-H-R2,-2*H],[W-H-R2,2*H],[W-S3,2*H]]);
15163: S+=xyang(R2,[W,0],-@pi+T2,@pi-T3);
15164: S+=xyline([W-T2,-H],[W-T2,-H]);
15165: S+=xyang(R1,[0,0],0,2*@pi-T1);
15166: S+=xyline([W-S2,-H],[S1,-H]);
15167: if(Ar>0){
15168: S+=xyang(Ar,[W/2,0],[0,0],8);
15169: S+=xyang(Ar,[W/2,-2*H],[0,-2*H],8);
15170: S+=xyang(Ar,[W/2-Ar,-H],[W,-H],8);
15171: S+=xyang(Ar,[W/2-Ar,H],[W,H],8);
15172: S+=xyang(Ar,[W-S3,2*H],[W-H-R2,2*H],8);
15173: }
15174: S+=xyput([R1,0,"$\\bullet$"]);
15175: S+=xyput([0,0,"$\\times$"]);
15176: S+=xyput([W,0,"$\\times$"]);
15177: if(TikZ) S=str_subst(S,";\n\\draw","\n");
15178: return S;
15179: }
15180:
1.6 takayama 15181: def ptaffine(M,L)
15182: {
15183: if(type(L)!=4&&type(L)!=5){
15184: erno(0);return L;
15185: }
15186: if(type(M)==7){ /* connect lists */
15187: if(M=="reverse"){
15188: for(LO=LR=[],F=0,LT=L; LT!=[]; LT=cdr(LT)){
15189: if(type(P=car(LT))==4 || type(P)==7){
15190: LR=cons(P,LR);
15191: continue;
15192: }else{
15193: if(P==-1){
15194: LL=reverse(LR);
15195: LO=append(reverse(cons(-1,cdr(LL))),LO);
15196: LO=cons(car(LL),LO);
15197: LR=[];
15198: }else if(P==1){
15199: LR=cons(car(LR),cons(1,cdr(LR)));
15200: }else if(P==0 || length(LT)==1){
15201: if(LO!=[] && car(LO)!=0 && (type(car(LO))==4 || car(LO)==1))
15202: LO=cons(0,LO);
15203: LO=append(LR,LO);
15204: if(length(LT)>1&&length(LO)>0&&car(LO)!=0) LO=cons(0,LO);
15205: LR=[];
15206: }
15207: }
15208: }
15209: return append(LR,LO);
15210: }
15211: if(type(L[0][0])!=4) L=[L];
15212: LO=[];
15213: if(M=="connect" || M=="close" || M=="loop"){
15214: Top=car(car(L));
15215: for(K=1,LL=L; LL!=[]; LL=cdr(LL)){
15216: for(F=0,LT=car(LL); LT!=[]; LT=cdr(LT),F++){
15217: if((LTT=car(LT))==0) LTT=1;
15218: if(F==0 && LO!=[]){
15219: LO0=car(LO);
15220: if(car(LO)!=1&&length(LO)>1) LO=cons(1,LO);
15221: if(LTT==LO0) continue;
15222: else LO=cons(1,cons(LTT, LO));
15223: }else LO=cons(LTT, LO);
15224: }
15225: }
15226: if(M!="connect"){
15227: if(Top==car(LO) || car(LO)==1 || M=="loop")
15228: LO=cons(-1,cdr(LO));
15229: else
15230: LO=cons(-1,cons(1,LO));
15231: }
15232: return reverse(LO);
15233: }
15234: if(M=="union"){
15235: for(LL=reverse(L); LL!=[]; LL=cdr(LL)){
15236: if(LO!=[]) LO=cons(0,LO);
15237: LO=append(car(LL),LO);
15238: }
15239: L=LO;
15240: }
15241: return L;
15242: }
15243: if(type(Arg=getopt(deg))==1)
15244: Arg=@pi*Arg/180;
15245: else Arg=getopt(arg);
15246: if(type(Arg)==2) Arg=deval(Arg);
15247: if(type(Arg)==1)
15248: M=M*mat([dcos(Arg),-dsin(Arg)],[dsin(Arg),dcos(Arg)]);
15249: if(type(Sft=getopt(org))==4){
15250: Sft=ltov(Sft);
15251: Sft-=M*Sft;
15252: }else Sft=ltov([0,0]);
15253: if(type(V=getopt(shift))==4)
15254: Sft+=ltov(V);
15255: if(getopt(proc)==1){
15256: if(Sft!=0&<ov(Sft)!=[0,0]) Sft=[["shift",vtol(Sft)]];
15257: else Sft=[];
15258: for(LO=[],LT=L;LT!=[];LT=cdr(LT)){
15259: if(type(car(T=car(LT)))<2){
15260: if((P=car(T))==0){ /* exedraw 0 */
15261: V=[[T[1][0],T[2][0]],[T[1][0],T[2][1]],[T[1][1],T[2][0]],[T[1][1],T[2][1]]];
15262: V=ptbbox(ptaffine(M,V|option_list=Sft));
15263: L1=cdr(cdr(cdr(T)));
15264: LO=cons(append([0,V[0],V[1]],L1),LO);
15265: continue;
15266: }else if(P==1){ /* exedraw 1 */
15267: L1=[];
15268: for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){
15269: D=car(TT);
15270: if(type(D[0][0])==4){
15271: for(L2=[],DT=D;DT!=[];DT=cdr(DT))
15272: L2=cons(ptaffine(M,car(DT)|option_list=Sft),L2);
15273: L1=cons(reverse(L2),L1);
15274: }else L1=cons(ptaffine(M,D|option_list=Sft),L1);
15275: }
15276: LO=cons(append([1,T[1]],reverse(L1)),LO);
15277: continue;
15278: }else if(P>=2 && P<=5){
15279: L1=ptaffine(M,cdr(cdr(T))|optilon_list=Sft);
15280: LO=cons(append([P,T[1]],L1),LO);
15281: continue;
15282: }
15283: }
15284: LO=cons(T,LO);
15285: }
15286: return reverse(LO);
15287: }
15288: F=0;
15289: if(type(L)==4){
15290: for(LT=L; LT!=[]; LT=cdr(LT)){
15291: if((T=type(car(LT)))==4||T==5){
15292: F=1; break;
15293: }
15294: }
15295: }
15296: if(F==0) return (Sft==0)?ptaffine(M,[L])[0]:ptaffine(M,[L]|shift=vtol(Sft))[0];
15297: for(LO=[],LT=L; LT!=[]; LT=cdr(LT)){
15298: if(((T=type(P=car(LT)))!=4 && T!=5)||type(P[0])>3) LO=cons(P,LO);
15299: else{
15300: if(T==4) P=ltov(P);
15301: V=M*P;
15302: if(Sft!=0) V+=Sft;
15303: if(T==4) V=vtol(V);
15304: LO=cons(V,LO);
15305: }
15306: }
15307: return reverse(LO);
15308: }
15309:
15310: def ptlattice(M,N,X,Y)
15311: {
15312: if(type(S=getopt(scale))!=1) S=1;
15313: if(type(Cond=getopt(cond))!=4) Cond=[];
15314: Line=getopt(line);
15315: if(Line==1 || Line==2) F=newmat(M,N);
15316: else Line=0;
15317: if(type(Org=getopt(org))==4) Org=ltov(Org);
15318: else Org=newvect(length(X));
15319: X=ltov(X); Y=ltov(Y);
15320: for(L=[],I=M-1;I>=0;I--){
15321: for(P0=P1=0,J=N-1;J>=0;J--){
15322: P=Org+I*X+J*Y;
15323: for(C=Cond; C!=[]; C=cdr(C))
15324: if(subst(car(C),x,P[0],y,P[1])<0) break;
15325: if(C!=[]) continue;
15326: if(Line) F[I][J]=1;
15327: else L=cons(vtol(S*P),L);
15328: }
15329: }
15330: if(Line==0) return L;
15331: for(I=M-1;I>=0;I--){
15332: for(T0=0,T1=J=N-1;J>=0;J--){
15333: if((K=F[I][J])!=0){
15334: if(T0==0) T0=J;
15335: else T1=J;
15336: }
15337: if(K==0 || T1==0){
15338: if(T1<T0){
15339: L=cons(vtol(S*(Org+I*X+T0*Y)), L);
15340: L=cons(vtol(S*(Org+I*X+T1*Y)), L);
15341: L=cons(0,L);
15342: }
15343: T0=0; T1=N-1;
15344: }
15345: }
15346: }
15347: for(J=N-1;J>=0;J--){
15348: for(T0=0,T1=I=M-1;I>=0;I--){
15349: if((K=F[I][J])!=0){
15350: if(T0==0) T0=I;
15351: else T1=I;
15352: }
15353: if(K==0 || T1==0){
15354: if(T1<T0){
15355: L=cons(vtol(S*(Org+T0*X+J*Y)), L);
15356: L=cons(vtol(S*(Org+T1*X+J*Y)), L);
15357: L=cons(0,L);
15358: }
15359: T0=0; T1=M-1;
15360: }
15361: }
15362: }
15363: return cdr(L);
15364: }
15365:
15366: def ptpolygon(N,R)
15367: {
15368: if(type(S=getopt(scale))!=1) S=1;
15369: if(type(Org=getopt(org))!=4) Org=[0,0];
15370: Pi=deval(@pi);
15371: if(type(Arg=getopt(deg))==1)
15372: Arg=Pi*Arg/180;
15373: else Arg=getopt(arg);
15374: if(type(Arg)==2) Arg=deval(Arg);
15375: if(type(Arg)!=1) Arg=0;
15376: Arg -= Pi*(1/2+1/N);
15377: D=Pi*2/N;
15378: for(L=[],I=N-1; I>=0; I--)
15379: L=cons([S*(Org[0]+R*dcos(Arg+I*D)),S*(Org[1]+R*dsin(Arg+I*D))],L);
15380: return L;
15381: }
15382:
15383: def ptwindow(L,X,Y)
15384: {
15385: if(type(S=getopt(scale))==1){
15386: X=[S*X[0],S*X[1]]; Y=[S*Y[0],S*Y[1]];
15387: }
15388: for(R=[],LT=L;LT!=[];LT=cdr(LT)){
15389: P=car(LT);
15390: if(P[0]<X[0] || P[0]>X[1] || P[1]<Y[0] || P[1]>Y[1])
15391: R=cons(0,R);
15392: else R=cons(P,R);
15393: }
15394: return reverse(R);
15395: }
15396:
15397: def lninbox(L,W)
15398: {
15399: if(L[0]==L[1]) return 0;
15400: R=newvect(2);C=newvect(2);
15401: for(J=0;J<2;J++){
15402: C[J]=L[1][J]-L[0][J];
15403: if(C[J]!=0){
15404: R[J]=[(W[J][0]-L[0][J])/C[J],(W[J][1]-L[0][J])/C[J]];
15405: if(R[J][0]>R[J][1]) R[J]=[R[J][1],R[J][0]];
15406: }
15407: }
15408: if(R[0]==0) R[0]=R[1];
15409: if(R[1]==0) R[1]=R[0];
15410: S0=(R[0][0]<R[1][0])?R[1][0]:R[0][0];
15411: S1=(R[0][1]<R[1][1])?R[0][1]:R[1][1];
15412: if(getopt(in)==1){
15413: if(S0<0) S0=0;
15414: if(S1>1) S1=1;
15415: }
15416: if(S0>S1) return 0;
15417: return [[L[0][0]+C[0]*S0,L[0][1]+C[1]*S0],[L[0][0]+C[0]*S1,L[0][1]+C[1]*S1]];
15418: }
15419:
15420: def ptbbox(L)
15421: {
15422: J=length(L[0]);
15423: if((Box=getopt(box))==1){
15424: for(R=[],I=0;I<J;I++){
15425: P=car(LT=L)[I][0];Q=car(LT)[I][1];
15426: for(;LT!=[];LT=cdr(LT)){
15427: if((type(T=car(LT))==4 || type(T)==5) && length(T)==J){
15428: if(T[I][0]<P) P=T[I][0];
15429: if(T[I][1]>Q) Q=T[I][1];
15430: }
15431: }
15432: R=cons([P,Q],R);
15433: }
15434: }else if(type(Box)==4) return ptbbox([ptbbox(L),Box]|box=1);
15435: else{
15436: for(R=[],I=0;I<J;I++){
15437: P=Q=car(LT=L)[I];LT=cdr(LT);
15438: for(;LT!=[];LT=cdr(LT)){
15439: if((type(T=car(LT))==4||type(T)==5) && type(T[0])<2 && length(T)==J){
15440: if((V=T[I])<P) P=V;
15441: else if(V>Q) Q=V;
15442: }
15443: }
15444: R=cons([P,Q],R);
15445: }
15446: }
15447: return reverse(R);
15448: }
15449:
15450: def iscombox(S,T)
15451: {
15452: for(;S!=[];S=cdr(S),T=cdr(T))
15453: if(car(S)[0]>car(T)[1] || car(S)[1]<car(T)[0]) return 0;
15454: return 1;
15455: }
15456:
15457: def ptcopy(L,V)
15458: {
15459: if(type(V[0])!=4) V=[V];
15460: for(F=0,LL=[]; V!=[]; V=cdr(V)){
15461: if(F) LL=append(LL,[0]);
15462: F++;
15463: LL=append(LL,ptaffine(1,L|shift=car(V)));
15464: }
15465: }
15466:
15467: def average(L)
15468: {
1.32 takayama 15469: if(getopt(opt)=="co"){
15470: S0=average(L[0]);V0=car(S0);
15471: S1=average(L[1]);V1=car(S1);
15472: L0=os_md.m2l(L[0]|flat=1);
15473: L1=os_md.m2l(L[1]|flat=1);
15474: for(S=0;L0!=[];L0=cdr(L0),L1=cdr(L1))
15475: S+=(car(L0)-V0)*(car(L1)-V1);
15476: S/=S0[1]*S1[1]*S0[2];
15477: S=[S,S0,S1];
15478: }else{
15479: L=os_md.m2l(L|flat=1);
15480: M0=M1=car(L);
15481: for(I=SS=0, LT=L; LT!=[]; LT=cdr(LT), I++){
15482: S+=(V=car(LT));
15483: SS+=V^2;
15484: if(V<M0) M0=V;
15485: else if(V>M1) M1=V;
15486: }
15487: SS=dsqrt(SS/I-S^2/I^2);
15488: S=[deval(S/I),SS,I,M0,M1];
1.6 takayama 15489: }
1.8 takayama 15490: if(isint(N=getopt(sint))) S=sint(S,N);
15491: return S;
1.6 takayama 15492: }
15493:
15494: def m2ll(M)
15495: {
15496: for(R=[],I=size(M)[0]-1; I>=0; I--)
15497: R=cons(vtol(M[I]),R);
15498: return R;
15499: }
15500:
15501: def madjust(M,W)
15502: {
15503: if(type(Null=getopt(null))<0) Null=0;
15504: if(type(M)==4 && type(M[0])==4){
15505: M=lv2m(M|null=Null);
15506: return m2ll(madjust(M,W|null=Null));
15507: }
15508: S=size(M);
15509: if(W<0){
15510: W=-W;
15511: T0=ceil(S[0]/W);
15512: T1=S[1]*W;
15513: N=newmat(T0,T1);
15514: for(I=0; I<T0; I++){
15515: for(K=0; K<W; K++){
15516: II=K*T0+I;
15517: for(J=0; J<S[1]; J++)
15518: N[I][S[1]*K+J]=(II<S[0])?M[II][J]:Null;
15519: }
15520: }
15521: }else{
15522: T1=W;
15523: T0=S[0]*(D=ceil(S[1]/T1));
15524: N=newmat(T0,T1);
15525: for(K=0; K<D; K++){
15526: for(J=0; J<W;J++){
15527: JJ=W*K+J;
15528: for(I=0; I<S[0]; I++)
15529: N[S[0]*K+I][J]=(JJ<S[1])?M[I][JJ]:Null;
15530: }
15531: }
15532: }
15533: return N;
15534: }
15535:
15536: def texcr(N)
15537: {
15538: if(!isint(N) || N<0 || N>127) return N;
15539: S=(iand(N,8))? "\\allowdisplaybreaks":"";
15540: if(iand(N,2)) S=S+"\\\\";
15541: if(iand(N,16)) S=S+"\\pause";
15542: if(iand(N,1)) S=S+"\n";
15543: if(iand(N,4)) S=S+"& ";
15544: else if(!iand(N,1)) S=S+" ";
15545: if(iand(N,64)) S=S+"=";
15546: if(iand(N,32)) S=","+S;
15547: return S;
15548: }
15549:
15550: def ltotex(L)
15551: {
15552: /* extern TeXLim; */
15553:
15554: if(type(L)==5)
15555: L = vtol(L);
15556: if(type(L) != 4)
15557: return my_tex_form(L);
15558: Opt=getopt(opt);
15559: Pre=getopt(pre);
15560: if(type(Var=getopt(var))<1) Var=0;
15561: Cr2="\n";
15562: if(type(Cr=getopt(cr))==4){
15563: Cr2=Cr[1];Cr=Cr[0];
15564: }
15565: if(isint(Cr)) Cr=texcr(Cr);
15566: if(type(Cr)!=7) Cr="\\\\\n & "; /* Cr=7 */
15567: if(type(Opt)==7) Opt=[Opt];
15568: if(type(Opt)!=4)
15569: Op = -1;
15570: else{
15571: Op=findin(Opt[0],["spt","GRS","Pfaff","Fuchs","vect","cr","text","spts","spts0",
15572: "dform","tab", "graph","coord"]);
15573: Opt=cdr(Opt);
15574: }
15575: if(Op==0){ /* spt */
15576: Out = str_tb("\\left\\{\n ",0);
15577: for(CC=0; L!=[]; L=cdr(L), CC++){
15578: if(CC>0) str_tb(",\\, ",Out);
15579: TP=car(L);
15580: if(Op!=0)
15581: str_tb(my_tex_form(TP),Out);
15582: else if(TP[0]==1)
15583: str_tb(my_tex_form(TP[1]),Out);
15584: else
15585: str_tb(["[", my_tex_form(TP[1]), "]_", rtotex(TP[0])],Out);
15586: }
15587: str_tb("%\n\\right\\}\n",Out);
15588: }else if(Op==1){ /* GRS */
15589: Out = string_to_tb("\\begin{Bmatrix}\n");
15590: if(type(Pre)==7) str_tb(Pre,Out);
15591: MC=length(M=ltov(L));
15592: for(ML=0, I=length(M); --I>=0; ){
15593: if(length(M[I]) > ML) ML=length(M[I]);
15594: }
15595: for(I=0; I<ML; I++){
15596: for(CC=J=0; J<MC; J++, CC++){
15597: if(length(M[J]) <= I){
15598: if(CC > 0) str_tb(" & ",Out);
15599: }else if(M[J][I][0] <= 1){
15600: if(M[J][I][0] == 0) str_tb(" & ",Out);
15601: else
15602: str_tb([(!CC)?" ":" & ", my_tex_form(M[J][I][1])], Out);
15603: }else
15604: str_tb([((!CC)?" [":" & ["), my_tex_form(M[J][I][1]), "]_",
15605: rtotex(M[J][I][0])], Out);
15606: }
15607: str_tb((I<ML-1)?"\\\\\n":"\n", Out);
15608: }
15609: str_tb("\\end{Bmatrix}",Out);
15610: }else if(Op==2){ /* Pfaff */
15611: V=monototex(Opt[0]);
15612: Out = string_to_tb("d"+V+"= \\Biggl(");
15613: Opt=cdr(Opt);
15614: II=length(Opt);
15615: for(I=0; I<II; I++){
15616: str_tb([(I>0)?" + ":" ",mtotex(L[I]),"\\frac{d",monototex(Opt[I]),"}{",
15617: my_tex_form(Opt[I]),(I==II-1)?"}\n":"}\n\\\\&\n"],Out);
15618: }
15619: str_tb(["\\Biggr)",V,"\n"],Out);
15620: }else if(Op==3){ /* Fuchs */
15621: Out = string_to_tb("\\frac{d");
15622: V=my_tex_form(Opt[0]);
15623: str_tb([V,"}{d",my_tex_form(Opt[1]),"}="] ,Out);
15624: Opt=cdr(Opt); Opt=cdr(Opt);
15625: II=length(Opt);
15626: for(I=0; I<II; I++){
15627: str_tb([(I>0)?" +":"\\Biggl(", " \\frac{",
15628: my_tex_form(L[I]),"}{", my_tex_form(Opt[I]),"}\n"],Out);
15629: }
15630: str_tb(["\\Biggr)",V,"\n"],Out);
15631: }else if(Op==4){ /* vect */
15632: Out=str_tb(mtotex(matc(L)|lim=0,var=Var),0);
15633: }else if(Op==5 || Op==6){ /* cr or text */
15634: Out = str_tb(0,0);
15635: if(type(Lim=getopt(lim))!=1) Lim=0;
15636: else if(Lim<30&&Lim>0) Lim=TeXLim;
15637: Str=getopt(str);
15638: if(length(Opt)==1 && (car(Opt)=="spts" || car(Opt)=="spts0") && type(Str)!=1)
15639: Str=2;
15640: for(K=I=0; L!=[]; I++, L=cdr(L)){
15641: LT=car(L);
15642: if((!Lim||Op==6)&&I>0) str_tb((Op==5)?Cr:"\n",Out);
15643: if(Op==6){
15644: if(type(LT)==7){
15645: str_tb([LT," "],Out);
15646: I=-1;
15647: continue;
15648: }
15649: str_tb("$",Out);
15650: }
15651: KK=0;
15652: if(Str>0 && type(LT)==4 && Opt!=[])
15653: S=ltotex(LT|opt=car(Opt),lim=0,str=Str,cr=Cr2,var=Var);
15654: else if(type(LT)==6){
15655: if(Lim>0){
15656: S=mtotex(LT|var=Var,lim=0,len=1);
15657: KK=S[1];
15658: S=S[0];
15659: }else S=mtotex(LT|var=Var,lim=0);
15660: }else if(type(LT)==3 || type(LT)==2)
15661: S=fctrtos(LT|TeX=2,lim=0,var=Var);
15662: else S=my_tex_form(LT);
15663: if(Op!=6&&I>0&&Lim){
15664: if(Lim<0){
15665: if(I%(-Lim)==0)
15666: str_tb((Op==5)?Cr:"\n",Out);
15667: }else if((K+=(KK=(KK)?KK:texlen(S)))>Lim){
15668: str_tb((Op==5)?Cr:"\n",Out);
15669: K=KK;
15670: }
15671: }
15672: str_tb(S,Out);
15673: if(Op==6) str_tb("$",Out);
15674: }
15675: }else if(Op==7||Op==8){ /* spts, spts0 */
15676: if(type(Lim=getopt(lim))!=1 || (Lim<30 && Lim!=0))
15677: Lim=TeXLim;
15678: Str=getopt(str);
15679: Out = str_tb(0,0);
15680: for(K=0; L!=[]; L=cdr(L)){
15681: LT=car(L);
15682: KK=0;
15683: if(type(LT)==7 && Str==1) S=LT;
15684: else if(type(LT)==3 || type(LT)==2)
15685: S=fctrtos(LT|TeX=2,lim=0,var=Var);
15686: else if(type(LT)==6){
15687: if(Lim){
15688: S=mtotex(LT|var=Var,lim=0,len=1);
15689: KK=S[1];
15690: S=S[0];
15691: }else S=mtotex(LT|var=Var,lim=0);
15692: }else
15693: S=my_tex_form(LT);
15694: if(Lim!=0){
15695: if(!KK) KK=texlen(S);
15696: if(K>0 && K+KK>Lim){
15697: str_tb(Cr,Out);
15698: K=0;
15699: }
15700: }
15701: if(K>0){
15702: str_tb((Op==7)?"\\ ":" ",Out);
15703: if(type(LT)>3 && type(LT)<7) str_tb("%\n",Out);
15704: }
15705: str_tb(S,Out);
15706: K+=KK;
15707: if(OP==7) K++;
15708: }
15709: }else if(Op==9){ /* dform */
15710: Out=str_tb(0,0);
15711: for(I=0;L!=[];L=cdr(L),I++){
15712: for(J=0,LT=car(L); LT!=[]; LT=cdr(LT),J++){
15713: if(J==0){
15714: if((V=car(LT))==0) continue;
15715: if(I>0){
15716: if(type(V)==1){
15717: if(V<0){
15718: str_tb("-",Out);
15719: V=-V;
15720: }
15721: else str_tb("+",Out);
15722: if(V==1 && length(LT)>1) continue;
15723: str_tb(monototex(V),Out);
15724: continue;
15725: }
15726: else str_tb("+",Out);
15727: }
15728: }else if(J>0) str_tb((J>1)?"\\wedge d":"\\,d",Out);
15729: V=monototex(car(LT));
15730: if(V<"-" || V>=".") str_tb(V,Out);
15731: else str_tb(["(",V,")"],Out);
15732: }
15733: }
15734: }else if(Op==10 && type(L)==4 && type(car(L))==4){ /* tab */
15735: if(type(Null=getopt(null))<0) Null="";
15736: if(getopt(vert)==1){
15737: M=lv2m(L|null=Null);
15738: L=m2ll(mtranspose(M));
15739: }
15740: if(type(W=getopt(width))==1)
15741: L=madjust(L,W|null=Null);
15742: LV=ltov(L);
15743: S=length(LV);
15744: #if 1
15745: if(type(T=getopt(left))==4){
15746: T=str_times(T,S);
15747: for(L=[],I=0;I<S;I++){
15748: L=cons(cons(car(T),LV[I]),L);
15749: T=cdr(T);
15750: }
15751: LV=reverse(L);
15752: }
15753: if(type(T=getopt(right))==4){
15754: T=str_times(T,S);
15755: for(L=[],I=0;I<S;I++){
15756: L=cons(append(LV[I],[car(T)]),L);
15757: T=cdr(T);
15758: }
15759: LV=reverse(L);
15760: }
15761: for(I=CS=0; I<S; I++)
15762: if(length(LV[I])>CS) CS=length(LV[I]);
15763: if(type(T=getopt(top))==4){
15764: LV=cons(str_times(T,CS),vtol(LV));
15765: S++;
15766: }
15767: if(type(T=getopt(last))==4){
15768: LV=append(vtol(LV),[str_times(T,CS)]);
15769: S++;
15770: }
15771: #else
15772: for(I=CS=0; I<S; I++)
15773: if(length(LV[I])>CS) CS=length(LV[I]);
15774: #endif
15775: if(type(Title=getopt(title))!=7) Title="";
15776: if(type(Vline=getopt(vline))!=4) Vline=[0,CS];
15777: else Vline=subst(Vline,z,CS);
15778: for(VV=[],VT=Vline;VT!=[];VT=cdr(VT)){
15779: if(type(T=car(VT))==4 && T[1]>0){
15780: for(I=T[0];I<=CS;I+=T[1]) VV=cons(I,VV);
15781: }else VV=cons(T,VV);
15782: }
15783: Vline=qsort(VV);
15784: Out=str_tb("\\begin{tabular}{",0);
15785: if(type(Al=getopt(align))==7 && str_len(Al)>1){
15786: str_tb(Al,Out);
15787: }else{
15788: if(type(Al)!=7 || str_len(Al)<1) Al="r";
15789: for(I=0;I<=CS;I++){
15790: if(I!=0) str_tb(Al,Out);
15791: while(Vline!=[] && car(Vline)==I){
15792: str_tb("|",Out);
15793: Vline=cdr(Vline);
15794: }
15795: }
15796: }
15797: str_tb("}",Out);
15798: if(Title!="")
15799: str_tb("\n\\multicolumn{"+rtostr(CS)+"}{c}{"+Title+"}\\\\",Out);
15800: if(type(Hline=getopt(hline))!=4) Hline=[0,S];
15801: else Hline=subst(Hline,z,S);
15802: for(VV=[],VT=Hline;VT!=[];VT=cdr(VT)){
15803: if(type(T=car(VT))==4 && T[1]>0){
1.14 takayama 15804: for(I=T[0];I<=S;I+=T[1]) VV=cons(I,VV);
1.6 takayama 15805: }else VV=cons(T,VV);
15806: }
15807: Hline=qsort(VV);
15808: while(Hline!=[] && car(Hline)==0){
15809: str_tb(" \\hline\n",Out);
15810: Hline=cdr(Hline);
15811: }
15812: /*
15813: if(type(getopt(left))==4) CS++;
15814: if(type(getopt(right))==4) CS++;
15815: if(type(T=getopt(top))==4){
15816: LV=cons(str_times(T,CS),vtol(LV));
15817: S++;
15818: }
15819: if(type(T=getopt(last))==4){
15820: LV=append(vtol(LV),[str_times(T,CS)]);
15821: S++;
15822: }
15823: if(type(T=getopt(left))==4){
15824: T=str_times(T,S);
15825: for(L=[],I=0;I<S;I++){
15826: L=cons(cons(car(T),LV[I]),L);
15827: T=cdr(T);
15828: }
15829: LV=reverse(L);
15830: }
15831: if(type(T=getopt(right))==4){
15832: T=str_times(T,S);
15833: for(L=[],I=0;I<S;I++){
15834: L=cons(append(LV[I],[car(T)]),L);
15835: T=cdr(T);
15836: }
15837: LV=reverse(L);
15838: }
15839: */
15840: for(I=0; I<S; I++){
15841: for(C=0,LT=LV[I];C<CS; C++){
15842: if(LT!=[]){
15843: P=car(LT);
15844: if(type(P)!=7) P="$"+my_tex_form(P)+"$";
15845: if(P!="") str_tb(P,Out);
15846: LT=cdr(LT);
15847: }
15848: if(C<CS-1) str_tb("& ",Out);
15849: }
15850: str_tb("\\\\",Out);
15851: while(Hline!=[] && car(Hline)==I+1){
15852: str_tb(" \\hline",Out);
15853: Hline=cdr(Hline);
15854: }
15855: str_tb("\n",Out);
15856: }
15857: str_tb("\\end{tabular}\n",Out);
15858: }else if(Op==11){ /* graph */
1.10 takayama 15859: if(type(Strip=getopt(strip))!=1) Strip=0;
15860: if(type(MX=getopt(max))!=1) MX=0;
15861: if(type(ML=getopt(mult))!=1) ML=0;
15862: if((REL=getopt(relative))!=1) REL=0;
15863: CL=getopt(color);
15864: OL=delopt(getopt(),["color","strip","mult"]);
15865: if(ML==1&&type(CL)==4){
15866: LL=L[1];L=L[0];K=length(L);S=T="";
15867: if(!MX){
15868: MX=vector(length(L[0]));
15869: for(LT=L;LT!=[];LT=cdr(LT)){
15870: for(I=0,LTT=car(LT);LTT!=[];I++,LTT=cdr(LTT)){
15871: if(REL==1) MX[I]+=car(LTT);
15872: else if(MX[I]<car(LTT)) MX[I]=car(LTT);
15873: }
15874: }
15875: MX=lmax(MX);
15876: OL=cons(["max",MX],OL);
15877: }
15878: if(REL==1) MX=newvect(length(L[0]));
15879: for(I=0;I<K;I++){
15880: for(R=[],J=length(L[I]);--J>=0;){
15881: if(REL==1){
15882: R=cons([MX[J],V=MX[J]+L[I][J]],R);
15883: MX[J]=V;
15884: }else R=cons([(!I)?0:L[I-1][J],L[I][J]],R);
15885: }
15886: OP=cons(["color",CL[I]],OL);
15887: S+=ltotex([R,LL]|option_list=cons(["value",0],cons(["strip",(!I)?1:2],OP)));
15888: T+=ltotex([R,LL]|option_list=cons(["strip",3],OP));
15889: }
15890: return(!Strip)?xyproc(S+T):(S+T);
15891: }else if(!TikZ) CL=0;
15892: if(type(Line=getopt(line))!=1){
15893: if(type(Line)==4){
15894: if(type(Line[0])==1 && (type(Line[1])==7 || type(Line[1])==1)){
15895: Opt=Line[1]; Line=Line[0];
15896: }else if(ML==1){
15897: OL=delopt(OL,"line");
15898: LL=L[1];L=L[0];K=length(L);S="";
15899: if(!MX){
1.15 takayama 15900: MX=newvect(length(L[0]));
1.10 takayama 15901: for(LT=L;LT!=[];LT=cdr(LT)){
15902: for(I=0,LTT=car(LT);LTT!=[];I++,LTT=cdr(LTT)){
15903: if(REL==1) MX[I]+=car(LTT);
15904: else if(MX[I]<car(LTT)) MX[I]=car(LTT);
15905: }
15906: }
15907: MX=lmax(MX);
15908: OL=cons(["max",MX],OL);
15909: }
1.15 takayama 15910: for(I=0;I<K;I++)
15911: S+=ltotex([L[I],LL]|option_list
1.10 takayama 15912: =cons(["line",Line[I]],cons(["strip",(!I)?1:2],OL)));
15913: return(!Strip)?xyproc(S):S;
15914: }
15915: }else Line=0;
15916: }else Opt="@{-}";
15917: Width=8; Hight=3; WRet=1/2; HMerg=(getopt(horiz)==1)?0.3:0.2;
1.6 takayama 15918: if(!TikZ){
1.7 takayama 15919: Width*=10; Hight*=10; HMerg*=10;
1.6 takayama 15920: }
1.10 takayama 15921: VMerg=HMerg;
15922: if(type(Shift=getopt(shift))!=1)
15923: Shift=0;
1.6 takayama 15924: if(type(V=getopt(size))==4){
15925: Width=V[0];Hight=V[1];
15926: if(length(V)>2) WRet=V[2];
1.10 takayama 15927: if(length(V)>3) VMerg=VMerg=V[3];
15928: if(length(V)>4) HMerg=V[4];
1.6 takayama 15929: }
15930: Val=getopt(value);
15931: if(!isint(Val)) Val=-1;
15932: if(type(Line=getopt(line))!=1){
15933: if(type(Line)==4 && type(Line[0])==1 && (type(Line[1])==7 || type(Line[1])==1)){
15934: Opt=Line[1]; Line=Line[0];
15935: }else Line=0;
15936: }else Opt="@{-}";
15937: if(type(car(L))==4){
15938: LL=L[1]; L=L[0];
15939: }else LL=[];
15940: if(Line==-1){
15941: for(Sum=0, LT=L; LT!=[]; LT=cdr(LT)){
15942: if((S=car(LT))<=0) return 0;
15943: Sum+=S;
15944: }
1.16 takayama 15945: for(R=[],LT=L;LT!=[];LT=cdr(LT)) R=cons(car(LT)/Sum,R);
1.6 takayama 15946: R=reverse(R);
15947: Opt0=Opt*2/3;
1.10 takayama 15948: Out=str_tb((Strip>0)?0:xyproc(1),0);
1.16 takayama 15949: if(type(CL)!=4) str_tb(xylines(ptpolygon(6,Opt)|close=1,curve=1),Out);
1.6 takayama 15950: for(S=0,RT=R,LT=LL;RT!=[];RT=cdr(RT)){
1.16 takayama 15951: SS=S+RT[0];
15952: if(type(CL)==4){
15953: str_tb(xyang(Opt,[0,0],(0.25-SS)*6.2832,(0.25-S)*6.2832|ar=1,opt=car(CL)),Out);
15954: if(length(CL)>0) CL=cdr(CL);
15955: }else str_tb(xyline([0,0],[Opt*dsin(S*6.2832),Opt*dcos(S*6.2832)]),Out);
15956: T=(S+SS)/2;
15957: S=SS;
1.6 takayama 15958: if(LT!=[]){
1.16 takayama 15959: str_tb(xyput([Opt0*dsin(T*6.2832),Opt0*dcos(T*6.2832),car(LT)]),Out);
1.6 takayama 15960: LT=cdr(LT);
15961: }
15962: }
1.10 takayama 15963: if(!Strip) str_tb(xyproc(0),Out);
1.6 takayama 15964: return str_tb(0,Out);
15965: }
15966: if(MX==0){
15967: for(MX=0,LT=L; LT!=[]; LT=cdr(LT))
15968: if(car(LT)>MX) MX=car(LT);
15969: }
15970: MX-=Shift;
15971: S=length(L);
15972: WStep=Width/S;
15973: WWStep=WStep*WRet;
1.10 takayama 15974: HStep=(Hight<0)?-Hight:Hight/MX;
1.7 takayama 15975: if(LL!=[]&&length(LL)==S-1) WS2=WStep/2;
15976: else WS2=0;
1.10 takayama 15977: Out=str_tb((Strip>0)?0:xyproc(1),0);
15978: Hori=getopt(horiz);
15979: if(Strip<2){
15980: if(Hori==1) str_tb(xyline([0,0],[0,Width-WStep+WWStep]),Out);
15981: else str_tb(xyline([0,0],[Width-WStep+WWStep,0]),Out);
15982: }
1.6 takayama 15983: for(I=0,LT=L;LT!=[]; LT=cdr(LT),I++){
1.10 takayama 15984: XP=WStep*I; XPM=XP+WWStep/2;
15985: if(type(LTT=car(LT))==4){
15986: YP0=(car(LTT)-Shift)*HStep;YP=(LTT[1]-Shift)*HStep;
15987: VL=LTT[1];
15988: if(REL) VL-=LTT[0];
15989: }else{
15990: YP0=0;YP=(LTT-Shift)*HStep;VL=LTT;
15991: }
15992: if(Hori==1){
15993: if(Line!=0){
15994: if(I>0)
15995: str_tb(xyarrow([XPM,YP],[XPM-WStep,YPP]|opt=Opt),Out);
15996: if(Val!=0)
15997: str_tb(xyput([YP+HMerg, XPM,car(LT)]),Out);
15998: if(Line==2)
15999: str_tb(xyput([YP,XPM,"$\\bullet$"]),Out);
16000: YPP=YP;
16001: }else if(YP!=0 || Val==1){
16002: if(Strip!=3){
16003: if(CL) str_tb(xybox([[YP,XP+WWStep], [YP0,XP]]|color=CL),Out);
16004: else str_tb(xybox([[YP,XP+WWStep],[YP0,XP]]),Out);
16005: }
16006: if(Val!=0) str_tb(xyput([(YP<0||REL==1)?(YP-HMerg):(YP+HMerg),XPM,VL]),Out);
16007: }
16008: if(LL!=[]&&I<length(LL)&&Strip<2) str_tb(xyput([-VMerg,XPM+WS2,LL[I]]),Out);
16009: }else{
16010: if(Line!=0){
16011: if(I>0)
16012: str_tb(xyarrow([XPM-WStep,YPP],[XPM,YP]|opt=Opt),Out);
16013: if(Val!=0)
16014: str_tb(xyput([XPM,YP+HMerg,car(LT)]),Out);
16015: if(Line==2)
16016: str_tb(xyput([XPM,YP,"$\\bullet$"]),Out);
16017: YPP=YP;
16018: }else if(YP!=0 || Val==1){
16019: if(Strip!=3){
16020: if(CL) str_tb(xybox([[XP,YP0],[XP+WWStep,YP]]|color=CL),Out);
16021: else str_tb(xybox([[XP,YP0],[XP+WWStep,YP]]),Out);
16022: }
16023: if(Val!=0) str_tb(xyput([XPM,(YP<0||REL==1)?(YP-HMerg):(YP+HMerg),VL]),Out);
1.6 takayama 16024: }
1.10 takayama 16025: if(LL!=[]&&I<length(LL)&&Strip<2) str_tb(xyput([XPM+WS2,-VMerg,LL[I]]),Out);
1.6 takayama 16026: }
16027: }
1.10 takayama 16028: if(!Strip)str_tb(xyproc(0),Out);
1.6 takayama 16029: }else if(Op==12){ /* coord */
16030: Out=str_tb("(",0);
16031: for(LT=L;;){
16032: X=car(LT);
16033: if(type(X)>3 || imag(X)==0) str_tb(my_tex_form(X),Out);
16034: else{
16035: XR=real(X);XI=imag(X);
16036: S=monototex(imag(X));
16037: if(S=="1") S="";
16038: else if(S=="- 1") S="-";
16039: if(getopt(cpx)==2) S=S+"\\sqrt{-1}";
16040: else S=S+"i";
16041: if(XR!=0){
16042: if(str_char(S,0,"-")==0) S=monototex(XR)+S;
16043: else S=monototex(XR)+"+"+S;
16044: }
16045: str_tb(S,Out);
16046: }
16047: if((LT=cdr(LT))==[]) break;
16048: else str_tb(",",Out);
16049: }
16050: str_tb(")",Out);
16051: }
16052: else return my_tex_form(L);
16053: S = str_tb(0,Out);
16054: return (getopt(small)==1)?smallmattex(S):S;
16055: }
16056:
16057:
16058: def str_tb(L,TB)
16059: {
16060: if(type(TB) == 0) TB = "";
16061: if(L == 0)
16062: return (type(TB) == 7)?string_to_tb(TB):tb_to_string(TB);
16063: if(type(L) == 7)
16064: L = [L];
16065: else if(type(L) != 4){
16066: erno(0);
16067: return 0;
16068: }
16069: if(type(TB) <= 7)
16070: TB = string_to_tb((type(TB)==7)?TB:"");
16071: for(; L != []; L = cdr(L))
16072: write_to_tb(car(L), TB);
16073: return TB;
16074: }
16075:
16076: /*
16077: def redgrs(M,T)
16078: {
16079: L = [zzz];
16080: for(I=S=0,Eq=[],MT=M; MT!=[]; I++, MT=cdr(MT)){
16081: for(J=LS=0, N=car(MT); N!=[]; N=cdr(N)){
16082: X = makev([z,I,z,J]);
16083: L=cons(X,L);
16084: LS += X;
16085: S += car(N)[1]*X;
16086: }
16087: Eq = cons(LS-zzz,Eq);
16088: }
16089: Eq = cons(S-T,Eq);
16090: Sol= lnsol(Eq,L);
16091: for(LS=[],S=Sol; S!=[]; S=cdr(S)){
16092: T=car(S);
16093: if(type(S)!=4) return 0;
16094: LS=cons(car(S)[0],LS);
16095: }
16096: }
16097: */
16098:
16099: /* T=0 : all reduction
16100: =1 : construction procedure
16101: =2 : connection coefficient
16102: =3 : operator
16103: =4 : series expansion
16104: =5 : expression by TeX
16105: =6 : Fuchs relation
16106: =7 : All
16107: =8 : basic
16108: =9 : ""
16109: =10: irreducible
16110: =11: recurrence */
16111: def getbygrs(M, TT)
16112: {
16113: /* extern TeXEq; */
16114:
16115: if(type(M)==7) M=s2sp(M);
16116: if(type(M) != 4 || TT =="help"){
16117: mycat(
16118: ["getbygrs(m,t) or getbygrs(m,[t,s_1,s_2,...]|perm=?,var=?,pt=?,mat=?)\n",
16119: " m: generalized Riemann scheme or spectral type\n",
16120: " t: reduction, construct, connection, series, operator, TeX, Fuchs, irreducible, basic, recurrence,\n",
16121: " All\n",
16122: " s: TeX dviout simplify short general operator irreducible top0 x1 x2 sft\n",
16123: "Ex: getbygrs(\"111,21,111\", [\"All\",\"dviout\",\"operator\",\"top0\"])\n"]);
16124: return 0;
16125: }
16126: if(type(TT) == 4){
16127: T = TT[0];
16128: T1 = cdr(TT);
16129: }else{
16130: T = TT;
16131: T1 = [];
16132: }
16133: if(type(T) == 7)
16134: T = findin(T,["reduction","construct","connection", "operator", "series",
16135: "TeX", "Fuchs", "All", "basic", "", "irreducible", "recurrence"]);
16136: TeX = findin("TeX", T1);
16137: Simp = findin("simplify", T1);
16138: Short = findin("short", T1);
16139: Dviout= findin("dviout", T1);
16140: General=findin("general", T1);
16141: Op =findin("operator", T1);
16142: Irr =findin("irreducible", T1);
16143: Top0 =findin("top0",T1);
16144: X1 =findin("x1",T1);
16145: X2 =findin("x2",T1);
16146: Sft =findin("sft",T1);
16147: Title = getopt(title);
16148: Mat = getopt(mat);
16149: if(Mat!=1 || T<0 ||(T!=0&&T!=1&&T!=5&&T!=6&&T!=8&&T!=10&&T!=9)) Mat = 0;
16150: if(findin("keep",T1) >= 0)
16151: Keep = Dviout = 1;
16152: else Keep = 0;
16153: if(Dviout >= 0 || T == 5) TeX = 1;
16154: for(J = 0, MM = M; J == 0 && MM != []; MM = cdr(MM)){
16155: for(MI = car(MM); MI != []; MI = cdr(MI)){
16156: if(type(car(MI)) != 1 || car(MI) <= 0){
16157: J = 1; break;
16158: }
16159: }
16160: }
16161:
16162: /* spectral type -> GRS */
16163: if(J == 0){
16164: for(R = [], S = J = 0, MM = M; MM != []; MM = cdr(MM), J++){
16165: MT = qsort(car(MM));
16166: R = cons(reverse(MT), R);
16167: if(J == 1){
16168: S = length(MT)-1;
16169: if(MT[S] > MT[0]) S = 0;
16170: }
16171: }
16172: M = reverse(R);
16173: R = getopt(var);
16174: if(type(R)<1){
16175: for(R = [], I = J-1; I >= 0; I--)
16176: R = cons(asciitostr([97+I]), R);
16177: }
16178: Sft=(Sft>=0)?1:0;
16179: if(General < 0)
16180: Sft=-Sft-1;
16181: M = sp2grs(M,R,Sft|mat=Mat);
16182: }
16183: for(M0=[],MM=M;MM!=[];MM=cdr(MM)){ /* change "?" -> z_z */
16184: for(M1=[],Mm=car(MM);Mm!=[];Mm=cdr(Mm)){
16185: Mt=car(Mm);
16186: if(type(Mt)==4 && Mt[1]=="?"){
16187: M1=cons([Mt[0],z_z],M1);
16188: continue;
16189: }else if(type(Mt)==7 && Mt=="?"){
16190: M1=cons(z_z,M1);
16191: continue;
16192: }
16193: M1=cons(Mt,M1);
16194: }
16195: M0=cons(reverse(M1),M0);
16196: }
16197: M = fspt(reverse(M0),5); /* short -> long */
16198: if(findin(z_z,vars(M))>=0)
16199: M=subst(M,z_z,lsol(chkspt(M|mat=Mat)[3],z_z)); /* Fuchs relation */
16200: NP = length(M);
16201: Perm = getopt(perm);
16202: if(type(Perm) == 4)
16203: M = mperm(M,Perm,0);
16204: if(T == 9){ /* "" */
16205: if(Short >= 0)
16206: M = chkspt(M|opt=4,mat=Mat);
16207: return M;
16208: }
16209: R = [0,M];
16210: ALL = [R];
16211:
16212: while(type(R = redgrs(R[1]|mat=Mat)) == 4)
16213: ALL = cons(R, ALL);
16214: if(R < 0)
16215: return 0;
16216:
16217: /* TeX */
16218: if(TeX >= 0 && !chkfun("print_tex_form", "names.rr"))
16219: return 0;
16220: if(Dviout >= 0 && type(Title) == 7)
16221: dviout(Title|keep=1);
16222: if(T == 7 && Dviout >= 0){
16223: S=["keep","simplify"];
16224: if(Top0 >= 0)
16225: S = cons("top0",S);
16226: getbygrs(M,cons(5,S)|title="\\noindent Riemann Scheme",mat=Mat);
16227: Same = 0;
16228: if(R > 0){
16229: MM = getbygrs(M,8|mat=Mat); /* basic GRS */
16230: MS = chkspt(MM|opt=0,mat=Mat); /* spectral type */
16231: if(M != MM)
16232: getbygrs(MM,cons(5,S)|title="Basic Riemann Scheme",mat=Mat);
16233: else{
16234: dviout("This is a basic Riemann Scheme.\n\n\\noindent"|keep=1);
16235: Same = 1;
16236: }
16237: dviout(MS|keep=1);
16238: }
16239: if(chkspt(ALL[0][1]|mat=Mat)[3] != 0)
16240: getbygrs(M,cons(6,S)|title="Fuchs condition",mat=Mat);
16241: if(Same == 0){
16242: M1 = M[1];
16243: if(M1[length(M1)-1][0]==1 && Mat!=1){
16244: M1=M[2];
16245: if(M1[length(M1)-1][0] == 1){
16246: getbygrs(M,cons(2,S)|title="Connection formula");
16247: if(M1[length(M[0][0])-1][0] == 1 && R==0)
16248: getbygrs(M,cons(11,S)|title="Recurrence relation shifting the last exponents at $\\infty$, 0, 1");
16249: }
16250: getbygrs(M,cons(1,S)|title="Integral representation");
16251: getbygrs(M,cons(4,S)|title="Series expansion");
16252: }
16253: if(Irr < 0){
16254: TI="Irreduciblity $\\Leftrightarrow$ any value of the following linear forms $\\notin\\mathbb Z$";
16255: if(R > 0)
16256: TI += " + fundamental irreducibility";
16257: getbygrs(M,cons(10,S)|title=TI,mat=Mat);
16258: dviout("which coorespond to the decompositions"|keep=1);
16259: sproot(chkspt(M|opt=0),"pairs"|dviout=1,keep=1);
16260: }
16261: }
16262: if(Op >= 0 && Mat!=1) getbygrs(M,cons(3,S)|title="Operator");
16263: dviout(" ");
16264: return 1;
16265: }
16266: if(T == 0 && TeX >= 0){
16267: T = 1; TeX = 16;
16268: }
16269: /* Fuchs */
16270: Fuc = chkspt(ALL[0][1]|Mat=mat)[3];
16271: if(Fuc == 0) Simp = -1;
16272: if(type(Fuc) == 1){
16273: print("Violate Fuchs condition");
16274: return 0;
16275: }
16276: if(T == 6){
16277: if(Dviout >= 0) dviout(Fuc|eq=0,keep=Keep);
16278: return (TeX >= 0)?my_tex_form(Fuc):Fuc;
16279: }
16280: Fuc = [Fuc];
16281: /* Generelized Riemann scheme */
16282: if(T == 5){
16283: M = ltov(M);
16284: for(ML=0, I=0; I<NP; I++){
16285: L = length(M[I]);
16286: if(L > ML) ML = L;
16287: }
16288: Out = string_to_tb("P\\begin{Bmatrix}\nx=");
16289: if(Top0 < 0)
16290: write_to_tb("\\infty & ",Out);
16291: Pt = getopt(pt);
16292: if(type(Pt) == 4){
16293: for(J = 3; J < NP; J++){
16294: str_tb(["& ",rtotex(car(Pt))],Out);
16295: Pt = cdr(Pt);
16296: }
16297: }
16298: else if(X2>=0)
16299: str_tb("0 & x_2",Out);
16300: else
16301: str_tb((X1>=0)?"x_1 & x_2":"0 & 1",Out);
16302: for(J = 3; J < NP; J++)
16303: str_tb(["& x_",rtotex(J)],Out);
16304: if(Top0 >= 0)
16305: write_to_tb("& \\infty",Out);
16306: write_to_tb("\\\\\n",Out);
16307: for(I = 0; I < ML; I++){
16308: for(CC = 0, J = (Top0 >= 0)?1:0; ; J++, CC++){
16309: if(J == NP){
16310: if(Top0 < 0) break;
16311: J = 0;
16312: }
16313: if(length(M[J]) <= I){
16314: if(CC > 0) write_to_tb(" & ",Out);
16315: }else if(M[J][I][0] <= 1){
16316: if(M[J][I][0] == 0) str_tb(" & ",Out);
16317: else
16318: str_tb([(!CC)?" ":" & ", my_tex_form(M[J][I][1])], Out);
16319: }else{
16320: str_tb([((!CC)?"[":" & ["), my_tex_form(M[J][I][1]),
16321: (Mat==1)?"]_{":"]_{("],Out);
16322: str_tb([my_tex_form(M[J][I][0]),(Mat==1)?"}":")}"],Out);
16323: }
16324: if(Top0 >= 0 && J == 0)
16325: break;
16326: }
16327: if(I == 0)
16328: str_tb("&\\!\\!;x",Out);
16329: str_tb("\\\\\n",Out);
16330: }
16331: str_tb("\\end{Bmatrix}",Out);
16332: Out = str_tb(0,Out);
16333: if(Dviout >= 0)
16334: dviout(Out|eq=0,keep=Keep);
16335: return Out;
16336: }
16337:
16338: /* Reduction */
16339: if(T == 0){
16340: if(Simp >= 0)
16341: ALL = simplify(ALL,Fuc,4);
16342: return reverse(ALL);
16343: }
16344: LA = length(ALL) - 1;
16345: NP = length(ALL[0][1]);
16346:
16347: /* irreducible */
16348: if(T == 10){
16349: for(IR=[], I = 0; I < LA; I++){
16350: AI = ALL[I]; AIT = AI[1];
16351: K = AI[0][0];
16352: P = -AIT[0][K][1];
16353: P -= cterm(P);
16354: IR = cons(P, IR);
16355: for(J = 0; J < NP; J++){
16356: K = AI[0][J];
16357: for(L = length(AIT[J]) - 1; L >= 0 ; L--){
16358: if(L == K || AIT[J][L][0] <= AIT[J][K][0])
16359: continue;
16360: P = AIT[J][L][1] - AIT[J][K][1];
16361: Q = cterm(P);
16362: if(dn(Q)==1)
16363: P -= Q;
16364: IR = cons(P,IR);
16365: }
16366: }
16367: }
16368: P=Fuc[0];
16369: Q=cterm(P);
16370: if(type(Q)==1 && dn(Q)==1){
16371: for(F=0,V=vars(P);V!=[];V=cdr(V)){
16372: R=mycoef(P,1,car(V));
16373: if(type(R)!=1 || Q%R!=0){
16374: F=1; break;
16375: }
16376: }
16377: if(F==0){
16378: P-=Q;
16379: Simp=0;
16380: }
16381: }
16382: if(Simp >= 0){
16383: IR=simplify(IR,[P],4);
16384: for(R=[]; IR!=[]; IR=cdr(IR)){
16385: P=car(IR);
16386: Q=cterm(P);
16387: if(dn(Q)==1) P-=Q;
16388: R=cons(P,R);
16389: }
16390: IR=R;
16391: }
16392: for(R=[]; IR!=[]; IR=cdr(IR)){
16393: P=car(IR);
16394: if(str_len(rtostr(P)) > str_len(rtostr(-P)))
16395: P = -P;
16396: R = cons(P,R);
16397: }
16398: R = ltov(R);
16399: #ifdef USEMODULE
16400: R = qsort(R,os_md.cmpsimple);
16401: #else
16402: R = qsort(R,cmpsimple);
16403: #endif
16404: R = vtol(R);
16405: if(TeX >= 0){
16406: Out = string_to_tb("");
16407: for(I=L=K=0; R!=[]; R=cdr(R),I++){
16408: K1 = K;
16409: RS = my_tex_form(car(R));
16410: K = nmono(car(R));
16411: L += K;
16412: if(I){
16413: if(K1 == K && L < 30)
16414: str_tb("\\quad ",Out);
16415: else{
16416: L = K;
16417: str_tb((TeXEq==5)?["\\\\%\n &"]:["\\\\%\n "],Out);
16418: }
16419: }
16420: str_tb(RS,Out);
16421: }
16422: R = Out;
16423: if(Dviout>=0){
16424: dviout(R|eq=0,keep=Keep);
16425: return 1;
16426: }
16427: }
16428: return R;
16429: }
16430:
16431: AL = []; SS = 0;
16432: for(I = 0; I <= LA; I++){
16433: AI = ALL[I]; AIT = AI[1]; /* AIT: GRS */
16434: if(I > 0){
16435: for(S = J = 0; J < NP; J++){
16436: GE = AIT[J][AI0[J]][1];
16437: S += GE;
16438: if(J == 0)
16439: SS = [];
16440: else
16441: SS = cons(GE,SS);
16442: }
16443: SS = cons(1-Mat-S, reverse(SS));
16444: }
16445: AI0 = AI[0];
16446: AL = cons([SS, cutgrs(AIT)], AL);
16447: }
16448: AL = reverse(AL);
16449: AD = newvect(NP);
16450: ALT = AL[0][1];
16451: for(J = 1; J < NP; J++){
16452: /* AD[J] = ALT[J][0][1]; [J][?][1] <- [J][?][0]: max */
16453: for(MMX=0, K = KM = length(ALT[J])-1; K >= 0; K--){
16454: if(MMX <= ALT[J][K][0]){
16455: if(J == 1 && MMX == ALT[J][K][0])
16456: continue;
16457: KM = K;
16458: MMX = ALT[J][K][0];
16459: }
16460: }
16461: AD[J] = ALT[J][KM][1];
16462: }
16463: AL = cdr(AL);
16464: AL = cons([vtol(AD), ALT], AL);
16465: AL = cons([0, mcgrs(ALT, [vtol(-AD)]|mat=Mat)], AL);
16466: if(Simp >= 0 && T != 3)
16467: AL = simplify(AL,Fuc,4);
16468: /* Basic */
16469: if(T == 8){
16470: ALT = AL[0][1];
16471: if(TeX >= 0){
16472: if(Dviout >= 0){
16473: return getbygrs(ALT,["TeX","dviout","keep"]);
16474: }
16475: return getbygrs(ALT,"TeX");
16476: }
16477: if(Short >= 0)
16478: ALT = chkspt(ALT|opt=4);
16479: return ALT;
16480: }
16481:
16482: /* Construct */
16483: if(T == 1){
16484: if(TeX >= 0){
16485: L = length(AL);
16486: I = Done = 0; Out0=Out1=""; NM = DN = [];
16487: if(TeX != 16){
16488: AL11=AL[L-1][1][1];
16489: AT = AL11[length(AL11)-1];
16490: if(type(AT) == 4){
16491: PW = (AT[0] > 1)?"":AT[1];
16492: }else PW = AT;
16493: }
16494: Out = string_to_tb("");
16495: while(--L >= 0){
16496: if(TeX == 16){
16497: if(Done)
16498: write_to_tb(":\\ ", Out);
16499: write_to_tb(getbygrs(AL[L][1],(Top0>=0)?["TeX", "top0"]:"TeX"|mat=Mat), Out);
16500: Done = 1;
16501: if(L != 0) write_to_tb((TeXEq==5)?
16502: "\\\\%\n&\\leftarrow ":"\\\\%\n\\leftarrow ", Out);
16503: }
16504: ALT = AL[L][0];
16505: if(TeX != 16){
16506: V1 = (I==0)?"x":V2;
16507: V2 = /* (I==0 && L<=2)?"s": */
16508: "s_"+rtotex(I);
16509: }else V1=V2="x";
16510: JJ = (type(ALT) == 4)?length(ALT):0;
16511: if(I > 0 && L > 0)
16512: write_to_tb("\n ", Out);
16513: for(Outt = "", J = 1; J < JJ; J++){
16514: if(ALT[J] == 0) continue;
16515: if(J == 1) Outt += V1;
16516: else if(J == 2) Outt += "(1-"+V1+")";
16517: else Outt += "(x_"+rtotex(J)+"-"+V1+")";
16518: Outt += "^"+ rtotex(ALT[J]);
16519: }
16520: if(TeX != 16) write_to_tb(Outt, Out);
16521: else if(Outt != "")
16522: str_tb(["\\mathrm{Ad}\\Bigl(",Outt,"\\Bigr)"], Out);
16523: if(JJ == 0){
16524: if(I != 0)
16525: Out1 = "ds_"+rtotex(I-1)+Out1;
16526: continue;
16527: }
16528: if(ALT[0] == 0) continue;
16529: Out0 += "\\int_p^{"+V1+"}";
16530: if(TeX == 16)
16531: str_tb(["mc_",rtotex(ALT[0])], Out);
16532: else{
16533: str_tb(["(",V1,"-",V2,")^",rtotex(-1+ALT[0])], Out);
16534: AL11=AL[L-1][1][1];
16535: AT = AL11[length(AL11)-1];
16536: if(type(AT) == 4) AT = AT[1];
16537: DN = cons(ALT[0]+AT+1,DN);
16538: NM = cons(AT+1,cons(ALT[0],NM));
16539: }
16540: if(L != 2) Out1 += "d"+V2;
16541: I++;
16542: }
16543: if(R){
16544: if(I == 0) Ov = "x";
16545: else Ov = "s_"+rtotex(I-1);
16546: Out1 = "u_B("+Ov+")"+Out1;
16547: }
16548: if(TeX != 16){
16549: Out0 = string_to_tb(Out0);
16550: str_tb([Out, Out1], Out0);
16551: Out = Out0;
16552: NM = simplify(NM, Fuc, 4);
16553: DN = simplify(DN, Fuc, 4);
16554: DNT = lsort(NM,DN,"reduce");
16555: NMT = DNT[0]; DNT = DNT[1];
16556: if(NMT != [] && PW != ""){
16557: write_to_tb((TeXEq==5)?"\\\\\n &\\sim\\frac{\n"
16558: :"\\\\\n \\sim\\frac{\n", Out);
16559: for(PT = NMT; PT != []; PT = cdr(PT))
16560: str_tb([" \\Gamma(",my_tex_form(car(PT)), ")\n"], Out);
16561: write_to_tb(" }{\n", Out);
16562: for(PT = DNT; PT != []; PT = cdr(PT))
16563: write_to_tb(" \\Gamma("+my_tex_form(car(PT))+")\n", Out);
16564: write_to_tb(" }", Out);
16565: if(R > 0) write_to_tb("C_0", Out);
16566: write_to_tb("x^"+rtotex(PW) +"\\ \\ (p=0,\\ x\\to0)", Out);
16567: }
16568: }else
16569: Out = str_tb(0, Out);
16570: if(Dviout >= 0){
16571: dviout(Out|eq=0,keep=Keep);
16572: return 1;
16573: }
16574: return O;
16575: }
16576: if(Short >= 0){
16577: for(ALL = [] ; AL != []; AL = cdr(AL)){
16578: AT = car(AL);
16579: ALL = cons([AT[0], chkspt(AT[1]|opt=4)], ALL);
16580: }
16581: AL = reverse(ALL);
16582: }
16583: return AL; /* AL[0][1] : reduced GRS, R==0 -> rigid */
16584: }
16585:
16586: if(T == 2 || T == 4 || T == 11){
16587: for(I = (T==2)?2:1; I >= (T==11)?0:1; I--){
16588: ALT = M[I];
16589: if(ALT[length(ALT)-1][0] != 1){
16590: mycat(["multiplicity for",I,":",ALT[length(ALT)-1][1],
16591: "should be 1"]);
16592: return;
16593: }
16594: }
16595: }
16596: LA++;
16597: NM = DN = [];
16598:
16599: /* Three term relation */
16600: if(T == 11){
16601: if(R > 0){
16602: print("This is not rigid\n");
16603: return 0;
16604: }
16605: for(I = 0; I <= LA; I++){
16606: if(I > 0){
16607: AI = AL[I][0]; /* operation */
16608: if(AI[0] != 0){
16609: DN = cons(simplify(AI1+1,Fuc,4),DN);
16610: NM = cons(simplify(AI1+AI[0]+1,Fuc,4),NM);
16611: }
16612: }
16613: ALT = AL[I][1][1]; AI1 = ALT[length(ALT)-1][1];
16614: }
16615: DNT = lsort(NM,DN,"reduce");
16616: if(TeX < 0) return DNT;
16617: NMT = DNT[0]; DNT = DNT[1];
16618: Out = str_tb("u_{0,0,0}-u_{+1,0,-1}=\\frac{","");
16619: for(PT = NMT; PT != []; PT = cdr(PT))
16620: str_tb(["(",my_tex_form(car(PT)),")"], Out);
16621: str_tb(["}\n{"],Out);
16622: for(PT = DNT; PT != []; PT = cdr(PT))
16623: str_tb(["(",my_tex_form(car(PT)),")"], Out);
16624: write_to_tb("}u_{0,+1,-1}",Out);
16625: if(Dviout >= 0){
16626: dviout(Out|eq=0,keep=Keep);
16627: return 1;
16628: }
16629: return Out;
16630: }
16631:
16632: AD=newvect(NP);
16633: for(I = 0; I <= LA; I++){
16634: if(I > 0){
16635: AI = AL[I][0]; /* operation */
16636: if(T == 2 && AI[0] != 0){
16637: DN = cons(simplify(-AI2,Fuc,4), cons(simplify(AI1+1,Fuc,4),DN));
16638: NM = cons(simplify(-AI2-AI[0],Fuc,4), cons(simplify(AI1+AI[0]+1,Fuc,4),
16639: NM));
16640: }
16641: for(J = 1; J < NP; J++)
16642: AD[J] += simplify(AI[J],Fuc,4);
16643: }
16644: if(T == 2){
16645: ALT = AL[I][1][1]; AI1 = ALT[length(ALT)-1][1];
16646: ALT = AL[I][1][2]; AI2 = ALT[length(ALT)-1][1];
16647: if(I == 0){
16648: C3 = AI1; C4 = AI2;
16649: }
16650: }
16651: }
16652:
16653: /* Connection */
16654: if(T == 2){
16655: DNT = lsort(NM,DN,"reduce");
16656: NMT = DNT[0]; DNT = DNT[1];
16657: if(TeX < 0) return [NMT,DNT,AD];
16658: C0 = M[1][length(M[1])-1][1];
16659: C1 = M[2][length(M[2])-1][1];
16660: M = AL[0][1];
16661: C3 = M[1][length(M[1])-1][1];
16662: C4 = M[2][length(M[2])-1][1];
16663: Out = str_tb(["c(0\\!:\\!", my_tex_form(C0),
16664: " \\rightsquigarrow 1\\!:\\!", my_tex_form(C1),")"], "");
16665: if(R > 0 && AMSTeX == 1 && (TeXEq == 4 || TeXEq == 5)){
16666: write_to_tb("\\\\\n", Out);
16667: if(TeXEq == 5) write_to_tb(" &", Out);
16668: }
16669: write_to_tb("=\\frac{\n",Out);
16670: for(PT = NMT; PT != []; PT = cdr(PT))
16671: write_to_tb(" \\Gamma("+my_tex_form(car(PT))+")\n", Out);
16672: write_to_tb(" }{\n",Out);
16673: for(PT = DNT; PT != []; PT = cdr(PT))
16674: write_to_tb(" \\Gamma("+my_tex_form(car(PT))+")\n",Out);
16675: write_to_tb(" }", Out);
16676: for(J = 3; J < length(AD); J++){
16677: if(AD[J] == 0) continue;
16678: str_tb(["\n (1-x_", rtotex(J), "^{-1})^", rtotex(AD[J])], Out);
16679: }
16680: if(R != 0)
16681: str_tb(["\n c_B(0\\!:\\!", my_tex_form(C3),
16682: " \\rightsquigarrow 1\\!:\\!", my_tex_form(C4), ")"], Out);
16683: Out = tb_to_string(Out);
16684: if(Dviout >= 0){
16685: dviout(Out|eq=0,keep=Keep);
16686: return 1;
16687: }
16688: return Out;
16689: }
16690:
16691: /* Series */
16692: if(T == 4){
16693: AL11 = AL[0][1][1];
16694: V = AL11[length(AL11)-1][1];
16695: S00 = -V; S01 = (R==0)?[]:[[0,0]];
16696: S1 = S2 = [];
16697: for(Ix = 1, ALL = cdr(AL); ALL != []; ){
16698: ALT = ALL[0][0];
16699: if(ALT[0] != 0){ /* mc */
16700: for(Sum = [], ST = S01; ST != []; ST = cdr(ST))
16701: Sum = cons(car(ST)[0], Sum);
16702: S1 = cons(cons(S00+1,Sum), S1);
16703: S2 = cons(cons(S00+1+ALT[0],Sum),S2);
16704: S00 += ALT[0];
16705: }
16706: ALL = cdr(ALL);
16707: for(I = 1; I < length(ALT); I++){ /* addition */
16708: if(I == 1){
16709: S00 += ALT[1];
16710: if(ALL == [])
16711: S00 = [S00];
16712: }else{
16713: if(ALT[I] == 0)
16714: continue;
16715: if(ALL != []){
16716: S1 = cons([-ALT[I],Ix],S1);
16717: S2 = cons([1,Ix],S2);
16718: S01= cons([Ix,I],S01);
16719: Ix++;
16720: }else
16721: S00 = cons([ALT[I],I],S00);
16722: }
16723: }
16724: }
16725: S00 = reverse(S00);
16726: S01 = qsort(S01); S1 = qsort(S1); S2 = qsort(S2);
16727: if(Simp >= 0){
16728: S00 = simplify(S00,Fuc,4);
16729: S01 = simplify(S01,Fuc,4);
16730: S1 = simplify(S1,Fuc,4);
16731: S2 = simplify(S2,Fuc,4);
16732: SS = lsort(S1,S2,"reduce");
16733: S1 = SS[0]; S2 = SS[1];
16734: }
16735:
16736: if(TeX >= 0){
16737: /* Top linear power */
16738: TOP = Ps = Sm = "";
16739: for(TOP = Ps = Sm = "", ST = cdr(S00); ST != []; ST = cdr(ST)){
16740: SP = car(ST);
16741: if(SP[0] != 0){
16742: if(SP[1] == 2)
16743: TOP += "(1-x)^"+rtotex(SP[0]);
16744: else
16745: TOP += "(1-x/x_"+rtotex(SP[1])+")^"+rtotex(SP[0]);
16746: }
16747: }
16748: /* Top power */
16749: PW = my_tex_form(car(S00));
16750: if(PW == "0")
16751: PW = "";
16752: NP = length(AL[0][1]);
16753: PWS = newvect(NP);
16754: for(I = 0; I < NP; I++)
16755: PWS[I] = "";
16756: for(S = S01, I = 0; S != []; S = cdr(S), I++){
16757: SI = rtotex(car(S)[0]);
16758: if(I > 0) Sm += ",\\ ";
16759: Sm += "n_"+SI+"\\ge0";
16760: if(PW != "")
16761: PW += "+";
16762: PW += "n_"+SI;
16763: if(car(S)[1] > 2)
16764: PWS[car(S)[1]] += "-n_"+rtotex(car(S)[0]);
16765: else if(car(S)[1] == 0)
16766: Ps = "C_{n_0}"+Ps;
16767: }
16768: for(I = 3; I < NP; I++){
16769: if(PWS[I] != "")
16770: Ps += "x_"+rtotex(I)+"^{"+PWS[I]+"}";
16771: }
16772: Out = str_tb([TOP, Ps, "x^{", PW, "}"], "");
16773: /* Gamma factor */
16774: for(I = 0, SS = S1; I <= 1; I++, SS = S2){
16775: PW = string_to_tb("");
16776: for(PW1=""; SS != [] ; SS = cdr(SS)){
16777: for(J = 0, SST = car(SS); SST != []; SST = cdr(SST), J++){
16778: if(J == 0){
16779: JJ = (car(SST) == 1)?((length(SST)==2)?(-1):0):1;
16780: if(JJ > 0)
16781: str_tb(["(", my_tex_form(car(SST)), ")_{"], PW);
16782: else if(JJ == 0)
16783: PW1 = "(";
16784: }else{
16785: if(JJ > 0){
16786: if(J > 1) write_to_tb("+", PW);
16787: str_tb(["n_", rtotex(car(SST))], PW);
16788: }else{
16789: if(J > 1) PW1 += "+";
16790: PW1 += "n_"+rtotex(car(SST));
16791: }
16792: }
16793: }
16794: if(JJ > 0) write_to_tb("}", PW);
16795: else PW1 += (JJ == 0)?")!":"!";
16796: }
16797: if(I == 0)
16798: Out0 = "\\frac";
16799: Out0 += "{"+tb_to_string(PW)+PW1+"}";
16800: PW = string_to_tb(""); PW1 = "";
16801: }
16802: if(Out0 == "\\frac{}{}")
16803: Out0 = "";
16804: Out = "\\sum_{"+Sm+"}"+Out0 + Top + tb_to_string(Out);
16805: if(length(S01) == 1){
16806: Out = str_subst(Out, "{n_"+SI+"}", "n");
16807: Out = str_subst(Out, "n_"+SI, "n");
16808: }
16809: if(Dviout >= 0)
16810: dviout(Out|eq=0,keep=Keep);
16811: return Out;
16812: }
16813: return [cons(S00, S01), S1, S2];
16814: }
16815:
16816: /* Operator */
16817: if(T==3){
16818: Fuc0 = car(Fuc);
16819: if(Fuc0 != 0){ /* Kill Fuchs relation */
16820: for(V = vars(Fuc0); V != []; V = cdr(V)){
16821: VT = car(V);
16822: if(deg(Fuc0,VT) == 1){
16823: AL = mysubst(AL, [VT, -red(coef(Fuc0,0,VT)/coef(Fuc0,1,VT))]);
16824: break;
16825: }
16826: }
16827: if(V == []){
16828: print("Fuchs condition has no variable with degree 1");
16829: return 0;
16830: }
16831: }
16832: L = newvect(NP);
16833: Pt = getopt(pt);
16834: for(I = NP-1; I >= 1; I--){
16835: if(type(Pt) == 4)
16836: L[I] = Pt[I-1];
16837: else if(I >= 3 || X1 >= 0 || (X2 >= 0 && I >= 2))
16838: L[I] = makev(["x_", I]);
16839: else L[I] = I-1;
16840: }
16841: if(R){ /* non-rigid basic */
16842: MM = AL[0][1]; /* Riemann scheme */
16843: for(OD = 0, MT = car(MM); MT != []; MT = cdr(MT))
16844: OD += car(MT)[0];
16845: for(V = DN = [], M = MM; M != []; M = cdr(M)){
16846: MT = car(M); /* exponents */
16847: for(K = KM = 0, NT = []; ; K++){
16848: for(J = 0, P = 1, MTT = MT; MTT != []; MTT = cdr(MTT)){
16849: if(J == 0 && car(MTT)[1] == 0)
16850: KM = car(MTT)[0];
16851: for(KK = car(MTT)[0] - K -1; KK >= 0; KK--)
16852: P *= (dx-car(MTT)[1]-KK);
16853: }
16854: if(P == 1) break;
16855: NT = cons(P,NT);
16856: }
16857: V = cons(reverse(NT), V);
16858: DN = cons(KM, DN);
16859: }
16860: V = ltov(reverse(V)); /* conditions for GRS */
16861: DN = ltov(reverse(DN)); /* dims of local hol. sol. */
16862: for(J = OD; J >= 0; J--){
16863: for(I = Q = 1; I < NP; I++){
16864: if(J > DN[I])
16865: Q *= (x-L[I])^(J-DN[I]);
16866: }
16867: K = mydeg(Q,x);
16868: if(J == OD){
16869: P = Q*dx^J;
16870: DM = K;
16871: }else{
16872: for(I = DM-OD+J-K; I >= 0; I--){
16873: X = makev(["r",J,"_",I]);
16874: P += Q*x^I*X*dx^J;
16875: }
16876: }
16877: }
16878: for(R = [], I = 0; I < NP; I++){
16879: Q = toeul(P, [x,dx], (I==0)?"infty":L[I]); /* Euler at I-th pt */
16880: for(VT = V[I], J=0; VT != [] ; VT = cdr(VT), J++){
16881: if(car(VT) != 0)
16882: R = cons(rpdiv(coef(Q,J,x), car(VT), dx)[0], R); /* equations */
16883: }
16884: }
16885: for(RR = RRR = [], I = OD-1; I>=0; I--){
16886: RR = [];
16887: for(RT = R; RT != [] ; RT = cdr(RT)){
16888: if( (VT = mycoef(car(RT), I, dx)) != 0)
16889: RR = cons(VT, RR); /* real linear eqs */
16890: }
16891: J = mydeg(mycoef(P,I,dx),x);
16892: for(S = 0, VVV = []; J >= 0; J--){
16893: X = makev(["r",I,"_",J]);
16894: VVV = cons(X, VVV); /* unknowns */
16895: }
16896: RR = lsol(RR,VVV);
16897: LN = length(RR);
16898: for(K=0; K<LN; K++){
16899: RRT = RR[K];
16900: if(type(RRT) != 4) continue;
16901: R = mysubst(R,RRT);
16902: P = mysubst(P,RRT);
16903: }
16904: }
16905: }else /* Rigid case */
16906: P = dx^(AL[0][1][0][0][0]);
16907: /* additions and middle convolutions */
16908: for(ALT = AL; ALT != []; ALT = cdr(ALT)){
16909: AI = car(ALT)[0];
16910: if(type(AI) != 4) continue;
16911: V = ltov(AI);
16912: if(V[0] != 0) P = mc(P,x,V[0]);
16913: for(I = 1; I < NP; I++){
16914: if(V[I] != 0)
16915: P = sftexp(P,x,L[I],-V[I]);
16916: }
16917: }
16918: P = (Simp>=0)? simplify(P,Fuc,4|var=[dx]):simplify(P,Fuc,4);
16919: if(TeX >= 0){
16920: Val = 1;
16921: if(mydeg(P,dx) > 2 && AMSTeX == 1 && TeXEq > 3)
16922: Val = (TeXEq==5)?3:2;
16923: Out = fctrtos(P|var=[dx,"\\partial"],TeX=Val);
16924: if(Dviout < 0) return Out;
16925: dviout(Out|eq=0,keep=Keep);
16926: return 1;
16927: }
16928: return P;
16929: }
16930: return 0;
16931: }
16932:
16933: def mcop(P,M,S)
16934: {
16935: for(V=[],ST=S;ST!=[];ST=cdr(ST))
16936: if(isvar(VT=car(ST))) V=cons(vweyl(VT),V);
16937: V=reverse(V);
16938: N=length(V);
16939: for(MT=M;MT!=[];MT=cdr(MT)){
16940: T=car(MT);
16941: if(T[0]!=0)
16942: P=mc(P,V[0],T[0]);
16943: for(TT=cdr(T),ST=cdr(S);ST!=[];TT=cdr(TT),ST=cdr(ST))
16944: if(car(TT)!=0) P=sftpexp(P,V,S[0]-ST[0],-car(TT));
16945: }
16946: return P;
16947: }
16948:
16949: /* option: zero, all, raw */
16950: def shiftop(M,S)
16951: {
16952: if(type(M)==7) M=s2sp(M);
16953: if(type(S)==7) S=s2sp(S);
16954: Zero=getopt(zero);
16955: NP=length(M);
16956: for(V=L=[],I=NP-1; I>=0; I--){
16957: V=cons(strtov(asciitostr([97+I])),V);
16958: if(I>2) L=cons(makev(["y_", I-1]),L);
16959: else L=cons(I-1,L);
16960: }
16961: if(type(M[0][0])==4){
16962: F=1;RS=M;SS=S;
16963: R=chkspt(M);
16964: if(R[2]!=2 || R[3]!=0){
16965: mycat("GRS is not valid!");return 0;
16966: }
16967: for(; S!=[]; S=cdr(S)){
16968: if(nmono(S[0][0])!=1) break;
16969: if(isint(S[0][1]-S[0][0])==0) break;
16970: }
16971: if(S!=[]){
16972: mycat("Error in shift!"); return 0;
16973: }
16974: }else{
16975: F=0;
16976: RS=sp2grs(M,V,[1,length(M[0]),1]);
16977: for(SS=S0=[],I=0; I<NP; I++){
16978: for(J=F=0; J<length(M[I]); J++){
16979: if(I==0 && J==length(M[0])-1) break;
16980: if((U=S[I][J])!=0){
16981: if(isint(U)!=1){
16982: mycat("Error in shift!"); return 0;
16983: }
16984: VT=RS[I][J][1];
16985: SS=cons([VT,VT+U],SS);
16986: }else if(I>0 && Zero==1 && F==0){
16987: RS=mysubst(RS,[RS[I][J][1],0]);
16988: F=J+1;
16989: }
16990: }
16991: if((F>0 && J==2) || (I==0 && J==1)){
16992: J=(I==0)?0:2-F; VT=RS[I][J][1];
16993: S0=cons([VT,strtov(asciitostr([strtoascii(rtostr(VT))[0]]))],S0);
16994: }
16995: }
16996: }
16997: RS1=mysubst(RS,SS);
16998: if(F==1){
16999: R=chkspt(RS1);
17000: if(R[2]!=2 || R[3]!=0){
17001: mycat("Error in shift!");
17002: return 0;
17003: }
17004: }
17005: R=getbygrs(RS,1); R1=getbygrs(RS1,1);
17006: RT=R[0][1][0];
17007: if(length(RT)!=1 || RT[0][0]!=1){
17008: mycat("Not rigid!");
17009: return 0;
17010: }
17011: P=dx;Q=Q1=1;
17012: for(RT = R, RT1=R1; RT != []; RT = cdr(RT), RT1=cdr(RT1)){
17013: V=car(RT)[0]; V1=car(RT1)[0];
17014: if(type(V) != 4) continue;
17015:
17016: if(V[0] != 0){
17017: P = mc(P,x,V[0]); /* middle convolution */
17018: QT = mc(Q,x,V[0]);
17019: }else QT=Q;
17020: D0=mydeg(Q,dx);D0T=mydeg(QT,dx);
17021: C0=red(mycoef(Q,D0,dx)/mycoef(QT,D0T,dx));
17022: if(C0!=1) QT=red(C0*QT);
17023:
17024: if(V1[0] != 0) Q1T = mc(Q1,x,V1[0]);
17025: else Q1T=Q1;
17026: D1=mydeg(Q1,dx);D1T=mydeg(Q1T,dx);
17027: C1=red(mycoef(Q1,D1,dx)/mycoef(Q1T,D1T,dx));
17028: if(C1!=1) Q1T=red(C1*Q1T);
17029: DD=(V[0]-V1[0])+(D0-D0T)-(D1-D1T);
17030: if(DD>0){
17031: QT=muldo(dx^DD,QT,[x,dx]);
17032: D0T+=DD;
17033: }else if(DD<0){
17034: Q1T=muldo(dx^(-DD),Q1T,[x,dx]);
17035: D1T-=DD;
17036: }
17037: C=mylcm(dn(QT),dn(Q1T),x);
17038: if(C!=1){
17039: QT=red(C*QT); Q1T=red(C*Q1T);
17040: }
17041: Q=QT;Q1=Q1T;
17042: for(I = 1; I < NP; I++){
17043: if(V[I]!=0){
17044: P = sftexp(P,x,L[I],-V[I]); /* addition u -> (x-L[I])^V[I]u */
17045: QT = sftexp(QT,x,L[I],-V[I]);
17046: }
17047: if(V1[I]!=0)
17048: Q1T = sftexp(Q1T,x,L[I],-V1[I]);
17049: }
17050: C=red(mycoef(QT,D0T,dx)*mycoef(Q1,D1T,dx)/(mycoef(Q,D0T,dx)*mycoef(Q1T,D1T,dx)));
17051: Q=red(dn(C)*QT);Q1=red(nm(C)*Q1T);
17052: for(I = 1; I < NP; I++){
17053: if((J=V[I]-V1[I])!=0){
17054: if(J>0) Q1*=(x-L[I])^J;
17055: else Q*=(x-L[I])^(-J);
17056: }
17057: while((QT=tdiv(Q,x-L[I]))!=0){
17058: if((Q1T=tdiv(Q1,x-L[I]))!=0){
17059: Q=QT;Q1=Q1T;
17060: }else break;
17061: }
17062: }
17063: }
17064: P1=mysubst(P,SS);
17065: if(type(S0)==4 && S0!=[]){
17066: P=mysubst(P,S0); Q=mysubst(Q,S0);
17067: P1=mysubst(P1,S0); Q1=mysubst(Q1,S0);
17068: RS=mysubst(RS,S0); RS1=mysubst(RS1,S0);
17069: }
17070: R=mygcd(Q1,P1,[x,dx]);
17071: if(findin(dx,vars(R[0]))>=0){
17072: mycat("Some error!");
17073: return 0;
17074: }
17075: Q=muldo(R[1]/R[0],Q,[x,dx]);
17076: R=divdo(Q,P,[x,dx]);
17077: Q=red(R[1]/R[2]);
17078: R=fctr(nm(Q));
17079: QQ=Q/R[0][0];
17080: R1=fctr(dn(QQ));
17081: for(RR=cdr(R1); RR!=[]; RR=cdr(RR)){
17082: VT=vars(car(RR)[0]);
17083: if(findin(x,VT)<0 && findin(dx,VT)<0){
17084: for(I=car(RR)[1];I>0;I--) QQ=red(QQ*car(RR)[0]);
17085: }
17086: }
17087: Raw=getopt(raw);
17088: Dviout=getopt(dviout);
17089: if(Dviout==1) Raw=4;
17090: if(Raw!=1){
17091: for(RR=cdr(R); RR!=[]; RR=cdr(RR)){
17092: VT=vars(car(RR)[0]);
17093: if(findin(x,VT)<0 && findin(dx,VT)<0){
17094: for(I=car(RR)[1];I>0;I--) QQ=red(QQ/car(RR)[0]);
17095: }
17096: }
17097: }
17098: if(Raw==2||Raw==3||Raw==4){
17099: R=mygcd(QQ,P,[x,dx]); /* R[0]=R[1]*QQ + R[2]*P */
17100: Q1=red(R[0]/R[2]);
17101: for(Q=1,RR=cdr(fctr(nm(Q1))); RR!=[]; RR=cdr(RR)){
17102: VT=vars(car(RR)[0]);
17103: if(findin(x,VT)<0){
17104: for(I=car(RR)[1];I>0;I--) Q*=car(RR)[0];
17105: }
17106: }
17107: if(Raw==3) QQ=[QQ,Q];
17108: else if(Raw==4) /* Q=Q*R[1]/R[0]*QQ+Q/R[0]*P */
17109: QQ=[QQ,Q,red(R[1]*Q/R[0])];
17110: else QQ=Q;
17111: }
17112: F=getopt(all);
17113: if(Dviout==1){
17114: Pre = " x=\\infty & 0 & 1";
17115: for(I=3; I<NP; I++) Pre = Pre+"& "+rtostr(L[I]);
17116: Pre = Pre+"\\\\\n";
17117: PW=str_tb(ltotex(RS|opt="GRS",pre=Pre),0);
17118: str_tb(
17119: "=\\{u\\mid Pu=0\\}\\\\\n&\\underset{Q_2}{\\overset{Q_1}{\\rightleftarrows}}\n",PW);
17120: str_tb([ltotex(RS1|opt="GRS",pre=Pre),"\\\\\n"],PW);
17121: R=fctrtos(QQ[0]|TeX=3,var=[dx,"\\partial"]);
17122: if(type(R)==4) R="\\frac1{"+R[1]+"}"+R[0];
17123: str_tb(["Q_1&=",R,"\\\\\n"],PW);
17124: R=fctrtos(QQ[2]|TeX=3,var=[dx,"\\partial"]);
17125: if(type(R)==4) R="\\frac1{"+R[1]+"}"+R[0];
17126: str_tb(["Q_2&=",R,"\\\\\n"],PW);
17127: str_tb(["Q_2Q_1&\\equiv ",fctrtos(QQ[1]|TeX=3),"\\mod W(x)P"],PW);
17128: if(F==1)
17129: str_tb(["\\\\\nP&=",fctrtos(P|TeX=3,var=[dx,"\\partial"])],PW);
17130: dviout(str_tb(0,PW)|eq=0,title="Shift Operator");
17131: }
17132: if(F==1) return [QQ,P,RS,P1,RS1];
17133: else if(F==0) return QQ;
17134: return [QQ,P,RS];
17135: }
17136:
17137: def conf1sp(M)
17138: {
17139: if(type(M)==7) M=s2sp(M);
17140: L0 = length(M);
17141: L1 = length(M[L0-1]);
17142: X2 = getopt(x2);
17143: Conf= getopt(conf);
17144: if(Conf != 0)
17145: Conf = -1;
17146: if((X2==1 || X2==-1) && Conf != 0){
17147: X1 = 0;
17148: X = x_1;
17149: }else{
17150: X1 = 1;
17151: X = x_2;
17152: }
17153: G = sp2grs(M,a,[L0,L1]);
17154: for(I = 0; I < L0-1; I++){
17155: V = makev([a,I-Conf,0]);
17156: G = subst(G,V,0);
17157: }
17158: L2 = length(M[1]);
17159: for(I=J=S0=S1=0; I < L2; I++){
17160: S1 += G[1][I][0];
17161: while(S0 < S1){
17162: S0 += G[0][J][0];
17163: if((V=G[0][J][1]) != 0)
17164: G = mysubst(G,[V,V-G[1][I][1]]);
17165: J++;
17166: }
17167: if(S0 > S1){
17168: print("Error in data!");
17169: return 0;
17170: }
17171: }
17172: if(Conf==0){
17173: for(L=[], I=L0-2; I>=0; I--)
17174: L=cons(I,L);
17175: L=cons(L0-1,L);
17176: P = getbygrs(G,["operator","x2"]|perm=L);
17177: }else if(X1)
17178: P = getbygrs(mperm(G,[[1,2]],[]), ["operator","x2"]);
17179: else
17180: P = getbygrs(G,["operator","x1"]);
17181: if(Conf==0)
17182: P=nm(mysubst(P,[X,c]));
17183: else{
17184: P = nm(mysubst(P,[X,1/c]));
17185: if(X2==-1){
17186: for(I=2; I<L0; I++){
17187: V=makev(["x_",I]); VC=makev([c,I]);
17188: P = nm(mysubst(P,[V,1/VC]));
17189: }
17190: }
17191: }
17192: for(I = 1; I < L2; I++){
17193: X = G[1][I][1];
17194: P = nm(mysubst(P,[X,X/c]));
17195: }
17196: VS = vars(P);
17197: while(VS!=[]){
17198: V = car(VS);
17199: if(str_chr(rtostr(V),0,"r")==0){
17200: CV = mycoef(P,1,V);
17201: D = mymindeg(CV,c);
17202: if(D > 0) P = mysubst(P,[V,V/c^D]);
17203: CV = mycoef(P,1,V);
17204: DD = mydeg(CV,dx);
17205: CVV = mycoef(CV,DD,dx);
17206: CD1 = mydeg(CVV,x);
17207: CD = (X==x1)?0:CD1;
17208: while(CD>=0 && CD<=CD1){
17209: CC = mycoef(CVV,CD,x);
17210: if(type(CC)==1){
17211: VT = mycoef(mycoef(mycoef(P,DD,dx),CD,x),0,V)/CC;
17212: if(VT != 0) P = mysubst(P,[V,V-VT]);
17213: break;
17214: }
17215: if(X==x1) CD++;
17216: else CD--;
17217: }
17218: while(subst(P,c,0,V,0) == 0)
17219: P = red(mysubst(P,[V,c*V])/c);
17220: }
17221: VS =cdr(VS);
17222: }
17223: return P;
17224: }
17225:
1.34 ! takayama 17226: def confexp(S)
! 17227: {
! 17228: V=x;E=[];
! 17229: for(P=0,Q=[],ST=S;ST!=[];ST=cdr(ST)){
! 17230: Q=cons(car(ST)[0],Q);
! 17231: P+=car(ST)[1]/(V-car(ST)[0]);
! 17232: P=red(P);
! 17233: }
! 17234: P=red(P*polbyroot(Q,V));
! 17235: Q=cdr(reverse(Q));
! 17236: for(I=(length(W=Q));I>=0;I--){
! 17237: C=mycoef(P,I,V);
! 17238: P-=C*polbyroot(W,V);
! 17239: W=cdr(W);
! 17240: E=cons(red(C),E);
! 17241: }
! 17242: return reverse(E);
! 17243: }
! 17244:
1.6 takayama 17245: def pgen(L,VV)
17246: {
17247: if(type(L[0])<4) L=[L];
17248: if(type(L)==4) L=ltov(L);
17249: K=length(L);
17250: V=newvect(K);
17251: if(type(Sum=getopt(sum))!=1) Sum=0;
17252: if((Num=getopt(num))!=1) Num=0;
17253: if((Sep=getopt(sep))!=1) Sep=0;
17254: if(type(Shift=getopt(shift))!=1) Shift=0;
17255: for(;;){
17256: for(PP=1,R=[],II=K-1; II>=0; II--){
17257: R=cons(V[II]+Shift,R);
17258: if(II>0 && Sep==1) R=cons("_",R);
17259: PP*=L[II][0]^V[II];
17260: }
17261: P+=makev(cons(VV,R)|num=Num)*PP;
17262: for(I=0;I<K;){
17263: if(++V[I]<=L[I][1]){
17264: if(Sum>0){
17265: for(S=II=0;II<K;) S+=V[II++];
17266: if(S>Sum){
17267: V[I++]=0;
17268: continue;
17269: }
17270: }
17271: }else{
17272: V[I++]=0;
17273: continue;
17274: }
17275: break;
17276: }
17277: if(I>=K) return P;
17278: }
17279: }
17280:
17281: def diagm(M,A)
17282: {
17283: return mgen(M,0,A,1);
17284: }
17285:
17286: def mgen(M,N,A,S)
17287: {
17288: if(M==0 && N==0){
17289: mycat([
17290: "mgen(m,n,a,s|sep=1) : generate a matrix of size m x n\n",
17291: " n : a number or \"diagonal\", \"highdiag\", \"lowdiag\",\"skew\",\"symmetric\",\"perm\" = 0,-1,-2,..\n",
17292: " a : a symbol or list (ex. a, [a], [a,b,c], [1,2,3])\n",
17293: " s : 0 or 1 (shift of suffix)\n"
17294: ]);
17295: return 0;
17296: }
17297: if(type(N)==7) N=-findin(N,["diag","highdiag","lowdiag","skew","symmetric","perm"]);
17298: Sep=(getopt(sep)==1)?1:0;
17299: if(S < 0 || S > 2)
17300: S = 0;
17301: if(M+S > 30 || N+S > 30){
17302: erno(1);
17303: return;
17304: }
17305: if(N==-5){
17306: NM=newmat(M,M);
17307: for(I=0;I<M;I++,A=cdr(A)) NM[I][car(A)-S]=1;
17308: return NM;
17309: }
17310: if(type(A) == 4)
17311: L = length(A)-1;
17312: else
17313: L = -1;
17314: if(N <= 0 && N >= -2){
17315: MM = newmat(M,M);
17316: J = K = 0;
17317: if(N == -1){
17318: K = 1; M--;
17319: }else if(N == -2){
17320: J = 1; M--;
17321: }
17322: for(I = 0; I < M; I++){
17323: if(L >= 0)
17324: MM[I+J][I+K] = A[(I > L)?L:I];
17325: else if(type(A)==7 || isvar(A))
17326: MM[I+J][I+K] = makev([A,S+I]|sep=Sep);
17327: else
17328: MM[I+J][I+K] = A;
17329: }
17330: return MM;
17331: }
17332: K = N;
17333: if(K < 0) N = M;
17334: MM = newmat(M,N);
17335: for(I = 0; I < M; I++){
17336: if(L >= 0)
17337: AA = rtostr(A[(I > L)?L:I]);
17338: else
17339: AA = rtostr(A)+rtostr(I+S);
17340: if(AA>="0" && AA<=":"){
17341: erno(0); return;
17342: }
17343: for(J = 0; J < N; J++){
17344: if(K < 0){
17345: if(I > J) continue;
17346: if(K == -3 && I == J) continue;
17347: }
17348: MM[I][J] = makev([AA,J+S]|sep=Sep);
17349: }
17350: }
17351: if(K < 0){
17352: for(I = 0; I < M; I++){
17353: for(J = 0; J < I; J++)
17354: MM[I][J] = (K == -4)?MM[J][I]:-MM[J][I];
17355: }
17356: }
17357: return MM;
17358: }
17359:
17360: def newbmat(M,N,R)
17361: {
17362: S = newvect(M);
17363: T = newvect(N);
17364: IM = length(R);
17365: for(I = 0; I < IM; I++){
17366: RI = R[I];
17367: JM = length(RI);
17368: for(J = 0; J < JM; J++){
17369: RIJ = RI[J];
17370: if(type(RIJ) == 6){
17371: S[I] = size(RIJ)[0];
17372: T[J] = size(RIJ)[1];
17373: }
17374: }
17375: }
17376: for(I = K = 0; I < M; I++){
17377: if(S[I] == 0)
17378: S[I] = 1;
17379: K += S[I];
17380: }
17381: for(J = L = 0; J < N; J++){
17382: if(T[J] == 0)
17383: T[J] = 1;
17384: L += T[J];
17385: }
17386: M = newmat(K,L);
17387: if(type(Null=getopt(null))>0){
17388: for(I=0;I<K;I++){
17389: for(J=0;J<L;J++) M[I][J]=Null;
17390: }
17391: }
17392: for(I0 = II = 0; II < IM; I0 += S[II++]){
17393: RI = R[II];
17394: JM = length(RI);
17395: for(J0 = JJ = 0; JJ < JM; J0 += T[JJ++]){
17396: if((RIJ = RI[JJ]) == 0)
17397: continue;
17398: Type = type(RIJ);
17399: for(I = 0; I < S[II]; I++){
17400: for(J = 0; J < T[JJ]; J++){
17401: if(Type == 6)
17402: M[I0+I][J0+J] = RIJ[I][J];
17403: else if(Type == 4 || Type == 5)
17404: M[I0+I][J0+J] = (I>0)?RIJ[I]:RIJ[J];
17405: else
17406: M[I0+I][J0+J] = RIJ;
17407: }
17408: }
17409: }
17410: }
17411: return M;
17412: }
17413:
17414: def unim(S)
17415: {
17416: if(!Rand++) random(currenttime());
17417: if(!isint(Wt=getopt(wt))||Wt<0||Wt>10) Wt=2;
17418: if(!isint(Xa=getopt(abs)) || Xa<1)
17419: Xa=9;
17420: if((Xaa=Xa)>10) Xaa=10;
17421: if(Xaa%2) Xaa++;
17422: Xh=Xaa/2;
17423: if(type(S0=SS=S)==4){
17424: Int=(getopt(int)==1)?1:0;
17425: U=[1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,4];
17426: M=newmat(S[0],S[1]);
17427: SS=cdr(S);SS=cdr(SS);
17428: if(Rk=length(SS)) L=SS;
17429: else{
17430: L=[0];
17431: I=(S[0]>S[1])?S[1]:S[0];
17432: if(I<=2) return 0;
17433: if(!isint(Rk=getopt(rank))||Rk<1||Rk>S[0]||Rk>S[1])
17434: Rk=random()%(I-1)+2;
17435: for(I=1;I<Rk;){
17436: P=random()%(S[1]+Wt)-Wt;
17437: if(P<=0) P=1;
17438: if(findin(P,L)!=0){
17439: L=cons(P,L);
17440: I++;
17441: }
17442: }
17443: }
17444: L=ltov(qsort(L));
17445: M[0][L[0]]=1;
17446: for(I=1;I<Rk;I++){
17447: P=Int?1:U[random()%length(U)];
17448: if(P>Xa) P=Xa;
17449: M[I][L[I]]=(random()%2)?P:(-P);
17450: }
17451: for(I=0;I<Rk;I++){
17452: if(I!=0&&abs(M[I][L[I]])>1) M[K=random()%I][KK=L[I]]=1;
17453: I0=(I==0)?1:L[I]+1;
17454: I1=(I==Rk-1)?S[1]:L[I+1];
17455: for(J=I0;J<I1;J++){
17456: for(K=1;K<=Xa;K++){
17457: P=random()%(I+1);
17458: if((random()%2)==1) M[P][J]++;
17459: else M[P][J]--;
17460: }
17461: }
17462: }
17463: S=M;
17464: Res=(getopt(res)==1)?dupmat(S):0;
17465: }
17466: Conj=0;
17467: if(type(S)<2){
17468: if(S<2||S>20) return 0;
17469: if(getopt(conj)==1){
17470: M=S+Wt;
17471: if(M>15) M=10;
17472: M0=floor((M-1)/2);
17473: for(R=[],I=0;I<S;I++) R=cons(random()%M-M0,R);
17474: R=qsort(R);
17475: M=diagm(S,R);
17476: if(getopt(diag)!=1){
17477: for(I=1;I<S;I++)
17478: if(M[I-1][I-1]==M[I][I] && random()%2) M[I-1][I]=1;
17479: }
17480: if(M[0][0]==M[S-1][S-1]){
17481: for(I=1;I<S;I++) if(M[I-1][I]==1) break;
17482: if(I==S){
17483: if(M[0][0]>0) M[0][0]--;
17484: else M[S-1][S-1]++;
17485: }
17486: }
17487: if(getopt(res)==1) RR=diagm(S,[1]);
17488: S1=S;
17489: Res=dupmat(S=M);
17490: if(isint(I=getopt(int))&&I>1&&random()%I==0){
17491: K=S[0][0];L=K+1;
17492: for(I=1;I<S1;I++){
17493: if(S[I][I]>L && S[I-1][I]==0 && (I==S1-1||S[I][I+1]==0)){
17494: L=S[I][I];
17495: if(RR){
17496: RR[I][I]=L-K;RR[0][I]=1;
17497: }
17498: S[0][I]=1;
17499: if(!(random()%3)) break;
17500: }
17501: }
17502: if(random()%3==0){
17503: for(I=0;I<S1-1;I++){
17504: if(iand(S[I][I],1)&&S[I][I+1]==1){
17505: for(J=I+2;J<S1&&S[I][J]==0;J++);
17506: if(J<S1) continue;
17507: for(J=I-1;J>=0&&S[J][I]==0;J--);
17508: if(J>=0) continue;
17509: S[I][I+1]=2;
17510: for(J=0;J<S1;J++) RR[I][J]*=2;
17511: break;
17512: }
17513: }
17514: }
17515: }
17516: }else{
17517: M=diagm(S,[1]);
17518: S1=S;
17519: }
17520: }
17521: if(type(S)==6){
17522: M=dupmat(S);
17523: S=size(S);
17524: S1=S[1];S=S[0];
17525: Nt=1;
17526: if(getopt(conj)==1&&S==S1) Conj=1;
17527: }
17528: if(!isint(Ct=getopt(time)))
17529: Ct=(S>3||S1>3)?100:200;
17530: if(getopt(both)==1){
17531: OL=delopt(getopt(),"both");
17532: M=unim(mtranspose(M)|option_list=OL);
17533: M=mtranspose(M);
17534: }
17535: Mx=20;
17536: for(I=K=LL=0;I<Ct+Mx;I++){
17537: P=random()%S;Q=random()%S;
17538: if(3*K>Ct) T=random()%Xaa-Xh;
17539: else if(5*K<Ct) T=random()%2-1;
17540: else T=random()%4-2;
17541: if(T>=0) T++;
17542: if(P==Q) continue;
17543: for(G=0,J=S1-1;J>=0;J--){
17544: if((H=abs(M[Q][J]+M[P][J]*T))>Xa&&(!Conj||J!=P)) break;
17545: if(K<Mx&&!Conj) G=igcd(G,H);
17546: }
17547: if(K<Mx && G>1) J=1;
17548: if(J>0) continue;
17549: if(J<0&&Conj==1){
17550: for(J=S1-1;J>=0;J--)
17551: if(J!=Q&&abs(M[J][P]-M[J][Q]*T)>Xa) break;
17552: if(J<0&&abs(M[Q][P]-M[Q][Q]*T+M[P][P]*T-M[P][Q]*T^2)>Xa) J=1;
17553: if(J<0&&M[P][P]==M[Q][Q]){
17554: LF=0;
17555: for(L=S1-1;J>=0;J--) if(L!=Q&&M[J][Q]!=0) LF++;
17556: for(L=S1-1;J>=0;J--) if(L!=P&&M[P][J]!=0) LF++;
17557: if(!LF) J=1;
17558: }
17559: }
17560: if(J<0){
17561: for(J=S1-1;J>=0;J--)
17562: M[Q][J]+=M[P][J]*T;
17563: if(Conj==1)
17564: for(J=S1-1;J>=0;J--) M[J][P]-=M[J][Q]*T;
17565: if(RR) for(J=S1-1;J>=0;J--) RR[Q][J]+=RR[P][J]*T;
17566: K++;
17567: }
17568: if(K%5==0){
17569: if(!Nt) M=mtranspose(M);
17570: else if(!Conj&&K%2==0){
17571: for(F=0;F<S;F++){
17572: if((V=lgcd(M[F]))>1){
17573: for(L=0;L<S1;L++) M[F][L]/=V;
17574: }
17575: }
17576: }
17577: }
17578: if(I>Ct){
17579: for(L=S-1;L>=0;L--){
17580: for(F=0,J=S1-1;J>=0;J--)
17581: if(M[L][J]!=0) F++;
17582: if(F<2){
17583: F=-1;break;
17584: }
17585: else F=0;
17586: }
17587: if(F<0 && LL++<5){
17588: I=(CT-CT%2)/2;K=1;
17589: }
17590: if(I>Ct) break;
17591: }
17592: }
17593: if(RR){
17594: for(I=F=0;I<S1;I++){
17595: V=Res[I][I];
17596: for(J=I+1;J<S1;J++){
17597: if(Res[J][J]!=V) break;
17598: for(LP=0;LP<2;LP++){
17599: if(J==S1-1||Res[J][J+1]==0){
17600: if(I==0||Res[I-1][I]==0){
17601: for(VL=VS=[],K=0;K<S1;K++){
17602: VL=cons(RR[K][J],VL);VS=cons(RR[K][I],VS);
17603: }
17604: VR=ldev(VL,VS);
17605: if(VR[0]){
17606: for(K=S1-1,VN=VR[1];K>=0;K--,VN=cdr(VN))
17607: RR[K][J]=car(VN);
17608: F=1;
17609: }
17610: }
17611: }
17612: K=I;I=J;J=K;
17613: }
17614: }
17615: if(F&&I==S1-1){
17616: F=0;I=-1;
17617: }
17618: }
17619: if(getopt(int)==1){
17620: N=mtranspose(M);
17621: for(F=I=0;I<S1;I++) if(lgcd(M[I])>1||lgcd(N[I])>1) F++;
17622: if(F){
17623: for(F=I=0;I<S1;I++){
17624: if(Res[I][I]==-1) F=ior(F,1);
17625: else if(Res[I][I]==1) F=ior(F,2);
17626: }
17627: C=0;
17628: if(!iand(F,1)) C=1;
17629: else if(!iand(F,2)) C=-1;
17630: if(C){
17631: for(I=0;I<S1;I++){
17632: M[I][I]+=C;Res[I][I]+=C;
17633: }
17634: }
17635: }
17636: }
17637: if(getopt(rep)!=1){
17638: for(Lp=0;Lp<5;Lp++){
17639: F=(M==Res||abs(lmax(RR))>Xa*10||abs(lmin(RR))>Xa*10)?1:0;
17640: for(I=0;!F&&I<S1&&Lp<4;I++){
17641: for(K=L=J=0;J<S1;J++){
17642: if(M[I][J]) K++;
17643: if(M[J][I]) L++;
17644: }
17645: if(K<2||L<2) F=1;
17646: }
17647: if(!F) break;
17648: R=unim(S0|option_list=cons(["rep",1],getopt()));
17649: M=R[0];Res=R[1];RR=R[3];
17650: }
17651: }
17652: }
17653: if(Res==0) return M;
17654: if(RR){
17655: for(I=K=V=0;I<S1;I++){
17656: for(J=0;J<S1;J++){
17657: if(RR[J][I]>0) V++;
17658: else if(RR[J][I]<0) V--;
17659: }
17660: if(I<S1-1&&Res[I][I+1]!=0) continue;
17661: if(V<0){
17662: for(;K<=I;K++) RR=colm(RR,K,-1);
17663: }
17664: K=I+1;V=0;
17665: }
17666: }
17667: if(getopt(rep)!=1){
17668: if((F=getopt(dviout))==1){
17669: if(getopt(conj)==1){
17670: if(RR) show([Res,"=",myinv(RR),M,RR]|opt="spts0",str=1,lim=200);
17671: }else{
17672: if(type(Lim=getopt(lim))==1)
17673: mtoupper(M,0|step=1,opt=7,dviout=1,pages=1,lim=Lim);
17674: else mtoupper(M,0|step=1,opt=7,dviout=1,pages=1);
17675: }
17676: }else if(F==-1){
17677: if(getopt(conj)==1){
17678: if(RR) return ltotex([Res,"=",myinv(RR),M,RR]|opt="spts0",str=1,lim=200);
17679: }else{
17680: if(type(Lim=getopt(lim))==1)
17681: return mtoupper(M,0|step=1,opt=7,pages=1,lim=Lim,dviout=-1);
17682: else return mtoupper(M,0|step=1,opt=7,pages=1,dviout=-1);
17683: }
17684: }
17685: }
17686: if(RR==0) return[M,Res];
17687: return [M,Res,myinv(RR),RR];
17688: }
17689:
17690: def pfrac(F,X)
17691: {
17692: F = red(F);
17693: FN = nm(F);
17694: FD = dn(F);
17695: if(mydeg(FD,X) == 0)
17696: return [[F,1,1]];
17697: R = rpdiv(FN,FD,X);
17698: FN = R[0]/R[1];
17699: R0 = R[2]/R[1];
17700: FC = fctr(FD);
17701: RT=[];
17702: if(getopt(root)==2){
17703: for(FE=[],FT=FC;FT!=[];FT=cdr(FT)){
17704: if(mydeg(P=car(FT)[0],X)==4 && vars(P)==[X] && pari(issquare,C=mycoef(P,4,X))){
17705: if((S=mycoef(P,3,X)/4/C)!=0) P=subst(P,X,X-S);
17706: if(mycoef(P,1,X)==0 && pari(issquare,C0=mycoef(P,0,X))){
17707: C=sqrtrat(C);C0=sqrtrat(C0);C1=2*C*C0-mycoef(P,2,X);
17708: if(C1>0){
17709: FE=cons([C*(X+S)^2-C1^(1/2)*(X+S)+C0,car(FT)[1]],FE);
17710: FE=cons([C*(X+S)^2+C1^(1/2)*(X+S)+C0,car(FT)[1]],FE);
17711: RT=cons(C1,RT);
17712: continue;
17713: }
17714: }
17715: }
17716: FE=cons(car(FT),FE);
17717: }
17718: FC=reverse(FE);
17719: }
17720: N = Q = 0;
17721: L = [];
17722: for(I = length(FC)-1; I >= 0; I--){
17723: if((D = mydeg(FC[I][0],X)) == 0) continue;
17724: for(K=1; K<=FC[I][1]; K++){
17725: for(J=P=0; J < D; J++){
17726: V = makev(["zz_",++N]);
17727: P = P*X + V;
17728: L = cons(V,L);
17729: }
17730: Q += P/(FC[I][0]^K);
17731: Q = red(Q);
17732: }
17733: }
17734: L=reverse(L);
17735: Q = nm(red(red(Q*FD)-FN));
17736: Q = ptol(Q,X);
17737: S = lsol(Q,L);
17738: R = (R0==0)?[]:[[R0,1,1]];
17739: for(N=0,I=length(FC)-1; I >= 0; I--){
17740: if((D = mydeg(FC[I][0],X)) == 0) continue;
17741: for(K=1; K<=FC[I][1]; K++){
17742: for(P=J=0; J < D; N++,J++)
17743: P = P*X + S[N][1];
17744: if(P!=0) R = cons([P,FC[I][0],K],R);
17745: }
17746: }
17747: for(;RT!=[];RT=cdr(RT)){
17748: RTT=car(RT);
17749: R=mtransbys(os_md.substblock,R,[RTT^(1/2),(RTT^(1/2))^2,RTT]);
17750: }
17751: TeX=getopt(TeX);
17752: if((Dvi=getopt(dviout))==1||TeX==1){
17753: V=strtov("0");
17754: for(S=L=0,RR=R;RR!=[];RR=cdr(RR),L++){
17755: RT=car(RR);
17756: S+=(RT[0]/RT[1]^RT[2])*V^L;
17757: }
17758: if(TeX!=1) fctrtos(S|var=[V,""],dviout=1);
17759: else return fctrtos(S|var=[V,""],TeX=3);
17760: }
17761: return reverse(R);
17762: }
17763:
17764: def cfrac(X,N)
17765: {
17766: F=[floor(X)];
17767: if(N<0){
17768: Max=N=-N;
17769: }
17770: X-=F[0];
17771: if(Max!=1)
17772: M=mat([F[0],1],[1,0]);
17773: for(;N>0 && X!=0;N--){
17774: X=1/X;
17775: F=cons(Y=floor(X),F);
17776: X-=Y;
17777: if(Max){
17778: M0=M[0][0];M1=M[1][0];
17779: M=M*mat([Y,1],[1,0]);
17780: if(M[0][0]>Max) return M0/M1;
17781: }
17782: }
17783: return (Max==0)?reverse(F):M[0][0]/M[1][0];
17784: }
17785:
17786: def sqrt2rat(X)
17787: {
17788: if(type(X)>3) return X;
17789: X=red(X);
17790: if(getopt(mult)==1){
17791: for(V=vars(X);V!=[];V=cdr(V)){
17792: T=funargs(F=car(V));
17793: if(type(T)==4&&length(T)>1){
17794: Y=T[1];
17795: Z=sqrt2rat(Y);
17796: if(Y!=Z){
17797: if(length(T)==2){
17798: T0=T[0];
17799: X=subst(X,F,T0(Z));
17800: }else if(T[0]==pow)
17801: X=subst(X,F,Y^T[2]);
17802: }
17803: }
17804: }
17805: }
17806: for(V=vars(X);V!=[];V=cdr(V)){ /* r(x)^(1/2+n) -> r(x)^n*r(x)^(1/2) */
17807: T=args(Y=car(V));
17808: if(functor(Y)==pow&&T[1]!=1/2&&isint(T2=2*T[1])){
17809: if(iand(T2,1)){
17810: R=(T[0])^(1/2);T2--;
17811: }else R=1;
17812: R*=T[0]^(T2/2);
17813: X=red(subst(X,Y,R));
17814: }
17815: }
17816: D=dn(X);N=nm(X);
17817: if(imag(D)!=0){
17818: N*=conj(D);
17819: D*=conj(D);
17820: return sqrt2rat(N/D);
17821: }
17822: for(V=vars(N);V!=[];V=cdr(V)){ /* (r(x)^(n/m))^k */
17823: T=args(Y=car(V));
17824: if(functor(Y)==pow&&(T[1]==0||(type(T[1])==1&&ntype(T[1])==0))){
17825: Dn=dn(T[1]);Nm=nm(T[1]);
17826: N=substblock(N,Y,Y^Dn,T[0]^Nm);
17827: }
17828: }
17829: for(V=vars(D);V!=[];V=cdr(V)){
17830: T=args(Y=car(V));
17831: if(functor(Y)==pow&&(T[1]==0||(type(T[1])==1&&ntype(T[1])==0))){
17832: Dn=dn(T[1]);Nm=nm(T[1]);
17833: D=substblock(D,Y,Y^Dn,T[0]^Nm);
17834: }
17835: }
17836: for(V=vars(D);V!=[];V=cdr(V)){
17837: T=args(Y=car(V));
17838: if(functor(Y)==pow&&T[1]==1/2&&mydeg(D,Y)==1){
17839: N*=mycoef(D,0,Y)-mycoef(D,1,Y)*Y;
17840: N=mycoef(N,0,Y)+mycoef(N,1,Y)*Y+mycoef(N,2,Y)*T[0];
17841: D=mycoef(D,0,Y)^2-mycoef(D,1,Y)^2*T[0];
17842: X=red(N/D);
17843: D=dn(X);N=nm(X);
17844: break;
17845: }
17846: }
17847: X=red(N/D);
17848: D=dn(X);N=nm(X);
17849: for(V=vars(D);V!=[];V=cdr(V)){
17850: T=args(Y=car(V));
17851: if(functor(Y)==pow&&T[1]==1/2)
17852: D=substblock(D,T[0]^T[1],(T[0]^T[1])^2,T[0]);
17853: }
17854: for(V=vars(N);V!=[];V=cdr(V)){
17855: T=args(Y=car(V));
17856: if(functor(Y)==pow&&T[1]==1/2)
17857: N=substblock(N,T[0]^T[1],(T[0]^T[1])^2,T[0]);
17858: }
17859: for(V=vars(N);V!=[];V=cdr(V)){
17860: T=args(Y=car(V));
17861: if(functor(Y)==pow&&T[1]==1/2){
17862: Ag=T[0];
17863: R=S=1;
17864: An=fctr(nm(Ag));
17865: CA=An[0][0];
17866: if(CA<0){
17867: CA=-CA;R=-1;
17868: }
17869: if(type(I=sqrtrat(CA))<2) S=I;
17870: else R*=CA;
17871: for(An=cdr(An);An!=[];An=cdr(An)){
17872: Pw=car(An)[1];I=iand(Pw,1);
17873: if(I) R*=car(An)[0];
17874: if((Q=(Pw-I)/2)>0) S*=car(An)[0]^Q;
17875: }
17876: for(An=fctr(dn(Ag));An!=[];An=cdr(An)){
17877: Pw=car(An)[1];I=iand(Pw,1);
17878: if(I) R/=car(An)[0]^I;
17879: if((Q=(Pw-I)/2)>0) S/=car(An)[0]^Q;
17880: }
17881: if(S!=1) N=subst(N,Y,R^(1/2)*S);
17882: }
17883: }
17884: for(V=vars(N);V!=[];V=cdr(V)){
17885: T=args(Y=car(V));
17886: if(functor(Y)==pow&&T[1]==1/2){
17887: C=mycoef(N,1,Y);
17888: for(VC=vars(C);VC!=[];VC=cdr(VC)){
17889: TC=args(YC=car(VC));
17890: if(functor(YC)==pow&&TC[1]==1/2){
17891: Ag=red(T[0]*TC[0]);
17892: R=S=1;
17893: An=fctr(nm(Ag));
17894: CA=An[0][0];
17895: if(CA<0){
17896: CA=-CA;R=-1;
17897: }
17898: if(type(I=sqrtrat(CA))<2) S=I;
17899: else R*=CA;
17900: for(An=cdr(An);An!=[];An=cdr(An)){
17901: Pw=car(An)[1];I=iand(Pw,1);
17902: if(I) R*=car(An)[0];
17903: if((Q=(Pw-I)/2)>0) S*=car(An)[0]^Q;
17904: }
17905: for(An=fctr(dn(Ag));An!=[];An=cdr(An)){
17906: Pw=car(An)[1];I=iand(Pw,1);
17907: if(I) R/=car(An)[0]^I;
17908: if((Q=(Pw-I)/2)>0) S/=car(An)[0]^Q;
17909: }
17910: CC=mycoef(C,1,YC);
17911: N=N-CC*YC*Y+CC*R^(1/2)*S;
17912: }
17913: }
17914: }
17915: }
17916: return red(N/D);
17917: }
17918:
17919: def cfrac2n(X)
17920: {
17921: if(type(L=getopt(loop))==1&&L>0)
17922: C=x;
17923: else{
17924: C=0;L=0;
17925: }
17926: if(L>1){
17927: for(Y=[];L>1;L--){
17928: Y=cons(car(X),Y);
17929: X=cdr(X);
17930: }
17931: if(X!=[]){
17932: P=cfrac2n(X|loop=1);
17933: for(V=P,Y=reverse(Y);Y!=[];Y=cdr(Y))
17934: V=sqrt2rat(car(Y)+1/V);
17935: return V;
17936: }else{
17937: C=0;X=reverse(Y);
17938: }
17939: }
17940: for(V=C,X=reverse(X);X!=[];X=cdr(X)){
17941: if(V!=0) V=1/V;
17942: V+=car(X);
17943: }
17944: if(C!=0){
17945: V=red(V);P=dn(V)*x-nm(V);
17946: S=getroot(P,x|cpx=2);
17947: T=map(eval,S);
17948: V=(T[0]>0)?S[0]:S[1];
17949: }
17950: return V;
17951: }
17952:
17953: def s2sp(S)
17954: {
17955: if(getopt(short)==1){
17956: if(type(F=getopt(std))==1) S=s2sp(S|std=F);
17957: if(type(S)!=7) S=s2sp(S);
17958: L=strtoascii(S);
17959: for(LS=[],F=C=0;L!=[];L=cdr(L)){
17960: if((G=car(L))!=F){
17961: LS=cons(G,LS);C=0;
17962: }else if(C<3){
17963: LS=cons(G,LS);
17964: }else if(C==3){
17965: LS=cdr(LS);LS=cdr(LS);
17966: LS=cons(94,LS);LS=cons(52,LS);
17967: }else if(C==9){
17968: LS=cdr(LS);LS=cons(97,LS);
17969: }else{
17970: K=car(LS);LS=cdr(LS);LS=cons(K+1,LS);
17971: }
17972: C++;F=G;
17973: }
17974: return asciitostr(reverse(LS));
17975: }
17976: if(type(F=getopt(std))==1){
17977: F=(F>0)?1:-1;
17978: if(type(S)==7) S=s2sp(S);
17979: for(L=[];S!=[];S=cdr(S))
17980: L=cons(os_md.msort(car(S),[-1,0]),L);
17981: return os_md.msort(L,[F,2]);
17982: }
17983: if(type(S)==7){
17984: S = strtoascii(S);
17985: if(type(S) == 5) S = vtol(S);
17986: for(N=0,R=TR=[]; S!=[]; S=cdr(S)){
17987: if(car(S)==45) /* - */
17988: N=1;
17989: else if(car(S)==47) /* / */
17990: N=2;
17991: if(N>0){
17992: while(car(S)<48&&car(S)!=40) S=cdr(S);
17993: }
17994: if((T=car(S))>=48 && T<=57) TR=cons(T-48,TR);
17995: else if(T>=97) TR=cons(T-87,TR);
17996: else if(T>=65 && T<=90) TR=cons(T-29,TR); /* A-Z */
17997: else if(T==44){
17998: R=cons(reverse(TR),R);
17999: TR=[];
18000: }else if(T==94){ /* ^ */
18001: S=cdr(S);
18002: if(car(S)==40){ /* ( */
18003: S=cdr(S);
18004: for(T=0; car(S)!=41 && S!=[]; S=cdr(S)){
18005: V=car(S)-48;
18006: if(V>=10) V-=39;
18007: T=10*T+V;
18008: }
18009: }else{
18010: while(car(S)<48) S=cdr(S);
18011: T=car(S)-48;
18012: if(T>=10) T-=39;
18013: }
18014: while(--T>=1) TR=cons(car(TR),TR);
18015: }else if(T==40){ /* ( */
18016: S=cdr(S);
18017: if(N==1){
18018: N=0; NN=1;
18019: }else NN=0;
18020: if(car(S)==45){ /* - */
18021: S=cdr(S);
18022: NN=1-NN;
18023: }
18024: for(I=0; I<2; I++){
18025: for(V=0; (SS=car(S))!=41 && SS!=47 && S!=[]; S=cdr(S)){
18026: T=SS-48;
18027: if(T>=10) T-=39;
18028: V=10*V+T;
18029: }
18030: if(NN==1){
18031: V=-V; NN=0;
18032: }
18033: TR=cons(V,TR);
18034: if(SS!=47) break;
18035: else{
18036: N=2; S=cdr(S);
18037: }
18038: }
18039: }else if(T==60){
18040: for(V=[],S=cdr(S);S!=[]&&car(S)!=62;S=cdr(S))
18041: V=cons(car(S),V);
18042: if(car(S)!=62) continue;
18043: TR=cons(eval_str(asciitostr(reverse(V))),TR);
18044: }else if(T<48) continue;
18045: if(N==1){
18046: T = car(TR);
18047: TR=cons(-T,cdr(TR));
18048: N=0;
18049: }else if(N==2){
18050: T=car(TR); TR=cdr(TR);
18051: TR=cons(car(TR)/T,cdr(TR));
18052: N=0;
18053: }
18054: }
18055: return reverse(cons(reverse(TR),R));
18056: }else if(type(S)==4){
18057: Num=getopt(num);
18058: for(R=[]; ; ){
18059: if(type(TS=car(S))!=4) return;
18060: for(; TS!=[]; TS=cdr(TS)){
18061: V=car(TS);
18062: if(type(V)>1||(type(V)==1&&ntype(V)>0)){
18063: V="<"+rtostr(V)+">";
18064: R=append(reverse(strtoascii(V)),R);
18065: continue;
18066: }
18067: if(dn(V)>1){
18068: P=reverse(strtoascii(rtostr(V)));
18069: R=append(P,cons(40,R));
18070: R=cons(41,R);
18071: continue;
18072: }
18073: if(V<0 && V>-10){
18074: V=-V;
18075: R=cons(45,R);
18076: }
18077: if(V<0 || V>35 || (V>9 && Num==1)){
18078: P=reverse(strtoascii(rtostr(V)));
18079: R=append(P,cons(40,R));
18080: V=41;
18081: }else if(V<10) V+=48;
18082: else V+=87;
18083: R=cons(V,R);
18084: }
18085: if((S=cdr(S))==[]) break;
18086: R=cons(44,R);
18087: }
18088: return asciitostr(reverse(R));
18089: }
18090: return 0;
18091: }
18092:
18093: def sp2grs(M,A,L)
18094: {
18095: MM = [];
18096: T0 = 0;
18097: Mat=getopt(mat);
18098: if(Mat!=1) Mat=0;
18099: if(type(M)==7) M=s2sp(M);
18100: if((LM = length(M)) > 10 && type(A) < 4)
18101: CK = 1;
18102: Sft = (type(L)==1)?L:0;
18103: if(type(L)==4 && length(L)>=3)
18104: Sft = L[2];
18105: if(Sft < 0){
18106: T0 = 1;
18107: Sft = -Sft-1;
18108: }
18109: for(I = LM-1; I >= 0; I--){
18110: MI = M[I]; MN = [];
18111: if(CK == 1 && length(MI) > 10){
18112: erno(1);
18113: return;
18114: }
18115: if(type(A) == 4)
18116: AA = rtostr(A[I]);
18117: else
18118: AA = rtostr(A)+rtostr(I);
18119: for(J = LM = length(MI)-1; J >= 0; J--){
18120: V = MI[J];
18121: if(type(V) > 3)
18122: V = V[0];
18123: if(T0 == 0 || I == 0)
18124: MN = cons([V, makev([AA,J+Sft])], MN);
18125: else{
18126: if(LM == 1)
18127: MN = cons([V, (J==0)?0:makev([AA])], MN);
18128: else if(I == 1 && Mat == 0)
18129: MN = cons([V, (J==length(MI)-1)?0:makev([AA,J+Sft])], MN);
18130: else
18131: MN = cons([V, (J==0)?0:makev([AA,J])], MN);
18132: }
18133: }
18134: MM = cons(MN, MM);
18135: }
18136: if(type(L) == 4 && length(L) >= 2){
18137: R = chkspt(MM|mat=Mat); /* R[3]: Fuchs */
18138: AA = var(MM[L[0]-1][L[1]-1][1]);
18139: if(AA==0) AA=var(R[3]);
18140: if(AA!=0 && (P = mycoef(R[3],1,AA))!=0){
18141: P = -mycoef(R[3], 0, AA)/P;
18142: MM = mysubst(MM,[AA,P]);
18143: }
18144: }
18145: return MM;
18146: }
18147:
18148: def intpoly(F,X)
18149: {
18150: if((T=ptype(F,X))<4){
18151: if(T<3){ /* polynomial */
18152: if(type(C=getopt(cos))>0){
18153: V=vars(F);
18154: Z=makenewv(V);
18155: W=makenewv(cons(Z,V));
18156: Q=intpoly(F,X|exp=Z);
18157: Q=(subst(Q,Z,@i*C)*(Z+@i*W)+subst(Q,Z,-@i*C)*(Z-@i*W))/2;
18158: return [mycoef(Q,1,Z),mycoef(Q,1,W)];
18159: }
18160: if(type(C=getopt(sin))>0){
18161: Q=intpoly(F,X|cos=C);
18162: return [-Q[1],Q[0]];
18163: }
18164: if(type(C=getopt(log))>0){
18165: Q=intpoly(F,X);
18166: if(C[0]==0) return [Q,0];
18167: if(length(C)<3) C=[C[0],C[1],1];
18168: Q-=subst(Q,X,-C[1]/C[0]);
18169: if(iscoef(Q,os_md.israt)) Q=red(Q);
18170: if(C[2]==0) return [Q];
18171: S=subst(-Q*C[0]*C[2],X,X-C[1]/C[0]);
18172: for(R=0,D=mydeg(S,X);D>0;D--) R+=mycoef(S,D,X)*X^(D-1);
18173: R=subst(R,X,X+C[1]/C[0]);
18174: return cons(Q,intpoly(R,X|log=[C[0],C[1],C[2]-1]));
18175: }
18176: if(type(C=getopt(exp))>0){
18177: D = mydeg(F,X);
18178: for(P=Q=F/C;D>=0;D--){
18179: Q=-mydiff(Q,X)/C;
18180: P+=Q;
18181: }
18182: return P;
18183: }
18184: for(P=0,I=mydeg(F,X);I >= 0;I--)
18185: P += mycoef(F,I,X)*X^(I+1)/(I+1);
18186: return P;
18187: }
18188: R=pfrac(F,X|root=2); /* rational */
18189: for(P=0;R!=[];R=cdr(R)){
18190: if(type(V=getopt(dumb))==5){
18191: for(PF=[],RR=R;RR!=[];RR=cdr(RR))
18192: PF=cons(RR[0][0]/RR[0][1]^RR[0][2],PF);
18193: PF=[cons(X,reverse(PF))];
18194: if(P) PF=cons([1,P],PF);
18195: V[0]=cons(PF,V[0]);
18196: }
18197: RT=car(R);
18198: if(mydeg(RT[1],X)==0) P+=intpoly(RT[0]*RT[2],X);
18199: else if((Deg=mydeg(RT[1],X))==1){
18200: if(RT[2]>1) P+=RT[0]*RT[1]^(1-RT[2])/(1-RT[2])/mycoef(RT[1],1,X);
18201: else P+=RT[0]*log(RT[1])/mycoef(RT[1],1,X);
18202: P=red(P);
18203: }else if(Deg==2){
18204: D1=diff(RT[1],X);C1=mycoef(D1,1,X);
18205: B=2*C1*mycoef(RT[1],0,X)-mycoef(RT[1],1,X)^2; /* ax^2+bx+c => B=4ac-b^2 */
18206: B=sqrt2rat(B);
18207: N=RT[0];
18208: for(I=RT[2];I>0&&N!=0;I--){
18209: C0=mycoef(N,1,X)/C1;N-=C0*D1;
18210: if(C0){
18211: if(I>1) P-=C0/RT[1]^(I-1)/(I-1);
18212: else P+=C0*log(RT[1]);
18213: }
18214: if(I>1){
18215: BB=B/C1;
18216: P+=N*X/RT[1]^(I-1)/(I-1)/BB;
18217: N*=(2*I-3)/(I-1)/BB;
18218: }else{
18219: if(type(BR=sqrtrat(B))>3){
18220: mycat(["Cannot obtain sqare root of ",B]);
18221: return [];
18222: }
18223: if(real(nm(BR))!=0){
18224: P+=(2*N/BR)*atan(sqrt2rat(D1/BR|mult=1));
18225: }else{
18226: BR*=@i;BRI=sqrt2rat(1/BR);
18227: R1=(-mycoef(RT[1],1,X)+BR)/C1;
18228: R2=(-mycoef(RT[1],1,X)-BR)/C1;
18229: P+=N*BRI*log( /* sqrt2rat */((x-R1)/(x-R2)));
18230: }
18231: }
18232: P=red(P);
18233: }
18234: P=sqrt2rat(P);
18235: }else{
18236: mycat(["Cannot get an indefinite integral of ",F]);
18237: return [];
18238: }
18239: }
18240: Q=simplog(P,X);
18241: if(type(V)==5&&nmono(P)!=nmono(Q)) V[0]=cons([[1,red(P)]],V[0]);
18242: return red(Q);
18243: }
18244: return [];
18245: }
18246:
18247: def fshorter(P,X)
18248: {
18249: Q=sqrt2rat(P);
18250: R=trig2exp(Q,X|inv=1);
18251: if(str_len(fctrtos(R))<str_len(fctrtos(Q))) Q=R;
18252: Var=pfargs(Q,X|level=1);
18253: for(C=F=0,R=1,V=Var;V!=[];V=cdr(V)){
18254: if(findin(car(V)[1],[cos,sin,tan])>=0){
18255: if(!C){
18256: F=car(V)[2];
18257: }else{
18258: R=red(car(V)[2]/F);
18259: if(type(R)!=1) break;
18260: F/=dn(R);
18261: }
18262: C++;
18263: }
18264: }
18265: if(getopt(period)==1) return F;
18266: if(!isint(Log=getopt(log))) Log=0;
18267: if(V==[]&&F!=0){
18268: if(iand(Log,1)){
18269: H=append(cdr(fctr(nm(Q))),cdr(fctr(dn(Q))));
18270: for(L=0;H!=[];H=cdr(H))
18271: L+=str_len(rtostr(car(H)[0]));
18272: }else L=str_len(fctrtos(Q));
18273: S=trig2exp(P,X);
18274: for(T=[sin(F),tan(F),cos(F),sin(F/2),cos(F/2),tan(F/2)];T!=[];T=cdr(T)){
18275: R=trig2exp(S,X|inv=car(T));
18276: if(iand(Log,1)){
18277: H=append(cdr(fctr(nm(R))),cdr(fctr(dn(R))));
18278: for(K=0;H!=[];H=cdr(H))
18279: K+=str_len(rtostr(car(H)[0]));
18280: }else K=str_len(fctrtos(R));
18281: if(K<L){
18282: Q=R;L=K;
18283: }
18284: }
18285: }
18286: return Q;
18287: }
18288:
18289: def isshortneg(P)
18290: {
18291: return(str_len(rtostr(P))>str_len(rtostr(-P)))?1:0;
18292: }
18293:
18294: def simplog(R,X)
18295: {
18296: for(V=[],Var=pfargs(R,X);Var!=[];Var=cdr(Var)){
18297: VT=car(Var);
18298: if(VT[1]==log && ptype(R,VT[0])==2 && mydeg(R,VT[0])==1)
18299: V=cons([VT[0],VT[2],mycoef(R,1,VT[0])],V);
18300: }
18301: for(;V!=[];V=cdr(V)){
18302: VT=car(V);
18303: for(V2=cdr(V);V2!=[];V2=cdr(V2)){
18304: Dn=1;
18305: if((C=red(car(V2)[2]/VT[2]))!=1&&C!=-1){
18306: if(getopt(mult)==1&&type(C)==1&&ntype(C)==0){
18307: Dn=dn(C);C*=Dn;
18308: }else continue;
18309: }
18310: Log=red(VT[1]^Dn*car(V2)[1]^(Dn*C));
18311: L=str_len(rtostr(dn(Log)))-str_len(rtostr(nm(Log)));
18312: if(L>0 || (L==0&&isshortneg(VT[2])) ){
18313: Dn=-Dn;Log=1/Log;
18314: }
18315: R=mycoef(R,0,VT[0]);R=mycoef(R,0,car(V2)[0]);
18316: return(R+VT[2]*log(Log)/Dn);
18317: }
18318: }
18319: return R;
18320: }
18321:
18322: def integrate(P,X)
18323: {
18324: Dvi=getopt(dviout);
18325: if(type(I=getopt(I))==4){
18326: if((R=integrate(P,X))==[]) II="?";
18327: else if(type(I[0])>3||type(I[1])>3){
18328: R=subst(R,X,x);
18329: V=flim(R,I[0]);VV=flim(R,I[1]);
18330: if(V==""||VV=="") II="?";
18331: else if(type(V)==7||type(VV)==7){
18332: if(V==VV) II="?";
18333: else II=(VV=="+"||V=="-")?"\\infty":"-\\infty";
18334: }else{
18335: II=VV-V;
18336: if(II>10^10) II="\\infty";
18337: else if(II<-10^10) II="-\\infty";
18338: }
18339: }else{
18340: V=subst(R,X,I[1])-subst(R,X,I[0]);
18341: VV=myval(V);
18342: II=(type(VV)>=2||ntype(VV)<1)?VV:evalred(V);
18343: }
18344: if(type(Dvi)!=1) return II;
18345: I=ltov(I);
18346: for(J=0;J<2;J++){
18347: if(type(I[J])>3){
18348: if(type(I[J])==4&&length(I[J])>1) I[J]=I[J][1];
18349: else I[J]=(J==0)?"-\\infty":"\\infty";
18350: }
18351: if(type(I[J])<4) I[J]=my_tex_form(I[J]);
18352: }
18353: S=(type(II)==7)?II:my_tex_form(II);
18354: S="\\int_{"+I[0]+"}^{"+I[1]+"}"+monototex(P)+"\\,d"+my_tex_form(X)+"&="+S;
18355: if(Dvi==1) dviout(texbegin("align",S));
18356: return S;
18357: }
18358: if(isint(Dvi)==1){
18359: if(Dvi==2||getopt(dumb)==-1){
18360: V=newvect(1);V[0]=[];
18361: }else V=0;
18362: if((RR=integrate(P,X|dumb=V))==[]) return R;
18363: S=fshorter(RR,X);
18364: VV=[X];
18365: if(V!=0){
18366: R=cons([[1,RR]],V[0]);
18367: if(S!=RR) R=cons([[1,RR=S]],R);
18368: for(V=FR=[];R!=[];R=cdr(R))
18369: if(car(R)!=FR) V=cons(FR=car(R),V);
1.21 takayama 18370: Var=varargs(V|all=2);
1.6 takayama 18371: for(S0=[x0,x1,x2,x3],S=[t,s,u,v,w];S0!=[]&&S!=[];){
18372: if(findin(car(S0),Var)<0){
18373: S0=cdr(S0); continue;
18374: }
18375: if(findin(car(S),Var)>=0){
18376: S=cdr(S); continue;
18377: }
18378: V=subst(V,[car(S0),car(S)]);S0=cdr(S0);S=cdr(S);
18379: }
18380: if(Dvi==-2) return V;
18381: S1="\\,dx&";
18382: }else{
18383: V=[[],[[1,RR=S]]];
18384: S1="\\,dx";
18385: }
18386: if(type(P)>2){
18387: if(type(nm(P))<2){
18388: P=P*dx;S1=V?"&":"";
18389: }
18390: S=fctrtos(P|TeX=2,lim=0);SV0=my_tex_form(P);
18391: if(str_len(SV0)<str_len(S)) S=SV0;
18392: }else S=monototex(P);
18393: if(Dvi!=-2) S="\\int "+S+S1;
18394: else S="";
18395: for(L=[],V=cdr(V);V!=[];V=cdr(V)){
18396: CL=car(V);S0=["="]; /* a line */
18397: for(FL=0;CL!=[];CL=cdr(CL),FL++){
18398: CT=car(CL); /* a term */
18399: if((Y=CT[0])==0){ /* a variable */
18400: CT=cdr(CT);
18401: if(length(CT)>2) CT=cdr(CT);
18402: S0=["\\qquad(",CT[0],"=",CT[1],")"];
18403: break;
18404: }else{
18405: for(FT=0,S2=[],CT=cdr(CT);CT!=[];CT=cdr(CT),FT++){
18406: SV=fctrtos(car(CT)|TeX=2,lim=0);SV0=my_tex_form(car(CT));
18407: if(str_len(SV0)<str_len(SV)) SV=SV0;
18408: if(FL||FT||(F&&type(Y)<2)) SV=minustos(SV);
18409: S2=append(["+",SV],S2);
18410: }
18411: S2=reverse(cdr(S2));
18412: if(type(Y)>1){
18413: if(length(S2)>1){
18414: S1="\\int\\left(";S3="\\right)\\,d";
18415: }else{
18416: S1="\\int";S3="\\,d";
18417: }
18418: S2=cons(S1,append(S2,[S3,Y]));
18419: if(findin(Y,VV)<0) VV=cons(Y,VV);
18420: }
18421: if(FL) S0=append(S0,cons("+",S2));
18422: else S0=append(S0,S2);
18423: }
18424: }
18425: L=append([S0],L);
18426: };
18427: V=pfargs(RR,X|level=1);
18428: for(Var=[];V!=[];V=cdr(V)) Var=cons(car(V)[0],Var);
18429: Var=reverse(Var);
18430: if(!isint(J=getopt(frac))) J=0;;
18431: if(!iand(J,4)&&(!iand(J,2)||length(Var)==1)&&(iand(J,8)==8||ptype(RR,Var)==2)){
18432: F=1;
18433: if(iand(J,1)){
18434: K=str_len(fctrtos(RR));
18435: I=str_len(fctrtos(RR|var=Var));
18436: if(I>=K) F=0;
18437: }
18438: if(F){
18439: V=[fctrtos(RR|var=Var,TeX=2)];
18440: if(Dvi!=-2) V=cons("=",V);
18441: if(length(L)>0) L=cdr(L);
18442: L=append([V],L);
18443: }
18444: }else if(ptype(RR,X)==2){
18445: L=cdr(L);
18446: V=[fctrtos(RR|var=X,TeX=2)];
18447: if(Dvi!=-2) V=cons("=",V);
18448: L=append([V],L);
18449: }
18450: S=texket(S+ltotex(reverse(L)|opt=["cr","spts0"],str=1));
18451: if(getopt(log)!=1){
18452: for(V=[];VV!=[];VV=cdr(VV))
18453: V=cons(strtoascii(my_tex_form(car(VV))),V);
18454: S1=strtoascii("\\log");
18455: for(F=1;F;){ /* log(log(x)) */
18456: F=FT=0;
18457: S0=strtoascii(S); /* log(x) -> log|x| */
18458: L=length(S0);
18459: S2=str_tb(0,0);
18460: for(I=0;;){
18461: if(I>=L||(J=str_str(S0,S1|top=I+FT))<0){
18462: S=str_tb(0,S2)+str_cut(S0,I,100000);
18463: break;
18464: }
18465: if((K=str_str(S0,40|top=J+4))<0
18466: ||(K!=J+4&&K!=J+9)||(N=str_pair(S0,K+1,40,41))<0){
18467: FT=J-I+4;continue;
18468: }
18469: FT=0;
18470: if(str_str(S0,V|top=K+1,end=N-1)[0]<0) S2=str_tb(str_cut(S0,I,N),S2);
18471: else{
18472: /* log(a) -> log(a) */
18473: F=1;
18474: if(N<L-1&&S0[N+1]==94){ /* log(x)^2 -> (log|x|)^2 */
18475: S2=str_tb([str_cut(S0,I,J-1),"\\left(",str_cut(S0,J,K-1),
18476: "|",str_cut(S0,K+1,N-1),"|\\right)"],S2);
18477: }
18478: else S2=str_tb([str_cut(S0,I,K-1),"|",str_cut(S0,K+1,N-1),"|"],S2);
18479: }
18480: I=N+1;
18481: }
18482: }
18483: }
18484: if(Dvi>0){
18485: dviout(texbegin("align*",S));
18486: return 1;
18487: }
18488: return S;
18489: } /* end of dviout */
18490: SM=["Cannot integrate",P,"at present"];
18491: P=sqrt2rat(P|mult=1);
18492: Dumb2=1;Dumb3=0;W=newvect(1);W[0]=[];
18493: if(type(Dumb=getopt(dumb))==5){
18494: Dumb2=Dumb3=Dumb;D2=W;
18495: }else if(!isint(Dumb)) Dumb=0;
18496: if(Dumb==-1){
18497: Dumb2=Dumb3=-1;
18498: }
18499: if(type(Dumb)!=5) D2=Dumb2;
18500: if(!isint(Mul=getopt(mult))) Mul=0;
18501: else Mul++;
18502: if(type(VAR=getopt(var))!=4) VAR=[];
18503: if(type(P)>4) return [];
18504: if(iand(T=ptype(P=red(P),X),63)>3||Mul>4){
18505: if(Dumb!=1) mycat(SM);
18506: return [];
18507: }
18508: if(Dumb==-1) mycat(["integrate", P]);
18509: else if(type(Dumb)==5) Dumb[0]=cons([[X,P]],Dumb[0]);
18510: if(T<4 && (T<3||iscoef(P,os_md.israt))){
18511: if(Dumb==-1) mycat(["rational function",P]);
18512: else if(type(Dumb)==5) Dumb[0]=cons([[X,P]],Dumb[0]);
18513: return intpoly(P,X|dumb=Dumb); /* rational function */
18514: }
18515: Var=pfargs(P,X);
18516: for(F=0,VV=Var;VV!=[];VV=cdr(VV)){
18517: /* p(x)*log(x^2-1), @e^x, a^x, f(x)^(m/n) etc.->simplify */
18518: V=car(VV);
18519: if(V[1]==log && (T=ptype(V[2],X))>1 && T<4){
18520: if(mydeg(dn(V[2]),X)>0||mydeg(nm(V[2]),X)>1){
18521: FC=pfctr(V[2],X);RV=1;
18522: if(length(FC)>2){
18523: RR=0;RV=1;
18524: if((F0=car(FC)[0])!=1){
18525: if(type(F0)!=1 && F0<0){
18526: for(FT=cdr(FT);FT!=[];FT=cdr(FT)){
18527: if(iand(car(FT)[1],1)){
18528: RV=-1;F0=-F0;break;
18529: }
18530: }
18531: }
18532: }
18533: if(F0!=1) RR=log(F0);
18534: for(FC=cdr(FC);FC!=[];FC=cdr(FC)){
18535: if(RV==-1&&iand(car(FC)[1],1)==1){
18536: RR+=car(FC)[1]*log(-car(FC)[0]);
18537: RV=1;
18538: }else
18539: RR+=car(FC)[1]*log(car(FC)[0]);
18540: }
18541: P=subst(P,V[0],RR);
18542: F=1;
18543: }
18544: }
18545: F=1;
18546: }else if(V[1]==pow){
18547: if(ptype(V[2],X)==1){
18548: F=1;
18549: if(V[2]==@e){ /* @e^(f(x)) */
18550: P=subst(P,V[0],exp(V[3]));
18551: }else P=subst(P,V[0],exp(log(V[2])*V[3]));
18552: }else if(type(V[3])<=1 && ntype(V[3])==0){ /* r(x)^(m/n) */
18553: if((Pw=floor(V[3]))!=0){
18554: R=V[2]^Pw;
18555: if((PF=V[3]-Pw)!=0) R*=V[2]^PF;
18556: P=subst(P,V[0],R);
18557: F=1;
18558: V=[V[2]^PF,V[1],V[2],PF];
18559: }
18560: if(ptype(nm(V[2]),X)<2&&V[3]>0){ /* (1/p(x))^(m/n) */
18561: P=subst(P,V[0],V[2]*red(1/V[2])^(1-V[3]));
18562: F=0;VV=cons(0,Var=pfargs(P,X));continue;
18563: }
18564: if(ptype(V[2],X)<4&&(K=dn(V[3]))>1){
18565: V2=red(V[2]);
18566: DN=mydeg(nm(V2),X);DD=mydeg(dn(V2),X);
18567: if(DN+DD>1){
18568: VF=pfctr(V2,X);
18569: R=car(VF)[0]^(car(VF)[1]);RR=0;
18570: for(VF=cdr(VF);VF!=[];VF=cdr(VF)){
18571: TV=car(VF);TM=TV[1];
18572: while(abs(TM)>=K){
18573: RR=1;
18574: if(TM>0){
18575: TM-=K;
18576: RR*=TV[0]^nm(V[3]);
18577: }else{
18578: TM+=K;
18579: RR/=TV[0]^nm(V[3]);
18580: }
18581: }
18582: if(TM!=0) R*=TV[0]^TM;
18583: }
18584: if(RR){
18585: P=subst(P,V[0],RR*red(R)^(V[3]));F=1;
18586: F=0;VV=cons(0,Var=pfargs(P,X));continue;
18587: }
18588: }
18589: }
18590: }
18591: }
18592: }
18593: if(F){
18594: P=sqrt2rat(P|mult=1);
18595: Var=pfargs(P=red(P),X);T=ptype(P,X);
18596: if(T<4 && (T<3||iscoef(P,os_md.israt))){
18597: if(Dumb==-1) mycat(["rational function",P]);
18598: else if(type(Dumb)==5){
18599: Dumb[0]=cons([[X,P]],Dumb[0]);
18600: return intpoly(P,X|dumb=Dumb3);
18601: }
18602: return intpoly(P,X); /* rational function */
18603: }
18604: }
18605: #if 1
18606: for(P0=P,V=pfargs(P,X|level=1);V!=[];V=cdr(V)) /* P:tan(x) -> P0:sin(x)/cos(x) */
18607: if(car(V)[1]==tan) P0=red(subst(P0,car(V)[0],sin(car(V)[2])/cos(car(V)[2])));
18608: if(iand(ptype(P0,X),128)){ /* (log f)'=f'/f */
18609: for(Df=cdr(fctr(dn(P0)));Df!=[];Df=cdr(Df)){
18610: if(!iand(ptype(car(Df)[0],X),64)) continue;
18611: Q=car(Df)[0]^(car(Df)[1]);QQ=red(dn(P0)/Q);
18612: DQ=red(diff(Q,X)*QQ);
18613: if(type(C=DQ/nm(P0))<2&&C!=0){
18614: PP=0;DN=[1];
18615: }else for(DN=cdr(fctr(DQ));DN!=[];DN=cdr(DN)){
18616: Y=car(DN)[0];
18617: if(!iand(ptype(Y,X),64)||(I=mydeg(nm(P0),Y))!=mydeg(DQ,Y)
18618: || ptype((C=red(mycoef(nm(P0),I,Y)/mycoef(DQ,I,Y))),X)>1||C==0) continue;
18619: PP=red(P0-C*diff(Q,X)/Q);
18620: if(nmono(P0)>nmono(PP)) break;
18621: }
18622: if(DN!=[]){
18623: R=C*log(Q);
18624: if(PP==0){
18625: if(P!=P0&&type(Dumb)==5) Dumb[0]=cons([[X,P0]],Dumb[0]);
18626: return R;
18627: }
18628: W[0]=[];
18629: S=integrate(PP,X|dumb=D2);
18630: if(S!=[]){
18631: if(type(Dumb)==5){
18632: Dumb[0]=cons([[X,red(P0-PP),PP]],Dumb[0]);
18633: TD=W[0];
18634: for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){
18635: if(car(TD)[0][0]){
18636: WL=cons([1,R],car(TD));
18637: Dumb[0]=cons(WL,Dumb[0]);
18638: }
18639: else Dumb[0]=cons(car(TD),Dumb[0]);
18640: }
18641: }
18642: return red(R+S);
18643: }
18644: }
18645: }
18646: }
18647: #endif
18648: if((length(Var)==1||getopt(exe)==1) && /* p(x)*atan(q(x))^m+r(x), etc */
18649: findin((VT=car(Var))[1],[atan,asin,acos,log])>=0 && ptype(P,VT[0])==2 &&
18650: (VT[1]!=log||(T!=65&&T!=66)||mydeg(VT[2],X)!=1)){ /* exclude x*log(x+1)^2 */
18651: for(R=0,D=mydeg(P,VT[0]);D>=0;D--){
18652: Q=S=mycoef(P,D,VT[0]);
18653: if(S){
18654: if(D>0){
18655: if((Q=integrate(S,X|mult=Mul))==[]) return Q;
18656: }else{
18657: W[0]=[];
18658: if((Q=integrate(S,X|dumb=D2,var=VAR,mult=Mul))==[]) return Q;
18659: if(type(Dumb)==5){
18660: TD=W[0];
18661: for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){
18662: if(car(TD)[0][0]){
18663: WL=cons([1,R],car(TD));
18664: Dumb[0]=cons(WL,Dumb[0]);
18665: }
18666: else Dumb[0]=cons(car(TD),Dumb[0]);
18667: }
18668: if(car(Dumb[0])!=[[1,R],[1,Q]])
18669: Dumb[0]=cons([[1,R,Q]],Dumb[0]);
18670: }
18671: return red(R+Q);
18672: }
18673: }else if(D>0) continue;
18674: if(D==0){
18675: if(Q!=0&&type(Dumb)==5) Dumb[0]=cons([[1,R,Q]],Dumb[0]);
18676: return red(Q+R);
18677: }
18678: R0=Q*VT[0]^D;
18679: P=(P0=P)-S*VT[0]^D-Q*diff(VT[0]^D,X);
18680: if(mydeg(P,VT[0])>=D){ /* (x+1)*log(x)/x^2 */
18681: if(mydeg(P,VT[0])==D &&
18682: ptype(C=red(mycoef(P,D,VT[0])/diff(VT[0],X)),VT[0])<2){
18683: P=P0-(S*VT[0]^D+Q*diff(VT[0]^D,X)+C*diff(VT[0]^(D+1),X)/(D+1));
18684: R0+=C*VT[0]^(D+1)/(D+1);
18685: }else{
18686: P=P0;
18687: if(Dumb!=1) mycat(SM);
18688: return [];
18689: }
18690: }
18691: if(type(Dumb)==5){
18692: if(P) Dumb[0]=cons([R?[1,R,R0]:[1,R0],[X,P]],Dumb[0]);
18693: else if(R!=0) Dumb[0]=cons([[1,R,R0]],Dumb[0]);
18694: }
18695: R+=R0;
18696: }
18697: }
18698: if(length(Var)==1 && (VT=car(Var))[1]==pow && mydeg(P,VT[0])==1 && (PT=ptype(VT[2],X))<4){
18699: PR=mycoef(P,0,VT[0]);
18700: if(RR!=0){
18701: RR=integrate(RR,X|dumb=Dumb3,var=Var);
18702: if(RR==[]) return RR;
18703: }
18704: PW=VT[3];
18705: if((D=mydeg(nm(V2=VT[2]),X))==2&&PT==2){ /* f(x)*(ax^2+bx+c)^(m/2)+r(x) */
18706: if(isint(2*PW)){
18707: C2=mycoef(V20=V2,2,X);F=1;
18708: if((C21=sqrtrat(C2))==[]) return [];
18709: if(imag(C21)!=0){
18710: if(real(C21)!=0) return [];
18711: C21=C21/@i;F=-1;
18712: }
18713: if(type(C21)>3) return [];
18714: P=subst(P,X,X/C21);VT=mysubst(VT,[X,X/C21]);V2=VT[2];
18715: C1=mycoef(V2,1,X)/F/2;
18716: if(C1!=0){
18717: P=subst(P,X,X-C1);VT=mysubst(VT,[X,X-C1]);V2=VT[2];
18718: }
18719: C0=mycoef(V2,0,X);
18720: if((C01=sqrtrat(C0))==[]) return [];
18721: if(imag(nm(C01))!=0){
18722: if(real(nm(C01))!=0) return [];
18723: C01=C01/@i;G=-1;
18724: }else G=1;
18725: if(type(C01)>3||(F==-1&&G==-1)) return [];
18726: Y=makenewv([P,VAR]|var=x);
18727: if(F==-1){ /* (c^2-x^2)^(1/2) */
18728: Q=subst(P,VT[0],(C01*cos(Y))^(2*PW),X,YX=C01*sin(Y))
18729: *C01*cos(Y)/C21;
18730: SY=(C21*X+C1);CY=V20;YY=asin(sqrt2rat((C21*X+C1)/C01|mult=1));
18731: }else if(G==-1){ /* (x^2-c^2)^(1/2) */
18732: Q=subst(P,VT[0],(C01*sin(Y)/cos(Y))^(2*PW),X,YX=C01/cos(Y))
18733: *C01*sin(Y)/cos(Y)^2/C21;
18734: SY=V20;CY=1/(C21*X+C1);YY=acos(sqrt2rat(C01*(C21*X+C1)|mult=1));
18735: }else{ /* (x^2+c^2)^(1/2) */
18736: Q=subst(P,VT[0],(C01/cos(Y))^(2*PW),X,YX=C01*sin(Y)/cos(Y))
18737: *C01/cos(Y)^2/C21;
18738: CY=V20; YY=atan(sqrt2rat((C21*X+C1)/C01|mult=1));
18739: }
18740: if(Dumb==-1) mycat([C21*X+C1,"=",YX]);
18741: else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,C21*X+C1,YX]],Dumb[0]);
18742: Q=sqrt2rat(Q);
18743: QQ=red(substblock(nm(Q),sin(Y),sin(Y)^2,1-cos(Y)^2)
18744: /substblock(dn(Q),sin(Y),sin(Y)^2,1-cos(Y)^2));
18745: if(cmpsimple(QQ,Q|comp=2)<0) Q=QQ;
18746: QQ=red(substblock(nm(Q),cos(Y),cos(Y)^2,1-sin(Y)^2)
18747: /substblock(dn(Q),cos(Y),cos(Y)^2,1-sin(Y)^2));
18748: if(cmpsimple(QQ,Q|comp=2)<0) Q=QQ;
18749: if((Q=integrate(Q,Y|dumb=Dumb2,var=cons(X,Var)))==[]) return [];
18750: Q=trig2exp(Q,Y|inv=cos(Y));
18751: for(V=vars(Q);V!=[];V=cdr(V)){
18752: FA=funargs(car(V));
18753: if(type(FA)==4&&FA[0]==log){
18754: QQ=trig2exp(FA[1],Y|inv=cos(Y));
18755: Q=mycoef(Q,0,car(V))+mycoef(Q,1,car(V))*log(QQ);
18756: }
18757: }
18758: if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]);
18759: if(F==-1) Q=subst(Q,sin(Y),SY/C01,cos(Y),CY^(1/2)/C01,Y,YY);
18760: else if(G==-1){
18761: Q=red(subst(Q,sin(Y),SY^(1/2)*cos(Y)/C01));
18762: Q=red(subst(Q,cos(Y),C01*CY,Y,YY));
18763: }else{
18764: Q=red(subst(Q,sin(Y),(C21*X+C1)*cos(Y)/C01));
18765: Nm=substblock(nm(Q),cos(Y),C01^2/CY,cos(Y)^2);
18766: Nm=subst(Nm,cos(Y),C01/CY^(1/2));
18767: Dn=substblock(dn(Q),cos(Y),C01^2/CY,cos(Y)^2);
18768: Dn=subst(Dn,cos(Y),C01/CY^(1/2));
18769: Q=red(subst(Nm/Dn,Y,YY));
18770: }
18771: if(findin(Y,vars(Q))>=0) return [];
18772: for(R=[],Var=vars(Q);Var!=[];Var=cdr(Var)){
18773: VT=funargs(V=car(Var));
18774: if(type(VT)==4&&VT[0]==log&&ptype(VT[1],X)>60&&mydeg(Q,V)==1)
18775: R=cons([mycoef(Q,1,V),V],R);
18776: }
18777: if(length(R)==2 && (R[0][0]==R[1][0]||R[0][0]+R[1][0]==0)){
18778: R0=args(R[0][1])[0];R1=args(R[1][1])[0];
18779: if(R[0][0]==R[1][0]) S=R0*R1;
18780: else S=R1/R0;
18781: Q=mycoef(Q,0,R[0][1]);Q=mycoef(Q,0,R[1][1]);
18782: Q+=R[1][0]*log(red(S));
18783: }
18784: for(Var=vars(Q);Var!=[];Var=cdr(Var)){
18785: VT=funargs(car(Var));
18786: if(type(VT)==4&&VT[0]==log&&ptype(VT[1],X)>60){
18787: S=trig2exp(VT[1],X|inv=cos(X),arc=1);
18788: if(ptype(dn(S),X)<2 && mydeg(Q,car(Var))==1
18789: && ptype(mycoef(Q,1,car(Var)),X)<2){
18790: S=nm(S);
18791: SF=fctr(S);
18792: S/=SF[0][0];
18793: }
18794: if(cmpsimple(S,-S)>0) S=-S;
18795: Q=subst(Q,car(Var),log(S));
18796: }
18797: } /* x/(1-x^2)^(1/2) */
18798: if(type(Q=red(Q+RR))==2&&type(Dumb)!=5) Q-=cterm(Q);
18799: if(Dumb==-1) mycat(["->",Q]);
18800: else if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]);
18801: return Q;
18802: }
18803: }else if(D==1 && mydeg(Dn=dn(V2),X)<2 && type(PW)==1 && ntype(PW)==0 &&
18804: (V2!=X||ptype(mycoef(P,1,VT[0]),X)>2)){ /* p(x)((ax+b)/(cx+d))^(m/n) */
18805: PN=nm(PW);PD=dn(PW);
18806: Y=makenewv([P,VAR]|var=x);Q=Y^PD*Dn-nm(V2);F=-mycoef(Q,0,X)/mycoef(Q,1,X);
18807: Q=red(subst(P,VT[0],Y^PN,X,F)*diff(F,Y));
18808: if(Dumb==-1) mycat([Y,"=",V2^(1/PD)]);
18809: else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,V2^(1/PD)]],Dumb[0]);
18810: if((Q=integrate(Q,Y|dumb=Dumb3,var=cons(X,Var)))==[]) return [];
18811: Q=red(Q);
18812: QN=subst(substblock(nm(Q),Y,Y^PD,V2),Y,V2^(1/PD));
18813: QD=subst(substblock(dn(Q),Y,Y^PD,V2),Y,V2^(1/PD));
18814: Q=red(QN/QD+RR);
18815: if(Dumb==-1) mycat(["->",Q]);
18816: else if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]);
18817: return Q;
18818: }
18819: }else if(length(Var)==2 && /* r(x,(ax+b)^(1/2),(cx+d)^(1/2)) */
18820: (VT=car(Var))[1]==pow && ptype(VT[2],X)==1 && mydeg(VT[2],X)==1 && VT[3]==1/2 &&
18821: (VS=car(car(Var)))[1]==pow && ptype(VS[2],X)==1 && mydeg(VS[2],X)==1 && VS[3]==1/2){
18822: Y=makenewv([P,VAR]|var=x);R=(Y^2-myceof(VS[0],0,X))/(C=mycoef(VS[0],1,X));
18823: if(Dumb==-1) mycat([Y,"=",VS[0]]);
18824: else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,VD[0]]],Dumb[0]);
18825: R=integrate(subst(P,VS[0],Y,X,R)*2*Y/C,Y|dumb=Dumb3,var=cons(X,Var));
18826: if(R!=[]){
18827: R=subst(substblock(R,Y,VS[0],Y^2),Y,VS[0]);
18828: if(Dumb==-1) mycat(["->",R]);
18829: else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]);
18830: }
18831: return R;
18832: }
18833: if(T==65||T==66){ /* polynomial including sin, exp etc */
18834: for(F=0,VT=Var;VT!=[];VT=cdr(VT)){
18835: VTT=car(VT);
18836: if(ptype(VTT[2],X)>2||mydeg(VTT[2],X)>1) F=ior(F,256); /* compos. or rat. or nonlin. */
18837: K=findin(VTT[1],[cos,sin,tan,exp,log,pow]);
18838: F=ior(F,2^(K+1)); /* 1:other,2:cos,4:sin,8:tan,16:exp,32:log,64:pow */
18839: if((Deg=mydeg(P,VTT[0]))>1&&K!=4) F=ior(F,1024); /* nonlinear */
18840: if(K==5 && (ptype(VTT[3],X)!=0 || VTT[2]!=x||Deg>1)) F=ior(F,8192); /* pow */
18841: for(;Deg>0;Deg--){ /* coef */
18842: if(ptype(mycoef(P,Deg,VTT[0]),X)>2){
18843: if(K==4||K==5) F=ior(F,2048); /* exp, log */
18844: else F=ior(F,4096);
18845: }
18846: }
18847: }
18848: if(!iand(F,1+8+64+256+512+2048+8192)){ /* cos,sin,exp,log^n,x^c */
18849: if(iand(F,1024+4096)&&!iand(F,32+64)){ /* cos,sin,exp */
18850: if(type(Dumb)==5){
18851: S=trig2exp(P,X|inv=1);
18852: if(P!=S) Dumb[0]=cons([[X,S]],Dumb[0]);
18853: }
18854: R=integrate(trig2exp(P,X),X);
18855: if(R!=[]) S=trig2exp(R,X|inv=1);
18856: R=fshorter(S,X);
18857: if(type(Dumb)==5&&R!=S){
18858: Dumb[0]=cons([[1,S]],Dumb[0]);
18859: }
18860: return R;
18861: }
18862: for(R=0,VT=Var;VT!=[];VT=cdr(VT)){
18863: CV=car(VT);
18864: C0=mycoef(CV[2],0,X);C1=mycoef(CV[2],1,X);
18865: Q=mycoef(P,1,CV[0]);
18866: if(CV[1]==sin||CV[1]==cos){
18867: TR=(CV[1]==sin)?intpoly(Q,X|sin=C1):intpoly(Q,X|cos=C1);
18868: R+=TR[0]*cos(CV[2])+TR[1]*sin(CV[2]);
18869: }else if(CV[1]==exp){
18870: QT=exp(CV[2]);
18871: for(V2=vars(C1);V2!=[];V2=cdr(V2)){ /* exp(2*log(a)*x) => a^(2*x) */
18872: if(vtype(VA=car(V2))==2&&functor(VA)==log){
18873: if(ptype(C1,VA)!=2||mydeg(C1,VA)==1&&mycoef(C1,0,VA)==0){
18874: QT=args(VA)[0]^(red(C1/VA)*X);
18875: if(C0!=0) QT*=exp(C0);
18876: break;
18877: }
18878: }
18879: }
18880: R+=intpoly(Q,X|exp=C1)*QT;
18881: }else if(CV[1]==pow)
18882: R+=intpoly(Q,X|pow=CV[2])*x^CV[2];
18883: else if(CV[1]==log){
18884: for(Deg=mydeg(P,CV[0]);Deg>0; Deg--){
18885: Q=mycoef(P,Deg,CV[0]);
18886: TR=intpoly(Q,X|log=[C1,C0,Deg]);
18887: for(I=0;TR!=[];I++,TR=cdr(TR)){
18888: if(I==Deg) R+=car(TR)-subst(car(TR),X,0);
18889: else R+=car(TR)*CV[0]^(Deg-I);
18890: }
18891: }
18892: }
18893: P=mycoef(P,0,CV[0]);
18894: }
18895: R+=intpoly(P,X);
18896: return R;
18897: }
18898: }
18899: for(K=0,VX=[],VT=Var;VT!=[];VT=cdr(VT)){ /* contain only both pow and trig */
18900: VTT=car(VT);
18901: if(findin(VTT[1],[cos,sin,tan])>=0){
18902: if(ptype(VTT[2],X)!=2||mydeg(VTT[2],X)!=1) break;
18903: VX=cons(VTT,VX);
18904: }else if(VTT[1]==pow) K=1;
18905: else break;
18906: }
18907: if(VT==[]&&K==1&&VX!=[]){
18908: D=VX[0][2];
18909: if(VX[0][1]==tan) D*=2;
18910: for(VT=cdr(VX);VT!=[];VT=cdr(VT)){
18911: K=VT[0][2]/D;
18912: if(VT[0][1]==tan) K*=2;
18913: if(type(K)!=1||ntype(K)!=0) break;
18914: D/=dn(K);
18915: }
18916: if(VT==[]){
18917: Y=makenewv([P,VAR]|var=x);
18918: for(Q=P,VT=VX;VT!=[];VT=cdr(VT)){
18919: VTT=car(VT);
18920: if(VTT[1]==cos||VTT[1]==sin){
18921: VV=trig2exp(VTT[0],X|inv=cos(D));
18922: VV=subst(VV,cos(D),(1-Y^2)/(1+Y^2),sin(D),2*Y/(Y^2+1));
18923: }else if(VTT[1]==tan){
18924: VV=trig2exp(VTT[0],X|inv=tan(D/2));
18925: VV=subst(VV,tan(D),Y);
18926: }
18927: Q=subst(Q,VTT[0],VV);
18928: }
18929: Q*=2/(Y^2+1);
18930: if(diff(Q,X)==0){
18931: if(Dumb==-1) mycat([Y,"=",tan(D/2)]);
18932: else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,tan(D/2)]],Dumb[0]);
18933: R=integrate(Q,Y|dumb=Dumb2,var=cons(X,Var));
18934: if(R!=[]){
18935: if(Dumb==-1) mycat(["->",R]);
18936: else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]);
18937: return sqrt2rat(subst(R,Y,tan(D/2))|mult=1);
18938: }
18939: }
18940: }
18941: }
18942: if(T>65||iand(F,8)){ /* rational for functions or tan */
18943: if(findin(X,vars(P))<0){
18944: for(XV=XE=0,VT=Var;VT!=[];VT=cdr(VT)){
18945: VTT=car(VT);
18946: if(mydeg(VTT[2],X)!=1) break;
18947: if(VTT[1]==cos||VTT[1]==sin||VTT[1]==tan){
18948: K=red(VTT[2]/X);
18949: if(type(K)>1||ntype(K)>0) break;
18950: if(XV==0) XV=K;
18951: else XV/=dn(K/XV);
18952: if(VTT[1]==tan) P=red(subst(P,VTT[0],sin(VTT[2])/cos(VTT[2])));
18953: }else if(VTT[1]==exp){
18954: K=red(VTT[2]/X);
18955: if(type(K)>1||ntype(K)>0) break;
18956: if(XE==0) XE=K;
18957: else XE/=dn(K/XE);
18958: }else break;
18959: }
18960: if(VT==[]&&XE*XV==0){
18961: if(XE){
18962: if(XE<0) XE=-XE;
18963: Y=makenewv([P,VAR]|var=x);
18964: for(F=0,VT=Var;VT!=[];VT=cdr(VT),F++){
18965: VTT=car(VT);C=red(VTT[2]/X/XE);
18966: P=subst(P,VTT[0],Y^C);
18967: if(!F){
18968: if(Dumb==-1) mycat([Y^C,"=",VTT[0]]);
18969: else if(type(Dumb)==5) Dumb[0]=cons([[0,Y^C,VTT[0]]],Dumb[0]);
18970: }
18971: }
18972: P/=XE*Y;
18973: Q=integrate(P,Y|dumb=Dumb3,var=cons(X,VAR));
18974: if(Q==[]) return [];
18975: Q=subst(Q,Y,exp(XE*X));
18976: Q=trig2exp(Q,X);
18977: if(Dumb==-1) mycat(["->",Q]);
18978: else if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]);
18979: return Q;
18980: }
18981: P=trig2exp(nm(P),X|inv=cos(XV*X))/trig2exp(dn(P),X|inv=cos(XV*X));
18982: Y=makenewv([P,VAR]|var=x);
18983: Q=red(subst(P,sin(XV*X),Y*cos(XV*X)));
18984: Q=substblock(nm(Q),cos(XV*X),cos(XV*X)^2,1/(Y^2+1))/
18985: (substblock(dn(Q),cos(XV*X),cos(XV*X)^2,1/(Y^2+1))*(Y^2+1));
18986: Q=red(Q);
18987: if(ptype(Q,X)<2){
18988: XV*=2;P=Q;
18989: }else{
18990: P=subst(P,cos(XV*X),(1-Y^2)/(1+Y^2),sin(XV*X),2*Y/(1+Y^2))*2/K/(1+Y^2);
18991: P=red(P);
18992: }
18993: if(Dumb==-1){
18994: mycat([Y,"=",tan(XV*X/2)]);
18995: mycat(["integrate",P]);
18996: }else if(type(Dumb)==5) Dumb[0]=cons([[Y,P]],cons([[0,Y,tan(XV*X/2)]],Dumb[0]));
18997: R=intpoly(P,Y|dumb=Dumb);
18998: if(R==[]) return R;
18999: if(Dumb==-1) mycat(["->",R]);
19000: else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]);
19001: for(Log=1,K=0,Var=pfargs(RR=R,Y);Var!=[];Var=cdr(Var)){
19002: VTT=car(Var);
19003: if(VTT[1]==log){
19004: C=mycoef(R,1,VTT[0]);
19005: VT2=VTT[2];
19006: if(K==0){
19007: K=C;Log=VT2;
19008: if(K<0){
19009: K=-K;Log=1/Log;
19010: }
19011: }else{
19012: if((V=red(C/K))<0){
19013: VT2=1/VT2;V=-V;
19014: }
19015: if(type(V)>1||ntype(V)>0){
19016: Log=1;break;
19017: }
19018: if(isint(V)) Log*=VT2^V;
19019: else{
19020: D=dn(V);K/=D;
19021: Log=Log^D*VT2^nm(V);
19022: }
19023: }
19024: RR=mycoef(RR,0,VTT[0]);
19025: }
19026: }
19027: if(Log!=1){
19028: R=RR;
19029: if(type(Dumb)==5){
19030: if(RR) Dumb[0]=cons([[1,K*log(Log),RR]],Dumb[0]);
19031: else Dumb[0]=cons([[1,K*log(Log)]],Dumb[0]);
19032: }
19033: Log=red(subst(red(Log),Y,sin(XV*X/2)/cos(XV*X/2)));
19034: Log=fshorter(Log,X|log=1); /* log(cos(2*x)+1)=-2*log(cos(x)) */
19035: Nm=fctr(nm(Log));
19036: for(T=[];Nm!=[];Nm=cdr(Nm)){
19037: if(ptype(car(Nm)[0],X)>1) T=cons(car(Nm),T);
19038: }
19039: Nm=fctr(dn(Log));
19040: for(;Nm!=[];Nm=cdr(Nm)){
19041: if(ptype(car(Nm)[0],X)>1) T=cons([car(Nm)[0],-car(Nm)[1]],T);
19042: }
19043: for(I=0,Nm=T;T!=[];T=cdr(T)){
19044: if(I=0) I=abs(car(T)[1]);
19045: else I=igcd(I,car(T)[1]);
19046: }
19047: for(Log=1;Nm!=[];Nm=cdr(Nm)) Log*=car(Nm)[0]^(car(Nm)[1]/I);
19048: K*=I;
19049: if(cmpsimple(nm(Log),dn(Log))<0){
19050: K=-K;Log=red(1/Log);
19051: }
19052: Log=K*log(Log);
19053: if(type(Dumb)==5){
19054: if(RR) Dumb[0]=cons([[1,Log,RR]],Dumb[0]);
19055: else Dumb[0]=cons([[1,Log]],Dumb[0]);
19056: }
19057: }else Log=0;
19058: for(Atan=0,Var=pfargs(RR=R,Y);Var!=[];Var=cdr(Var)){
19059: VTT=car(Var);
19060: if(VTT[1]==atan){
19061: W=subst(VTT[2],Y,sin(XV*X/2)/cos(XV*X/2));
19062: W=trig2exp(W,X|inv=1);
19063: V2=funargs(dn(W));
19064: if(type(V2)==4&&length(V2)==2){
19065: V3=V2[1]*mycoef(R,1,VTT[0]);
19066: Z=0;
19067: if(V2[0]==cos)
19068: Z=red(W*cos(V2[1])/sin(V2[1]));
19069: else if(V2[0]==sin){
19070: Z=red(W*sin(V2[1])/cos(V2[1]));
19071: V3=-V3;
19072: }
19073: if(Z==1){
19074: Atan+=V3;W=0;
19075: }else if(Z==-1){
19076: Atan-=V3;W=0;
19077: }
19078: }
19079: R0=mycoef(R,0,VTT[0]);
19080: if(W!=0) Atan+=subst(R-R0,VTT[0],atan(W)); /* atan(W); */
19081: R=R0;
19082: }
19083: }
19084: if(R!=0){
19085: R=subst(R,Y,sin(XV*X/2)/cos(XV*X/2));
19086: R=red(R);
19087: R=trig2exp(nm(R),X|inv=1)/trig2exp(dn(R),X|inv=1);
19088: }
19089: if(type(Dumb)==5){
19090: F=0;WL=[];
19091: if(R){
19092: WL=cons(R,WL);
19093: F++;
19094: }
19095: if(Atan){
19096: WL=cons(Atan,WL);
19097: F++;
19098: }
19099: if(Log){
19100: WL=cons(Log,WL);
19101: F++;
19102: }
19103: WL=cons(1,WL);
19104: if(F>1) Dumb[0]=cons([WL],Dumb[0]);
19105: }
19106: R=red(R+Log+Atan);
19107: if(Dumb==-1) mycat(["->",R]);
19108: else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]);
19109: return fshorter(R,X);
19110: }
19111: }
19112: }
19113: VT=pfargs(Q=P,X|level=1);
19114: V=(iand(ptype(P,X),7)<3)?[X]:[];
19115: for(;VT!=[];VT=cdr(VT))
19116: if(ptype(P,car(VT)[0])<3) V=cons(car(VT)[0],V);
19117: if(length(V)>0){ /* 1/x+tan(x)+... etc.: sums */
19118: for(R=0;V!=[];V=cdr(V)){
19119: T=mycoef(Q,0,car(V));
19120: W[0]=[];
19121: S=integrate(TD=red(Q-T),X|dumb=D2,mult=Mul,exe=1);
19122: if(S==[]) continue;
19123: if(type(Dumb)==5){
19124: WL=0;
19125: if(T!=0) WL=[[X,TD,T]];
19126: if(R!=0) WL=cons([1,R],WL);
19127: if(WL) Dumb[0]=cons(WL,Dumb[0]);
19128: TD=W[0];
19129: if(R!=0||T!=0){
19130: for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){
19131: if(car(TD)[0][0]){
19132: WL=(!T)?[]:[[X,T]];
19133: WL=append(car(TD),WL);
19134: if(R!=0) WL=cons([1,R],WL);
19135: }else WL=car(TD);
19136: Dumb[0]=cons(WL,Dumb[0]);
19137: }
19138: }else Dumb[0]=append(TD,Dumb[0]);
19139: }
19140: R+=S;Q=T;
19141: if(!Q) return red(R);
19142: }
19143: W[0]=[];
19144: if(P!=Q&&type(S=integrate(Q,X|dumb=D2,mult=Mul))<4){
19145: RR=red(R+S);
19146: if(type(Dumb)==5){
19147: TD=W[0];
19148: for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){
19149: if(car(TD)[0][0]){
19150: WL=cons([1,R],car(TD));
19151: Dumb[0]=cons(WL,Dumb[0]);
19152: }
19153: else Dumb[0]=append(TD,Dumb[0]);
19154: }
19155: if(nmono(R)+nmono(S)!=nmono(RR)) Dumb[0]=cons([[1,R,S]],Dumb[0]);
19156: }
19157: return RR;
19158: }
19159: }
19160: if(Dumb!=1) mycat(SM);
19161: return [];
19162: }
19163:
19164: def fimag(P)
19165: {
19166: for(V=vars(P);V!=[];V=cdr(V)){
19167: Q=[];
19168: if(vtype(VF=car(V))==2){
19169: VAA=args(VF);
19170: if(VAA==[]) continue;
19171: VA=sqrt2rat(VAA[0]);
19172: if(functor(VF)==exp){
19173: if(imag(VA)!=0){
19174: R=(real(VA)!=0)?exp(real(VA)):1;
19175: Q=subst(P,VF,R*(cos(imag(VA))+sin(imag(VA))*@i));
19176: }
19177: }else if(functor(VF)==pow){
19178: VA=sqrt2rat(VAA[1]);
19179: if(imag(VA)!=0){
19180: R=(real(VA)!=0)?VAA[0]^(real(VA)):1;
19181: L=(VAA[0]!=@e)?log(VAA[0]):1;
19182: Q=subst(P,VAA[0]^(VAA[1]),R*(cos(L*imag(VA))+sin(L*imag(VA))*@i));
19183: }else if(VAA[1]!=(V0=fimag(VA)))
19184: Q=subst(P,VAA[0]^(VAA[1]),VAA[0]^(V0));
19185: }
19186: V0=VA;
19187: if(length(VAA)==1&&(VAA[0]!=V0||VA!=(V0=fimag(VA))))
19188: Q=subst(P,VF,subst(VF,VAA[0],V0));
19189: }
19190: if(Q!=[]&&P!=Q){
19191: P=Q;V=cons(0,vars(P));
19192: }
19193: }
19194: return P;
19195: }
19196:
19197:
19198: def trig2exp(P,X)
19199: {
19200: if(iand(ptype(P,X),128)){
19201: OL=getopt();
19202: Nm=trig2exp(nm(P),X|option_list=OL);
19203: Dn=trig2exp(dn(P),X|option_list=OL);
19204: R=red(Nm/Dn);
19205: if(getopt(arc)==1) return sqrt2rat(R);
19206: }
19207: if((Inv=getopt(inv))==1||type(Inv)==2){
19208: for(VT=T=vars(P);T!=[];T=cdr(T)){
19209: if(findin(functor(car(T)),[cos,sin,tan])>=0){
19210: P=trig2exp(P,X);VT=vars(P);break;
19211: }
19212: }
19213: for(;VT!=[];VT=cdr(VT)){
19214: if(functor(CT=car(VT))==exp){
19215: if((Re=real(args(CT)[0]))!=0){
19216: if(isint(Re)) S=@e^Re;
19217: else S=exp(Re);
19218: }else S=1;
19219: if((Im=imag(args(CT)[0]))!=0){
19220: Q=nm(Im);Q=mycoef(Q,mydeg(Q,X),X);
19221: if(-Q>Q) S*=cos(-Im)-@i*sin(-Im);
19222: else S*=cos(Im)+@i*sin(Im);
19223: }
19224: P=subst(P,CT,S);
19225: }
19226: }
19227: P=red(P);
19228: U=vars(Inv);
19229: if(length(U)!=1||((F=functor(car(U)))!=sin&&F!=cos&&F!=tan)) return P;
19230: XX=args(car(U))[0];
19231: if(mydeg(XX,X)!=1) return P;
19232: if(!isvar(XX)) P=subst(P,X,(X-mycoef(XX,0,X))/mycoef(XX,1,X));
19233: for(VT=vars(P);VT!=[];VT=cdr(VT)){
19234: if(vtype(CT=car(VT))<2) continue;
19235: TX=args(CT)[0];
19236: if(mydeg(TX,X)!=1) continue;
19237: if(!isint(C1=mycoef(TX,1,X))) continue;
19238: if((C0=mycoef(TX,0,X))==0){
19239: CC=1;CS=0;
19240: }else if(vars(C0)==[@pi]){
19241: CC=myval(cos(C0));
19242: if(CC!=0&&type(CC)==1&&ntype(CC)!=0){
19243: CC=cos(C0);CS=sin(C0);
19244: }else CS=myval(sin(C0));
19245: }else{
19246: CC=cos(C0);CS=sin(C0);
19247: }
19248: K=C1;
19249: if(K<0) K=-K;
19250: for(CC1=0,I=K;I>=0;I-=2) CC1+=(-1)^((K-I)/2)*binom(K,I)*cos(X)^I*sin(X)^(K-I);
19251: for(CS1=0,I=K-1;I>=0;I-=2) CS1+=(-1)^((K-I-1)/2)*binom(K,I)*cos(X)^I*sin(X)^(K-I);
19252: if(C1<0) CS1=-CS1;
19253: if((TF=functor(CT))==cos) P=subst(P,cos(TX),CC1*CC-CS1*CS);
19254: else if(TF==sin) P=subst(P,sin(TX),CS1*CC+CC1*CS);
19255: }
19256: if(F==sin)
19257: P=substblock(P,cos(X),cos(X)^2,1-sin(X)^2);
19258: else{
19259: P=substblock(P,sin(X),sin(X)^2,1-cos(X)^2);
19260: if(F==tan){
19261: P=subst(P,sin(X),cos(X)*tan(X));
19262: P=substblock(P,cos(X),cos(X)^2,1/(tan(X)^2+1));
19263: }
19264: }
19265: if(!isvar(XX)) P=subst(P,X,XX);
19266:
19267: if(getopt(arc)==1){
19268: for(VT=vars(P);VT!=[];VT=cdr(VT)){
19269: FA=funargs(car(VT));
19270: if(type(FA)==4&&(FA[0]==cos||FA[0]==sin)&&ptype(FA[1],X)>60){
19271: VTT=vars(FA[1]);
19272: if(type(FA[1])!=2||length(VTT)!=1) break;
19273: FB=funargs(VTT[0]);
19274: if(type(FB)!=4||(FF=findin(FB[0],[asin,acos,atan]))<0) break;
19275: if(!isint(2*(C=mycoef(FA[1],1,VTT[0])))||mycoef(FA[1],0,VTT[0])!=0) break;
19276: if(C==1/2){
19277: if(FF==1){
19278: U=(FA[0]==cos)?(1+FB[1])/2:(1-FB[1])/2;
19279: P=subst(P,car(VT),red(U)^(1/2));
19280: }else if(FF==2){
19281: if(FA[0]==sin){
19282: FB1=red(FB[1]);
19283: Nm=nm(FB1);CC=fctr(Nm)[0][0];Dn=dn(FB1);
19284: if(CC<0) CC=-CC;
19285: Nm/=CC;Dn/=CC;
19286: NN=Nm^2+Dn^2;
19287: P=subst(P,car(VT),((NN)^(1/2)-Dn)/Nm*cos(FA[1]));
19288: }
19289: }
19290: P=red(P);
19291: }else if(C==1){
19292: if(FF==1){
19293: if(FA[0]==cos) P=subst(P,car(VT),FB[1]);
19294: else P=subst(P,car(VT),(1-FB[1])^(1/2));
19295: }else if(FF==0){
19296: if(FA[0]==sin) P=subst(P,car(VT),FB[1]);
19297: else P=subst(P,car(VT),(1-FB[1])^(1/2));
19298: }
19299: P=red(P);
19300: }
19301: }
19302: }
19303: P=sqrt2rat(P);
19304: }
19305: return red(P);
19306: }
19307: Var=pfargs(P,X);
19308: for(VT=Var;VT!=[];VT=cdr(VT)){
19309: CT=car(VT);
19310: if(CT[1]==cos)
19311: P=subst(P,CT[0],exp(CT[2]*@i)/2+exp(-CT[2]*@i)/2);
19312: else if(CT[1]==sin)
19313: P=subst(P,CT[0],exp(-CT[2]*@i)*@i/2-exp(CT[2]*@i)*@i/2);
19314: else if (CT[1]==tan)
19315: P=subst(P,CT[0],(exp(-CT[2]*@i)*@i-exp(CT[2]*@i)*@i)/(exp(CT[2]*@i)+exp(-CT[2]*@i)));
19316: else if(CT[1]==pow){
19317: if(ptype(CT[2],X)>1) continue;
19318: if(CT[2]==@e) P=subst(P,CT[0],exp(CT[3]));
19319: else P=subst(P,CT[0],exp(log(CT[2])*exp(CT[3])));
19320: }
19321: }
19322: P=red(P);
19323: for(PP=1,Lp=(dn(P)==1)?1:0;Lp<2;Lp++){
19324: PP=1/PP;
19325: U=(Lp==0)?dn(P):nm(P);
19326: if(U==1) continue;
19327: Var=vars(U);
19328: for(R=[],VT=Var;VT!=[];VT=cdr(VT))
19329: if(functor(car(VT))==exp) R=cons(car(VT),R);
19330: RR=os_md.terms(U,R);
19331: for(Q=0,RRT=RR;RRT!=[];RRT=cdr(RRT)){
19332: for(S=0,CT=cdr(car(RRT)),CR=R,UT=U;CR!=[];CR=cdr(CR),CT=cdr(CT)){
19333: UT=mycoef(UT,car(CT),car(CR));S+=car(CT)*args(car(CR))[0];
19334: }
19335: if(S==0) Q+=UT;
19336: else Q+=UT*exp(S);
19337: }
19338: PP*=Q;
19339: }
19340: return PP;
19341: }
19342:
19343: def powsum(N)
19344: {
19345: if (N < 0) return 0;
19346: if (N == 0) return x;
19347: P = intpoly(N*powsum(N-1),x);
19348: C = subst(P,x,1);
19349: return P+(1-C)*x;
19350: }
19351:
19352: def bernoulli(N)
19353: {
19354: return mydiff(powsum(N),x) - N*x^(N-1);
19355: }
19356:
19357: /* linfrac01([x,y]) */
19358: /* linfrac01(newvect(10,[0,1,2,3,4,5,6,7,8,9]) */
19359: /* 0:x=0, 1:x=y, 2:x=1, 3:y=0, 4:y=1, 5:x=\infty, 6:y=\infty, 7:x=y=0, 8:x=y=1, 9:x=y=\infty
19360: 10:y_2=0, 11:y_2=x, 12:y_2=y, 13: y_2=1, 14: y_2=\infty
19361: 15:y_3=0, 16:y_3=x, 17:y_3=y, 18: y_3=y_2, 19: y_3=1, 20:y_3=\infty
19362: X[0],X[11],X[2],X[10],X[13],X[5],X[14],X[7],X[8],X[9],
19363: X[3],X[1],X[12],X[4],X[6]
19364:
19365: T=0 (x_2,x_1,x_3,x_4,...)
19366: T=-j (x_1,x_2,..,x_{j-1},x_{j+1},x_j,x_{j+2},...)
19367: T=1 (1-x_1,1-x_2,1-x_3,1-x_4,...)
19368: T=2 (1/x_1,1/x_2,1/x_3,1/x_4,...)
19369: T=3 (x_1,x_1/x_2,x_1/x_3,x_1/x_4,...)
19370: */
19371:
19372: def lft01(X,T)
19373: {
19374: MX=getopt();
19375: if(type(X)==4){
19376: K=length(X);
19377: if(K>=1) D=1;
19378: }
19379: if(type(X)==5){
19380: K=length(X);
19381: for(J=5, F=K-10; F>0; F-=J++);
19382: if(F==0) D=2;
19383: }
19384: if(D==0) return 0;
19385: if(T==0){ /* x <-> y */
19386: if(D==1){
19387: R=cdr(X); R=cdr(R);
19388: R=cons(X[0],R);
19389: return cons(X[1],R);
19390: }
19391: R=newvect(K,[X[3],X[1],X[4],X[0],X[2],X[6],X[5]]);
19392: for(I=7;I<K;I++) R[I]=X[I];
19393: for(I=11,J=5; I<K; I+=J++){
19394: R[I]=X[I+1]; R[I+1]=X[I];
19395: }
19396: return R;
19397: }
19398: if(T==1){
19399: if(D==1){
19400: for(R=[];X!=[];X=cdr(X)) R=cons(1-car(X),R);
19401: return reverse(R);
19402: }
19403: R=newvect(K,[X[2],X[1],X[0],X[4],X[3],X[5],X[6],X[8],X[7],X[9]]);
19404: for(I=11;I<K;I++) R[I]=X[I];
19405: for(I=10, J=5; I<K; I+=J++){
19406: R[I]=X[I+J-2]; R[I+J-2]=X[I];
19407: }
19408: return R;
19409: }
19410: if(T==2){
19411: if(D==1){
19412: for(R=[]; X!=[]; X=cdr(X)) R=cons(red(1/car(X)),R);
19413: return reverse(R);
19414: }
19415: R=newvect(K,[X[5],X[1],X[2],X[6],X[4],X[0],X[3],X[9],X[8],X[7]]);
19416: for(I=11;I<K;I++) R[I]=X[I];
19417: for(I=10,J=5; I<K; I+=J++){
19418: R[I]=X[I+J-1]; R[I+J-1]=X[I];
19419: }
19420: return R;
19421: }
19422: if(T==3){
19423: if(D==1){
19424: T=car(X);
19425: for(R=[T],X=cdr(X); X!=[]; X=cdr(X))
19426: R=cons(red(T/car(X)),R);
19427: return reverse(R);
19428: }
19429: R=newvect(K,[X[7],X[4],X[2],X[6],X[1],X[9],X[3],X[0],X[8],X[5]]);
19430: for(I=10,J=5; I<K; I+=J++){
19431: R[I]=X[I+J-1]; R[I+1]=X[I+J-2]; R[I+J-2]=X[I+1]; R[I+J-1]=X[I];
19432: }
19433: return R;
19434: }
19435: if(T==-1){
19436: if(D==1){
19437: return append([X[1],X[2],X[0]],cdr(cdr(cdr(X))));
19438: }
19439: R=newvect(K,[X[0],X[11],X[2],X[10],X[13],X[5],X[14],X[7],X[8],X[9],
19440: X[3],X[1],X[12],X[4],X[6]]);
19441: for(I=11;I<K;I++) R[I]=X[I];
19442: for(I=17,J=5; I<K; I+=J++){
19443: R[I]=X[I+1]; R[I+1]=X[I];
19444: }
19445: return R;
19446: }
19447: if(T<0){
19448: if(D==1){
19449: for(R=[],I=0; X!=[]; X=cdr(X),I--){
19450: if(I==T){
19451: R=cons(X[1],R);
19452: R=cons(X[0],R);
19453: X=cdr(X);
19454: }
19455: else R=cons(car(X),R);
19456: }
19457: return reverse(R);
19458: }
19459: T=3-T;
19460: R=newvect(K);
19461: for(I=0;I<K;I++) R[I]=X[I];
19462: for(I=10,J=5;J<T;I+=J++);
19463: for(II=0; II<J-2; II++){
19464: R[I]=X[I+J]; R[I+J]=R[I];
19465: }
19466: for( ; II<J; II++){
19467: R[I]=X[I+J+1]; R[I+J+1]=X[I];
19468: }
19469: return R;
19470: }
19471: return 0;
19472: }
19473:
19474: def linfrac01(X)
19475: {
19476: if(type(X)==4) K=length(X)-2;
19477: else if(type(X)==5){
19478: L=length(X);
19479: for(K=0,I=10,J=5; I<L; K++,I+=J++);
19480: if(I!=L) return 0;
19481: }
19482: if(K>3 && getopt(over)!=1) return(-1);
19483: II=(K==-1)?3:4;
19484: for(CC=C=1,L=[X]; C!=0; CC+=C){
19485: for(F=C,C=0,R=L; F>0; R=cdr(R), F--){
19486: P=car(R);
19487: for(I=-K; I<II; I++){
19488: S=lft01(P,I);
19489: if(findin(S,L) < 0){
19490: C++; L=cons(S,L);
19491: }
19492: }
19493: }
19494: }
19495: return L;
19496: }
19497:
19498:
19499: def varargs(P)
19500: {
1.21 takayama 19501: if((All=getopt(all))!=1&&All!=2) All=0;
1.6 takayama 19502: V=vars(P);
19503: for(Arg=FC=[];V!=[];V=cdr(V)){
1.21 takayama 19504: if(vtype(CV=car(V))==0&&All!=0){
1.6 takayama 19505: Arg=lsort([CV],Arg,0);
19506: }
19507: if(vtype(CV)!=2) continue;
19508: if(findin(F=functor(CV),FC)<0) FC=cons(F,FC);
19509: for(AT=vars(args(CV));AT!=[];AT=cdr(AT)){
19510: if(vtype(X=car(AT))<2){
19511: if(findin(X,Arg)<0) Arg=cons(X,Arg);
19512: }else if(vtype(X)==2){
19513: R=varargs(X);
19514: if(R[1]!=[]){
19515: Arg=lsort(R[1],Arg,0);
19516: FC=lsort(R[0],FC,0);
19517: }
19518: }
19519: }
19520: }
1.21 takayama 19521: Arg=reverse(Arg);
19522: return (All==2)?Arg:[reverse(FC),Arg];
1.6 takayama 19523: }
19524:
19525: def pfargs(P,X)
19526: {
19527: if(type(L=getopt(level))!=1) L=0;
19528: for(Var=[],V=vars(P);V!=[];V=cdr(V)){
19529: if(vtype(car(V))==2){
19530: VT=funargs(car(V));
19531: if(length(VT)>1){
19532: if(L<2 &&(ptype(VT[1],X)>1 || (length(VT)>2 && ptype(VT[2],X)>1)))
19533: Var=cons(cons(car(V),VT),Var);
19534: if(L!=1 && (R=pfargs(VT[1],X|level=L-1))!=[]) Var=append(R,Var);
19535: }
19536: }
19537: }
19538: return reverse(Var);
19539: }
19540:
19541: def ptype(P,L)
19542: {
19543: if((T=type(P))<2 || T>3) return T;
19544: if(type(L)!=4) L=[L];
19545: F=0;
19546: if(lsort(L,varargs(dn(P))[1],2)!=[]) F=128;
19547: if(lsort(L,varargs(nm(P))[1],2)!=[]) F+=64;
19548: if(lsort(L,vars(dn(P)),2)!=[]) return F+3;
19549: return (lsort(L,vars(nm(P)),2)==[])?(F+1):(F+2);
19550: }
19551:
19552: def nthmodp(X,N,P)
19553: {
19554: X=X%P;
19555: for(Z=1;;){
19556: if((W=iand(N,1))==1) Z=(Z*X)%P;
19557: if((N=(N-W)/2)<=0) return Z;
19558: X=irem(X*X,P);
19559: }
19560: }
19561:
19562: def issquaremodp(X,P)
19563: {
19564: N=getopt(power);
19565: if(!isint(N)) N=2;
19566: if(P<=1 || !isint(P) || !pari(ispsp,P) || !isint(X) || !isint(N) || N<1){
19567: errno(0);
19568: return -2;
19569: }
19570: M=(P-1)/igcd(N,P-1);
19571: if((X%=P) == 0) return 0;
19572: if(X==1 || M==P-1) return 1;
19573: return (nthmodp(X,M,P)==1)?1:-1;
19574: }
19575:
19576: def iscoef(P,F)
19577: {
19578: if(P==0) return 1;
19579: if(type(P)==1) return F(P);
19580: if(type(P)==2) {
19581: X=var(P);
19582: for(I=deg(P,X); I>=0; I--){
19583: if(!iscoef(mycoef(P,I,X),F)) return 0;
19584: }
19585: }else if(type(P)==3){
19586: if(!iscoef(nm(P),F)||!iscoef(dn(P),F)) return 0;
19587: }else if(type(P)==4){
19588: for(;P!=[];P=cdr(P)) if(!iscoef(P,F)) return 0;
19589: }else if(type(P)>4 && type(P)<7) return iscoef(m2l(PP),F);
19590: else return 0;
19591: return 1;
19592: }
19593:
19594: def rootmodp(X,P)
19595: {
19596: X%=P;
19597: if(X==0) return [0];
19598: N=getopt(power);
19599: PP=pari(factor,P);
19600: P0=PP[0][0]; P1=PP[0][1];
19601: P2=pari(phi,P);
19602: if(!isint(N)) N=2;
19603: N%=P2;
19604: if(P0==2 || size(PP)[0]>1){
19605: for(I=1,R=[]; I<P2; I++)
19606: if(nthmodp(I,N,P)==X) R=cons(I,R);
19607: return qsort(R);
19608: }
19609: Y=primroot(P);
19610: if(Y==0) return 0;
19611: Z=nthmodp(Y,N,P);
19612: G=igcd(N,P2);
19613: P3=P2/G;
19614: for(I=0, W=1; I<P3;I++){
19615: if(W==X) break;
19616: W=(W*Z)%P;
19617: }
19618: if(I==P3) return [];
19619: W=nthmodp(Y,I,P);
19620: Z=nthmodp(Y,P3,P);
19621: for(I=0,R=[];;){
19622: R=cons(W,R);
19623: if(++I>=G) break;
19624: W=(W*Z)%P;
19625: }
19626: return qsort(R);
19627: }
19628:
19629: def primroot(P)
19630: {
19631: PP=pari(factor,P);
19632: P0=PP[0][0]; P1=PP[0][1];
19633: S=size(PP);
19634: if(S[0]>1 || !isint(P) || P0<=2){
19635: print("Not odd prime(power)!");
19636: return 0;
19637: }
19638: if(isint(Ind=getopt(ind))){
19639: Ind %= P;
19640: if(Ind<=0 || igcd(Ind,P)!=1 || (Z=primroot(P))==0){
19641: print("Not exist!");
19642: return 0;
19643: }
19644: P2=P0^(P1-1)*(P0-1);
19645: for(I=1,S=1; I<P2; I++)
19646: if((S = (S*Z)%P) == Ind) return I;
19647: return 0;
19648: }
19649: if(getopt(all)==1){
19650: I=primroot(P);
19651: P2=P0^(P1-1)*(P0-1);
19652: for(L=[],J=1; J<P2; J++){
19653: if(P1>1 && igcd(P0,J)!=1) continue;
19654: if(igcd(P0-1,J)!=1) continue;
19655: L=cons(nthmodp(I,J,P),L);
19656: }
19657: return qsort(L);
19658: }
19659: if(PP[0][1]>1){
19660: I=primroot(P0);
19661: P2=P0^(P1-2)*(P0-1);
19662: if(nthmodp(I,P2,P)==1) I+=P0;
19663: return I;
19664: }
19665: F=pari(factor,P-1);
19666: SF=size(F)[0];
19667: for(I=2; I<P; I++){
19668: for(J=0; J<SF; J++)
19669: if(nthmodp(I,(P-1)/F[J][0],P)==1) break;
19670: if(J==SF) return I;
19671: }
19672: }
19673:
19674: def rabin(P,X)
19675: {
19676: for(M=0,Q=P-1;iand(Q,1)==0;M++,Q/=2);
19677: Z=nthmodp(X,Q,P);
19678: for(N=M;M>0&&Z!=1&&Z!=P-1;M--,Z=(Z*Z)%P);
19679: return (M<N&&(M==0||Z==1))?0:1;
19680: }
19681:
19682: def powprimroot(P,N)
19683: {
19684: if(P<3) P=3;
19685: FE=getopt(exp);
19686: if(FE!=1) FE=0;
19687: if((Log=getopt(log))==1||Log==2) FE=-1;
19688: else if(Log==3){
19689: FE=-2;
19690: for(PP=1, L0=["$r$","$p/a$"];;){
19691: PP=pari(nextprime,PP+1);
19692: if(PP>=P) break;
19693: L0=cons(PP, L0);
19694: }
19695: L0=reverse(L0);
19696: }
19697: if(FE==0) All=getopt(all);
19698: for(I=0, PP=P, LL=[]; I<N; I++,PP++){
19699: PP=pari(nextprime,PP);
19700: if(All==1){
19701: PR=primroot(PP|all=1);
19702: LL=cons(cons(PP,PR),LL);
19703: continue;
19704: }
19705: PR=primroot(PP);
19706: if(FE==-2){ /* log=3 */
19707: LT=cdr(L0);LT=cdr(L0);
19708: for(L=[PP];LT!=[];LT=cdr(LT))
19709: L=cons(primroot(PP|ind=car(LT)),L);
19710: LL=cons(reverse(L),LL);
19711: if(I<N-1) L0=append(L0,[PP]);
19712: }else if(FE){
19713: for(J=1, L=[PP], K=1; J<PP; J++){
19714: if(FE==-1){ /* log=1,2 */
19715: K=primroot(PP|ind=J);
19716: if(K==0 && Log==2) K=PP-1;
19717: }
19718: else K=(K*PR)%PP; /* exp=1 */
19719: L=cons(K,L);
19720: }
19721: LL=cons(reverse(L),LL);
19722: }else
19723: LL=cons([PP,PR],LL); /* default */
19724: }
19725: LL=reverse(LL);
19726: if(!FE) return LL;
19727: PP--;
19728: if(FE==-2) return append(LL,[L0]);
19729: for(I=1,L=["$p$"];I<PP; I++) L=cons(I,L);
19730: return cons(reverse(L),LL);
19731: }
19732:
19733: def ntable(F,II,D)
19734: {
19735: F=f2df(F|opt=-1);
19736: Df=getopt(dif);
1.16 takayama 19737: Str=getopt(str);
1.6 takayama 19738: if(Df!=1) Df=0;
1.16 takayama 19739: L=[];
19740: if(type(D)==4){
19741: if(type(II[0])==4){
19742: T1=II[0][1]-II[0][0];T2=II[1][1]-II[1][0];
19743: for(L0=[],I=0;I<D[0];I++){
19744: for(R=[],J=0;J<D[1];J++)
19745: R=cons(myf2eval(F,II[0][0]+I*T1/D[0],II[1][0]+J*T2/D[1]),R);
19746: L=cons(reverse(R),L);L0=cons(II[0][0]+I*T1/D[0],L0);
19747: }
19748: }else{
19749: for(T=II[1]-II[0],L0=[],I=0;I<D[0];I++){
19750: for(R=[],J=0;J<D[1];J++)
19751: R=cons(myfdeval(F,II[0]+I*T/D[0]+J*T/D[0]/D[1]),R);
19752: L=cons(reverse(R),L);L0=cons(II[0]+I*T/D[0],L0);
19753: }
19754: }
19755: L=reverse(L);L0=reverse(L0);
19756: if(type(Str)==4){
19757: L0=mtransbys(os_md.sint,L0,[Str[0]]|str=1,zero=0);
19758: L=mtransbys(os_md.sint,L,[Str[1]]|str=1,zero=0);
19759: if(Df==1){
19760: for(DT=[],RT=L,I=0;RT!=[];){
19761: for(LT=[],TT=car(RT);TT!=[];TT=cdr(TT)){
19762: VV=car(TT);
19763: if((J=str_char(VV,0,"."))>=0){
19764: if(J==0) VV=str_cut(VV,1,10000);
19765: else VV=str_cut(VV,0,J-1)+str_cut(VV,J+1,10000);
19766: }
19767: V1=eval_str(VV);
19768: if(I++) LT=cons(V1-V0,LT);
19769: V0=V1;
19770: }
19771: DT=cons(LT,DT);
19772: if((RT=cdr(RT))==[]){
19773: VE=rint(myfdeval(F,II[1])*10^Str[1]);
19774: DT=cons([VE-V0],DT);
19775: }
19776: }
19777: for(I=0,D=[],TT=DT;TT!=[];TT=cdr(TT)){
19778: if(!I++) V=car(TT)[0];
19779: else{
19780: T1=reverse(cons(V,car(TT)));
19781: V=car(T1);
19782: if(length(TT)>1) T1=cdr(T1);
19783: D=cons(T1,D);
19784: }
19785: }
19786: for(DD=[],TT=D;TT!=[];TT=cdr(TT))
19787: DD=cons([os_md.lmin(car(TT)),os_md.lmax(car(TT))],DD);
19788: DD=reverse(DD);
19789: L=lsort(L,DD,"append");
19790: }
19791: }
19792: L=lsort(L,L0,"cons");
19793: if(type(Top=getopt(top))==4||getopt(TeX)==1){
19794: if(type(Top)==4){
19795: K=length(L[0])-length(Top);
19796: if(K>0&&K<4){
19797: if(K>1){
19798: Top=append(Top,["",""]);
19799: K-=2;
19800: }
19801: if(K) Top=cons("",Top);
19802: }
19803: L=cons(Top,L);
19804: }
19805: if(type(H=getopt(hline))!=4) H=[0,1,z];
19806: if(type(V=getopt(vline))!=4) V=[0,1,(DF)?z-2:z];
19807: if(type(T=getopt(title))!=7) Out=ltotex(L|opt="tab",hline=H,vline=V);
19808: else Out=ltotex(L|opt="tab",hline=H,vline=V,title=T);
19809: if(Df) Out=str_subst(Out,"\\hline","\\cline{1-"+rtostr(length(L[0])-2)+"}");
19810: return Out;
19811: }
19812: return L;
19813: }
1.6 takayama 19814: for(L=[],I=0;I<=D;I++){
19815: X=II[0]+I*T/D;
19816: L=cons([X,myfdeval(F,X)],L);
19817: }
19818: if(Df==1){
19819: for(LD=[],LL=L;LL!=[];LL=cdr(LL)){
19820: if(LD==[]) LD=cons([car(LL)[0],car(LL)[1],0],LD);
19821: else LD=cons([car(LL)[0],car(LL)[1],abs(car(LL)[1]-car(LD)[1])],LD);
19822: }
19823: L=reverse(LD);
19824: }
1.16 takayama 19825: if(type(Str)==4){
1.6 takayama 19826: if(length(Str)==1) Str=[Str[0],Str[0]];
1.16 takayama 19827: if(Df==1 && length(Str)==2) Str=[Str[0],Str[1],Str[1]];
1.6 takayama 19828: for(S=Str,Str=[];S!=[];S=cdr(S)){
19829: if(type(car(S))!=4) Str=cons([car(S),3],Str);
19830: else Str=cons(car(S),Str);
19831: }
19832: Str=reverse(Str);
19833: for(LD=[],LL=L;LL!=[];LL=cdr(LL)){
19834: for(K=[],J=length(Str); --J>=0; )
19835: K=cons(sint(car(LL)[J],Str[J][0]|str=Str[J][1]),K);
19836: LD=cons(K,LD);
19837: }
19838: L=LD;
19839: }else
19840: L=reverse(L);
19841: if(type(M=getopt(mult))==1){
19842: Opt=[["opt","tab"],["vline",[[0,2+Df]]],["width",-M]];
19843: if(type(T=getopt(title))==7)
19844: Opt=cons(["title",T],Opt);
19845: if(type(Tp=getopt(top))==4)
19846: Opt=cons(["top",Tp],Opt);
19847: L=ltotex(L|option_list=Opt);
19848: }
19849: return L;
19850: }
19851:
19852: def distpoint(L)
19853: {
19854: L=m2l(L|flat=1);
19855: if(getopt(div)==5) Div=5;
19856: else Div=10;
19857: V=newvect(100/Div);
19858: for(LT=L,LL=[],N=0; LT!=[]; LT=cdr(LT)){
19859: if(type(K=car(LT))>1||K<0){
19860: N++; continue;
19861: }
19862: LL=cons(K,LL);
19863: T=idiv(K,Div);
19864: if(Div==10 && T>=9) T=9;
19865: else if(Div==5 && T>=19) T=19;
19866: V[T]++;
19867: }
19868: V=vtol(V);
19869: if((Opt=getopt(opt))=="data") return V;
19870: Title=getopt(title);
19871: OpList=[["opt","tab"]];
19872: if(type(Title=getopt(title)) == 7)
19873: OpList=cons(["title",Title],OpList);
19874: if(Opt=="average"){
19875: T=isMs()?["平均点","標準偏差","最低点","最高点","受験人数"]:
19876: ["average","deviation","min","max","examinees"];
19877: L=average(LL);
19878: L=[sint(L[0],1),sint(L[1],1),L[3],L[4],L[2]];
19879: if(N>0){
19880: T=append(T,[isMs()?"欠席者":"absentees"]);L=append(L,[N]);
19881: }
19882: OpList=cons(["align","c"],OpList);
19883: return ltotex([T,L]|option_list=OpList);
19884: }
19885:
19886: if(getopt(opt)=="graph"){
19887: Mul=getopt(size);
19888: if(Div==5){
19889: V0=["00","05","10","15","20","25","30","35","40","45","50","55",
19890: "60","65","70","75","80","85","90","95"];
19891: if(type(Mul)!=4){
19892: Size = (TikZ)?[12,3,1/2,0.2]:[120,30,1/2,2];
19893: }
19894: }else{
19895: V0=["00-","10-","20-","30-","40-","50-","60-","70-","80-","90-"];
19896: if(type(Mul)!=4){
19897: Size = (TikZ)?[8,3,1/2,0.2]:[80,30,1/2,2];
19898: }
19899: }
19900: return ltotex([V,V0]|opt="graph",size=Size);
19901: }
19902: if(Div==5)
19903: V0=["00--04","05--09","10--14","15--19", "20--24", "25--29", "30--34", "35-39",
19904: "40--44", "45--49","50--54", "55--59","60--64", "65--69",
19905: "70--74", "75--79","80--84", "85--89","90--94", "95--100"];
19906: else
19907: V0=["00--09","10--19","20--29","30--39","40--49","50--59","60--69",
19908: "70--79","80--89","90--100"];
19909: Title=getopt(title);
19910: return ltotex([V0,V]|option_list=OpList);
19911: }
19912:
19913: def keyin(S)
19914: {
19915: print(S,2);
19916: purge_stdin();
19917: S=get_line();
19918: L=length(S=strtoascii(S));
19919: if(L==0) return "";
19920: return str_cut(S,0,L-2);
19921: }
19922:
19923: def init() {
1.16 takayama 19924: LS=["DIROUT","DVIOUTA","DVIOUTB","DVIOUTH","DVIOUTL","TeXLim","TeXEq","TikZ",
1.6 takayama 19925: "XYPrec","XYcm","Canvas"];
19926: if(!access(get_rootdir()+"/help/os_muldif.dvi")||!access(get_rootdir()+"/help/os_muldif.pdf"))
19927: mycat(["Put os_muldif.dvi and os_muldif.pdf in", get_rootdir()+(isMs()?"\\help.":"/help.")]);
19928: if(!isMs()){
19929: DIROUT="%HOME%/asir/tex";
19930: DVIOUTA=str_subst(DVIOUTA,[["\\","/"],[".bat",".sh"]],0);
19931: DVIOUTB=str_subst(DVIOUTB,[["\\","/"],[".bat",".sh"]],0);
19932: DVIOUTL=str_subst(DVIOUTL,[["\\","/"],[".bat",".sh"]],0);
19933: DVIOUTH="%ASIRROOT%/help/os_muldif.pdf";
19934: }
19935: Home=getenv("HOME");
19936: if(type(Home)!=7) Home="";
19937: for(Id=-7, F=Home; Id<-1;){
19938: G = F+"/.muldif";
19939: if(access(G)) Id = open_file(G);
19940: else Id++;
19941: if(Id==-6) F+="/asir";
19942: else if(Id==-5) F=get_rootdir();
19943: else if(Id==-4) F+="/bin";
19944: else if(Id==-3) F=get_rootdir()+"/lib-asir-contrib";
19945: }
19946: if(Id>=0){
19947: while((S=get_line(Id))!=0){
1.18 takayama 19948: if(type(P=str_str(S,LS))==4 && (P0=str_char(S,P[1]+4,"="))>0){
1.6 takayama 19949: if(P[0]<5){
19950: P0=str_chr(S,P0+1,"\"");
19951: if(P0>0){
19952: for(P1=P0;(P2=str_char(S,P1+1,"\""))>0; P1=P2);
19953: if(P1>P0+1){
19954: SS=str_cut(S,P0+1,P1-1);
19955: SS=str_subst(SS,["\\\\","\\\""],["\\","\""]);
19956: if(P[0]==0) DIROUT=SS;
19957: else if(P[0]==1) DVIOUTA=SS;
19958: else if(P[0]==2) DVIOUTB=SS;
19959: else if(P[0]==3) DVIOUTH=SS;
19960: else if(P[0]==4) DVIOUTL=SS;
19961: }
19962: }
19963: if(P0<0 || P1<P0+2) mycat(["Error! Definiton of", LS[P[0]],
19964: "in .muldif"]);
19965: }else{
19966: SV=eval_str(str_cut(S,P0+1,str_len(S)-1));
1.16 takayama 19967: if(P[0]==5) TeXLim=SV;
19968: else if(P[0]==6) TeXEq=SV;
19969: else if(P[0]==7) TikZ=SV;
19970: else if(P[0]==8) XYPrec=SV;
19971: else if(P[0]==9) XYcm=SV;
1.18 takayama 19972: else if(P[0]==10) Canvas=SV;
1.6 takayama 19973: }
19974: }
19975: }
19976: close_file(Id);
19977: }
19978: chkfun(1,0);
19979: }
19980:
19981: #ifdef USEMODULE
19982: endmodule;
19983: os_md.init()$
19984: #else
19985: init()$
19986: #endif
19987:
19988: end$