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1.3 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.4 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.3 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.7 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/engine/F.c,v 1.6 2001/04/20 02:34:21 noro Exp $
1.3 noro 49: */
1.1 noro 50: #include "ca.h"
51: #include <math.h>
52:
53: void homfctr();
54:
55: void fctrp(vl,f,dcp)
56: VL vl;
57: P f;
58: DCP *dcp;
59: {
60: VL nvl;
61: DCP dc;
62:
63: if ( !f || NUM(f) ) {
64: NEWDC(dc); COEF(dc) = f; DEG(dc) = ONE;
65: NEXT(dc) = 0; *dcp = dc;
66: return;
67: } else if ( !qpcheck((Obj)f) )
68: error("fctrp : invalid argument");
69: else {
70: clctv(vl,f,&nvl);
71: if ( !NEXT(nvl) )
72: ufctr(f,1,dcp);
73: else
74: mfctr(nvl,f,dcp);
75: }
76: }
77:
78: void homfctr(vl,g,dcp)
79: VL vl;
80: P g;
81: DCP *dcp;
82: {
83: P s,t,u,f,h,x;
84: Q e;
85: int d,d0;
86: DCP dc,dct;
87:
88: substp(vl,g,vl->v,(P)ONE,&t); fctrp(vl,t,&dc); MKV(vl->v,x);
89: for ( dct = dc; dct; dct = NEXT(dct) )
90: if ( !NUM(dc->c) ) {
91: for ( s = 0, f = dc->c, d = d0 = homdeg(f); f; d = homdeg(f) ) {
92: exthp(vl,f,d,&h); STOQ(d0-d,e); pwrp(vl,x,e,&t);
93: mulp(vl,t,h,&u); addp(vl,s,u,&t); s = t;
94: subp(vl,f,h,&u); f = u;
95: }
96: dc->c = s;
97: }
98: *dcp = dc;
99: }
100:
101: void mfctr(vl,f,dcp)
102: VL vl;
103: P f;
104: DCP *dcp;
105: {
106: DCP dc,dc0,dct,dcs,dcr;
107: P p,pmin,ppmin,cmin,t;
108: VL mvl;
109: Q c;
110:
111: ptozp(f,1,&c,&p);
112: NEWDC(dc0); dc = dc0; COEF(dc) = (P)c; DEG(dc) = ONE; NEXT(dc) = 0;
113: msqfr(vl,p,&dct);
114: for ( ; dct; dct = NEXT(dct) ) {
115: mindegp(vl,COEF(dct),&mvl,&pmin);
116: #if 0
117: minlcdegp(vl,COEF(dct),&mvl,&pmin);
118: min_common_vars_in_coefp(vl,COEF(dct),&mvl,&pmin);
119: #endif
120: pcp(mvl,pmin,&ppmin,&cmin);
121: if ( !NUM(cmin) ) {
122: mfctrmain(mvl,cmin,&dcs);
123: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
124: DEG(dcr) = DEG(dct);
125: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
126: }
127: for ( ; NEXT(dc); dc = NEXT(dc) );
128: NEXT(dc) = dcs;
129: }
130: mfctrmain(mvl,ppmin,&dcs);
131: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
132: DEG(dcr) = DEG(dct);
133: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
134: }
135: for ( ; NEXT(dc); dc = NEXT(dc) );
136: NEXT(dc) = dcs;
137: }
138: adjsgn(f,dc0); *dcp = dc0;
139: }
140:
1.2 noro 141: #if 0
1.1 noro 142: void adjsgn(p,dc)
143: P p;
144: DCP dc;
145: {
146: int sgn;
147: DCP dct;
148: P c;
149:
150: for ( dct = dc, sgn = headsgn(p); dct; dct = NEXT(dct) )
151: if ( !EVENN(NM(dct->d)) )
152: sgn *= headsgn(COEF(dct));
153: if ( sgn < 0 ) {
154: chsgnp(COEF(dc),&c); COEF(dc) = c;
155: }
156: }
1.2 noro 157: #else
158: void adjsgn(p,dc)
159: P p;
160: DCP dc;
161: {
162: int sgn;
163: DCP dct;
164: P c;
165:
166: if ( headsgn(COEF(dc)) != headsgn(p) ) {
167: chsgnp(COEF(dc),&c); COEF(dc) = c;
168: }
169: for ( dct = NEXT(dc); dct; dct = NEXT(dct) )
170: if ( headsgn(COEF(dct)) < 0 ) {
171: chsgnp(COEF(dct),&c); COEF(dct) = c;
172: }
173: }
174: #endif
1.1 noro 175:
176: int headsgn(p)
177: P p;
178: {
179: if ( !p )
180: return 0;
181: else {
182: while ( !NUM(p) )
183: p = COEF(DC(p));
184: return SGN((Q)p);
185: }
186: }
187:
188: void fctrwithmvp(vl,f,v,dcp)
189: VL vl;
190: P f;
191: V v;
192: DCP *dcp;
193: {
194: VL nvl;
195: DCP dc;
196:
197: if ( NUM(f) ) {
198: NEWDC(dc); COEF(dc) = f; DEG(dc) = ONE;
199: NEXT(dc) = 0; *dcp = dc;
200: return;
201: }
202:
203: clctv(vl,f,&nvl);
204: if ( !NEXT(nvl) )
205: ufctr(f,1,dcp);
206: else
207: mfctrwithmv(nvl,f,v,dcp);
208: }
209:
210: void mfctrwithmv(vl,f,v,dcp)
211: VL vl;
212: P f;
213: V v;
214: DCP *dcp;
215: {
216: DCP dc,dc0,dct,dcs,dcr;
217: P p,pmin,ppmin,cmin,t;
218: VL mvl;
219: Q c;
220:
221: ptozp(f,1,&c,&p);
222: NEWDC(dc0); dc = dc0; COEF(dc) = (P)c; DEG(dc) = ONE; NEXT(dc) = 0;
223: msqfr(vl,p,&dct);
224: for ( ; dct; dct = NEXT(dct) ) {
225: if ( !v )
226: mindegp(vl,COEF(dct),&mvl,&pmin);
227: else {
228: reordvar(vl,v,&mvl); reorderp(mvl,vl,COEF(dct),&pmin);
229: }
230: pcp(mvl,pmin,&ppmin,&cmin);
231: if ( !NUM(cmin) ) {
232: mfctrmain(mvl,cmin,&dcs);
233: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
234: DEG(dcr) = DEG(dct);
235: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
236: }
237: for ( ; NEXT(dc); dc = NEXT(dc) );
238: NEXT(dc) = dcs;
239: }
240: mfctrmain(mvl,ppmin,&dcs);
241: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
242: DEG(dcr) = DEG(dct);
243: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
244: }
245: for ( ; NEXT(dc); dc = NEXT(dc) );
246: NEXT(dc) = dcs;
247: }
248: *dcp = dc0;
249: }
250:
251: void ufctr(f,hint,dcp)
252: P f;
253: int hint;
254: DCP *dcp;
255: {
256: P p,c;
257: DCP dc,dct,dcs,dcr;
258:
259: ptozp(f,SGN((Q)UCOEF(f)),(Q *)&c,&p);
260: NEWDC(dc); COEF(dc) = c; DEG(dc) = ONE; NEXT(dc) = 0;
261: usqp(p,&dct);
262: for ( *dcp = dc; dct; dct = NEXT(dct) ) {
263: ufctrmain(COEF(dct),hint,&dcs);
264: for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
265: DEG(dcr) = DEG(dct);
266: for ( ; NEXT(dc); dc = NEXT(dc) );
267: NEXT(dc) = dcs;
268: }
269: }
270:
271: void mfctrmain(vl,p,dcp)
272: VL vl;
273: P p;
274: DCP *dcp;
275: {
1.5 noro 276: int i,j,k,*win,np,x;
1.1 noro 277: VL nvl,tvl;
278: VN vn,vnt,vn1;
279: P p0,f,g,f0,g0,s,t,lp,m;
280: P *fp0,*fpt,*l,*tl;
281: DCP dc,dc0,dcl;
282: int count,nv;
1.5 noro 283: int *nonzero;
1.1 noro 284:
285: if ( !cmpq(DEG(DC(p)),ONE) ) {
286: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
287: *dcp = dc; return;
288: }
289: lp = LC(p); fctrp(vl,lp,&dcl); clctv(vl,p,&nvl);
290: for ( nv = 0, tvl = nvl; tvl; tvl = NEXT(tvl), nv++);
291: W_CALLOC(nv,struct oVN,vn); W_CALLOC(nv,struct oVN,vnt);
292: W_CALLOC(nv,struct oVN,vn1);
1.5 noro 293: W_CALLOC(nv,int,nonzero);
294:
1.1 noro 295: for ( i = 0, tvl = NEXT(nvl); tvl; tvl = NEXT(tvl), i++ )
296: vn1[i].v = vn[i].v = tvl->v;
297: vn1[i].v = vn[i].v = 0;
1.5 noro 298:
299: /* determine a heuristic bound of deg(GCD(p,p')) */
300: while ( 1 ) {
301: for ( i = 0; vn1[i].v; i++ )
302: vn1[i].n = ((unsigned int)random())%256+1;
303: substvp(nvl,LC(p),vn1,&p0);
304: if ( p0 ) {
305: substvp(nvl,p,vn1,&p0);
306: if ( sqfrchk(p0) ) {
307: ufctr(p0,1,&dc0);
308: if ( NEXT(NEXT(dc0)) == 0 ) {
309: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
310: *dcp = dc;
311: return;
312: } else {
313: for ( dc0 = NEXT(dc0), np = 0; dc0; dc0 = NEXT(dc0), np++ );
314: break;
315: }
316: }
317: }
318: }
319:
1.6 noro 320: /* determine the position of variables which is not allowed to
321: be set to 0 */
1.5 noro 322: for ( i = 0; vn1[i].v; i++ ) {
323: x = vn1[i].n; vn1[i].n = 0;
324: substvp(nvl,LC(p),vn1,&p0);
325: if ( !p0 )
326: vn1[i].n = x;
327: else {
328: substvp(nvl,p,vn1,&p0);
329: if ( !sqfrchk(p0) )
330: vn1[i].n = x;
331: else {
332: ufctr(p0,1,&dc0);
333: for ( dc0 = NEXT(dc0), j = 0; dc0; dc0 = NEXT(dc0), j++ );
334: if ( j > np )
335: vn1[i].n = x;
336: }
337: }
338: }
339: for ( i = 0; vn1[i].v; i++ )
340: if (vn1[i].n )
341: nonzero[i] = 1;
342:
1.1 noro 343: count = 0;
344: while ( 1 ) {
345: while ( 1 ) {
346: count++;
347: for ( i = 0, j = 0; vn[i].v; i++ )
348: if ( vn[i].n )
349: vnt[j++].v = (V)i;
350: vnt[j].n = 0; mulsgn(vn,vnt,j,vn1);
351: for ( i = 0; vn1[i].v; i++ )
352: if ( vn1[i].n ) {
353: if ( vn1[i].n > 0 )
354: vn1[i].n = sprime[vn1[i].n];
355: else
356: vn1[i].n = -sprime[-vn1[i].n];
357: }
358: if ( valideval(nvl,dcl,vn1) ) {
359: substvp(nvl,p,vn1,&p0);
360: if ( sqfrchk(p0) ) {
361: ufctr(p0,1,&dc0);
362: if ( NEXT(NEXT(dc0)) == 0 ) {
363: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
364: *dcp = dc;
365: return;
1.5 noro 366: } else {
367: for ( dc = NEXT(dc0), i = 0; dc; dc = NEXT(dc), i++ );
368: if ( i <= np )
369: goto MAIN;
370: if ( i < np )
371: np = i;
372: }
373: }
1.1 noro 374: }
375: if ( nextbin(vnt,j) )
376: break;
377: }
1.5 noro 378: while ( 1 ) {
379: next(vn);
380: for ( i = 0; vn[i].v; i++ )
381: if ( nonzero[i] && !vn[i].n )
382: break;
383: if ( !vn[i].v )
384: break;
385: }
1.1 noro 386: }
387: MAIN :
388: #if 0
389: for ( i = 0; vn1[i].v; i++ )
390: fprintf(stderr,"%d ",vn1[i].n);
391: fprintf(stderr,"\n");
392: #endif
393: for ( np = 0, dc = NEXT(dc0); dc; dc = NEXT(dc), np++ );
394: fp0 = (P *)ALLOCA((np + 1)*sizeof(P));
395: fpt = (P *)ALLOCA((np + 1)*sizeof(P));
396: l = tl = (P *)ALLOCA((np + 1)*sizeof(P));
397: for ( i = 1, dc = NEXT(dc0); dc; i++, dc = NEXT(dc) )
398: fp0[i-1] = COEF(dc);
399: #if 0
400: sort_by_deg(np,fp0,fpt);
401: sort_by_deg_rev(np-1,fpt+1,fp0+1);
402: #endif
403: #if 0
404: sort_by_deg_rev(np,fp0,fpt); fp0[0] = fpt[0];
405: sort_by_deg(np-1,fpt+1,fp0+1); fp0[np] = 0;
406: #endif
407: fp0[np] = 0;
408: win = W_ALLOC(np + 1); f = p; divsp(vl,p0,COEF(dc0),&f0);
409: for ( k = 1, win[0] = 1, --np; ; ) {
410: P h0,lcg,lch;
411: Q c;
412:
413: g0 = fp0[win[0]];
414: for ( i = 1; i < k; i++ ) {
415: mulp(vl,g0,fp0[win[i]],&m); g0 = m;
416: }
417: mulq((Q)LC(g0),(Q)COEF(dc0),&c); estimatelc(nvl,c,dcl,vn1,&lcg);
418: divsp(nvl,f0,g0,&h0);
419: mulq((Q)LC(h0),(Q)COEF(dc0),&c); estimatelc(nvl,c,dcl,vn1,&lch);
420: mfctrhen2(nvl,vn1,f,f0,g0,h0,lcg,lch,&g);
421: if ( g ) {
422: *tl++ = g; divsp(vl,f,g,&t);
423: f = t; divsp(vl,f0,g0,&t); ptozp(t,1,(Q *)&s,&f0);
424: for ( i = 0; i < k - 1; i++ )
425: for ( j = win[i] + 1; j < win[i + 1]; j++ )
426: fp0[j - i - 1] = fp0[j];
427: for ( j = win[k - 1] + 1; j <= np; j++ )
428: fp0[j - k] = fp0[j];
429: if ( ( np -= k ) < k ) break;
430: if ( np - win[0] + 1 < k )
431: if ( ++k <= np ) {
432: for ( i = 0; i < k; i++ ) win[i] = i + 1;
433: continue;
434: } else
435: break;
436: else for ( i = 1; i < k; i++ ) win[i] = win[0] + i;
437: } else {
438: if ( ncombi(1,np,k,win) == 0 )
439: if ( k == np ) break;
440: else for ( i = 0, ++k; i < k; i++ ) win[i] = i + 1;
441: }
442: }
443: *tl++ = f; *tl = 0;
444: for ( dc0 = 0; *l; l++ ) {
445: NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = *l;
446: }
447: NEXT(dc) = 0; *dcp = dc0;
448: }
449:
450: void ufctrmain(p,hint,dcp)
451: P p;
452: int hint;
453: DCP *dcp;
454: {
455: ML list;
456: DCP dc;
457:
458: if ( NUM(p) || (UDEG(p) == 1) ) {
459: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
460: *dcp = dc;
461: } else if ( iscycm(p) )
462: cycm(VR(p),UDEG(p),dcp);
463: else if ( iscycp(p) )
464: cycp(VR(p),UDEG(p),dcp);
465: else {
466: hensel(5,5,p,&list);
467: if ( list->n == 1 ) {
468: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
469: *dcp = dc;
470: } else
471: dtest(p,list,hint,dcp);
472: }
473: }
474:
475: struct oMF {
476: int m;
477: P f;
478: };
479:
480: void calcphi();
481:
482: void cycm(v,n,dcp)
483: V v;
484: register int n;
485: DCP *dcp;
486: {
487: register int i,j;
488: struct oMF *mfp;
489: DCP dc,dc0;
490:
491: if ( n == 1 ) {
492: NEWDC(dc); mkssum(v,1,1,-1,&COEF(dc)); DEG(dc) = ONE;
493: } else {
494: mfp = (struct oMF *) ALLOCA((n+1)*sizeof(struct oMF));
495: bzero((char *)mfp,(int)(sizeof(struct oMF)*(n+1)));
496: for ( i = 1, j = 0; i <= n; i++ )
497: if ( !(n%i) ) mfp[j++].m = i;
498: mkssum(v,1,1,-1,&mfp[0].f);
499: for ( i = 1; i < j; i++ )
500: calcphi(v,i,mfp);
501: for ( dc0 = 0, i = 0; i < j; i++ ) {
502: NEXTDC(dc0,dc); COEF(dc) = mfp[i].f; DEG(dc) = ONE;
503: }
504: }
505: NEXT(dc) = 0; *dcp = dc0;
506: }
507:
508: void cycp(v,n,dcp)
509: V v;
510: register int n;
511: DCP *dcp;
512: {
513: register int i,j;
514: int n0;
515: struct oMF *mfp;
516: DCP dc,dc0;
517:
518: if ( n == 1 ) {
519: NEWDC(dc); mkssum(v,1,1,1,&COEF(dc)); DEG(dc) = ONE;
520: } else {
521: n0 = n; n *= 2;
522: mfp = (struct oMF *) ALLOCA((n+1)*sizeof(struct oMF));
523: bzero((char *)mfp,(int)(sizeof(struct oMF)*(n+1)));
524: for ( i = 1, j = 0; i <= n; i++ )
525: if ( !(n%i) ) mfp[j++].m = i;
526: mkssum(v,1,1,-1,&mfp[0].f);
527: for ( i = 1; i < j; i++ )
528: calcphi(v,i,mfp);
529: for ( dc0 = 0, i = 0; i < j; i++ )
530: if ( n0 % mfp[i].m ) {
531: NEXTDC(dc0,dc); COEF(dc) = mfp[i].f; DEG(dc) = ONE;
532: }
533: }
534: NEXT(dc) = 0; *dcp = dc0;
535: }
536:
537: void calcphi(v,n,mfp)
538: V v;
539: int n;
540: register struct oMF *mfp;
541: {
542: register int i,m;
543: P t,s,tmp;
544:
545: for ( t = (P)ONE, i = 0, m = mfp[n].m; i < n; i++ )
546: if ( !(m%mfp[i].m) ) {
547: mulp(CO,t,mfp[i].f,&s); t = s;
548: }
549: mkssum(v,m,1,-1,&s); udivpz(s,t,&mfp[n].f,&tmp);
550: if ( tmp )
551: error("calcphi: cannot happen");
552: }
553:
554: void mkssum(v,e,s,sgn,r)
555: V v;
556: int e,s,sgn;
557: P *r;
558: {
559: register int i,sgnt;
560: DCP dc,dc0;
561: Q q;
562:
563: for ( dc0 = 0, i = s, sgnt = 1; i >= 0; i--, sgnt *= sgn ) {
564: if ( !dc0 ) {
565: NEWDC(dc0); dc = dc0;
566: } else {
567: NEWDC(NEXT(dc)); dc = NEXT(dc);
568: }
569: STOQ(i*e,DEG(dc)); STOQ(sgnt,q),COEF(dc) = (P)q;
570: }
571: NEXT(dc) = 0; MKP(v,dc0,*r);
572: }
573:
574: int iscycp(f)
575: P f;
576: {
577: DCP dc;
578: dc = DC(f);
579:
580: if ( !UNIQ((Q)COEF(dc)) )
581: return ( 0 );
582: dc = NEXT(dc);
583: if ( NEXT(dc) || DEG(dc) || !UNIQ((Q)COEF(dc)) )
584: return ( 0 );
585: return ( 1 );
586: }
587:
588: int iscycm(f)
589: P f;
590: {
591: DCP dc;
592:
593: dc = DC(f);
594: if ( !UNIQ((Q)COEF(dc)) )
595: return ( 0 );
596: dc = NEXT(dc);
597: if ( NEXT(dc) || DEG(dc) || !MUNIQ((Q)COEF(dc)) )
598: return ( 0 );
599: return ( 1 );
600: }
601:
602: void sortfs(dcp)
603: DCP *dcp;
604: {
605: int i,k,n,k0,d;
606: DCP dc,dct,t;
607: DCP *a;
608:
609: dc = *dcp;
610: for ( n = 0, dct = dc; dct; dct = NEXT(dct), n++ );
611: a = (DCP *)ALLOCA((n+1)*(sizeof(DCP)));
612: for ( i = 0, dct = dc; dct; dct = NEXT(dct), i++ )
613: a[i] = dct;
614: a[n] = 0;
615:
616: for ( i = 0; i < n; i++ ) {
617: for ( k0 = k = i, d = UDEG(COEF(a[i])); k < n; k++ )
618: if ( (int)UDEG(COEF(a[k])) < d ) {
619: k0 = k;
620: d = UDEG(COEF(a[k]));
621: }
622: if ( i != k0 ) {
623: t = a[i]; a[i] = a[k0]; a[k0] = t;
624: }
625: }
626: for ( *dcp = dct = a[0], i = 1; i < n; i++ )
627: dct = NEXT(dct) = a[i];
628: NEXT(dct) = 0;
629: }
630:
631: void sortfsrev(dcp)
632: DCP *dcp;
633: {
634: int i,k,n,k0,d;
635: DCP dc,dct,t;
636: DCP *a;
637:
638: dc = *dcp;
639: for ( n = 0, dct = dc; dct; dct = NEXT(dct), n++ );
640: a = (DCP *)ALLOCA((n+1)*(sizeof(DCP)));
641: for ( i = 0, dct = dc; dct; dct = NEXT(dct), i++ )
642: a[i] = dct;
643: a[n] = 0;
644:
645: for ( i = 0; i < n; i++ ) {
646: for ( k0 = k = i, d = UDEG(COEF(a[i])); k < n; k++ )
647: if ( (int)UDEG(COEF(a[k])) > d ) {
648: k0 = k;
649: d = UDEG(COEF(a[k]));
650: }
651: if ( i != k0 ) {
652: t = a[i]; a[i] = a[k0]; a[k0] = t;
653: }
654: }
655: for ( *dcp = dct = a[0], i = 1; i < n; i++ )
656: dct = NEXT(dct) = a[i];
657: NEXT(dct) = 0;
658: }
659:
660: void nthrootchk(f,dc,fp,dcp)
661: P f;
662: struct oDUM *dc;
663: ML fp;
664: DCP *dcp;
665: {
666: register int i,k;
667: int e,n,dr,tmp,t;
668: int *tmpp,**tmppp;
669: int **pp,**wpp;
670: LUM fpa,tpa,f0l;
671: UM wt,wq,ws,dvr,f0,fe;
672: N lc;
673: int lcm;
674: int m,b;
675:
676: m = fp->mod; b = fp->bound; fe = *((UM *)fp->c);
677: e = dc->n; f0 = dc->f; nthrootn(NM((Q)COEF(DC(f))),e,&lc);
678: if ( !lc ) {
679: *dcp = 0;
680: return;
681: }
682: lcm = rem(lc,m); W_LUMALLOC(DEG(f0),b,f0l);
683: for ( i = DEG(f0), tmppp = COEF(f0l), tmpp = COEF(f0);
684: i >= 0; i-- )
685: *(tmppp[i]) = dmb(m,tmpp[i],lcm,&tmp);
686: dtestroot(m,1,f,f0l,dc,dcp);
687: if ( *dcp )
688: return;
689: n = UDEG(f); W_LUMALLOC(n,b,fpa); W_LUMALLOC(n,b,tpa);
690: ptolum(m,b,f,fpa);
691: dvr = W_UMALLOC(n); wq = W_UMALLOC(n);
692: wt = W_UMALLOC(n); ws = W_UMALLOC(n);
693: cpyum(fe,dvr); divum(m,dvr,f0,wq);
694: t = dmb(m,pwrm(m,lcm,e-1),e,&tmp); DEG(dvr) = DEG(wq);
695: for ( k = 0; k <= DEG(wq); k++ )
696: COEF(dvr)[k] = dmb(m,COEF(wq)[k],t,&tmp);
697: for ( i = 1; i < b; i++ ) {
698: pwrlum(m,i+1,f0l,e,tpa);
699: for ( k = 0, pp = COEF(fpa), wpp = COEF(tpa);
700: k <= n; k++ )
701: COEF(wt)[k] = (pp[k][i]-wpp[k][i]+m)%m;
702: degum(wt,n); dr = divum(m,wt,dvr,ws);
703: if ( dr >= 0 ) {
704: *dcp = 0;
705: return;
706: }
707: for ( k = 0, pp = COEF(f0l); k <= DEG(ws); k++ )
708: pp[k][i] = COEF(ws)[k];
709: dtestroot(m,i+1,f,f0l,dc,dcp);
710: if ( *dcp )
711: return;
712: }
713: }
714:
715: void sqfrp(vl,f,dcp)
716: VL vl;
717: P f;
718: DCP *dcp;
719: {
720: P c,p;
721: DCP dc,dc0;
722:
723: if ( !f || NUM(f) ) {
724: NEWDC(dc0); *dcp = dc0; DEG(dc0) = ONE;
725: COEF(dc0) = f; NEXT(dc0) = 0;
726: } else if ( !qpcheck((Obj)f) )
727: error("sqfrp : invalid argument");
728: else {
729: NEWDC(dc0); *dcp = dc0; DEG(dc0) = ONE;
730: ptozp(f,1,(Q *)&c,&p); msqfr(vl,p,&dc);
731: COEF(dc0) = c; NEXT(dc0) = dc;
732: adjsgn(f,dc0);
733: }
734: }
735:
736: /*
737: * f : must be a poly with int coef, ignore int content
738: */
739: void msqfr(vl,f,dcp)
740: VL vl;
741: P f;
742: DCP *dcp;
743: {
744: DCP dc,dct,dcs;
745: P c,p,t,s,pc;
746: VL mvl;
747:
748: ptozp(f,1,(Q *)&c,&t); monomialfctr(vl,t,&p,&dc);
749: if ( NUM(p) ) {
750: *dcp = dc;
751: return;
752: }
753: mindegp(vl,p,&mvl,&s);
754: #if 0
755: minlcdegp(vl,p,&mvl,&s);
756: min_common_vars_in_coefp(vl,p,&mvl,&s);
757: #endif
758: pcp(mvl,s,&p,&pc);
759: if ( !NUM(pc) ) {
760: msqfr(mvl,pc,&dcs);
761: if ( !dc )
762: dc = dcs;
763: else {
764: for ( dct = dc; NEXT(dct); dct = NEXT(dct) );
765: NEXT(dct) = dcs;
766: }
767: }
768: msqfrmain(mvl,p,&dcs);
769: for ( dct = dcs; dct; dct = NEXT(dct) ) {
770: reorderp(vl,mvl,COEF(dct),&t); COEF(dct) = t;
771: }
772: if ( !dc )
773: *dcp = dcs;
774: else {
775: for ( dct = dc; NEXT(dct); dct = NEXT(dct) );
776: NEXT(dct) = dcs; *dcp = dc;
777: }
778: }
779:
780: void usqp(f,dcp)
781: P f;
782: DCP *dcp;
783: {
784: int index,nindex;
785: P g,c,h;
786: DCP dc;
787:
788: ptozp(f,1,(Q *)&c,&h);
789: if ( SGN((Q)LC(h)) < 0 )
790: chsgnp(h,&g);
791: else
792: g = h;
793: for ( index = 0, dc = 0; !dc; index = nindex )
794: hsq(index,5,g,&nindex,&dc);
795: *dcp = dc;
796: }
797:
798: void msqfrmain(vl,p,dcp)
799: VL vl;
800: P p;
801: DCP *dcp;
802: {
803: int i,j;
804: VL nvl,tvl;
805: VN vn,vnt,vn1;
806: P gg,tmp,p0,g;
807: DCP dc,dc0,dcr,dcr0;
808: int nv,d,d1;
809: int found;
810: VN svn1;
811: P sp0;
812: DCP sdc0;
813:
814: if ( deg(VR(p),p) == 1 ) {
815: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
816: *dcp = dc;
817: return;
818: }
819: clctv(vl,p,&nvl);
820: for ( nv = 0, tvl = nvl; tvl; tvl = NEXT(tvl), nv++);
821: if ( nv == 1 ) {
822: usqp(p,dcp);
823: return;
824: }
825: #if 0
826: if ( heusqfrchk(nvl,p) ) {
827: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
828: *dcp = dc;
829: return;
830: }
831: #endif
832: W_CALLOC(nv,struct oVN,vn);
833: W_CALLOC(nv,struct oVN,vnt);
834: W_CALLOC(nv,struct oVN,vn1);
835: W_CALLOC(nv,struct oVN,svn1);
836: for ( i = 0, tvl = NEXT(nvl); tvl; tvl = NEXT(tvl), i++ )
837: vn1[i].v = vn[i].v = tvl->v;
838: vn1[i].v = vn[i].v = 0;
1.5 noro 839:
840: /* determine a heuristic bound of deg(GCD(p,p')) */
841: while ( 1 ) {
842: for ( i = 0; vn1[i].v; i++ )
843: vn1[i].n = ((unsigned int)random())%256+1;
844: substvp(nvl,LC(p),vn1,&tmp);
845: if ( tmp ) {
846: substvp(nvl,p,vn1,&p0);
847: usqp(p0,&dc0);
848: for ( d1 = 0, dc = dc0; dc; dc = NEXT(dc) )
849: if ( DEG(dc) )
850: d1 += (QTOS(DEG(dc))-1)*UDEG(COEF(dc));
851: if ( d1 == 0 ) {
852: /* p is squarefree */
853: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
854: *dcp = dc;
855: return;
856: } else {
1.7 ! noro 857: d = d1+1; /* XXX : try searching better evaluation */
! 858: found = 0;
1.5 noro 859: break;
860: }
861: }
862: }
1.1 noro 863:
1.6 noro 864: for ( dcr0 = 0, g = p; ; ) {
1.1 noro 865: while ( 1 ) {
866: for ( i = 0, j = 0; vn[i].v; i++ )
867: if ( vn[i].n ) vnt[j++].v = (V)i;
868: vnt[j].n = 0;
869:
870: mulsgn(vn,vnt,j,vn1);
871: substvp(nvl,LC(g),vn1,&tmp);
872: if ( tmp ) {
873: substvp(nvl,g,vn1,&p0);
874: usqp(p0,&dc0);
875: for ( d1 = 0, dc = dc0; dc; dc = NEXT(dc) )
876: if ( DEG(dc) )
877: d1 += (QTOS(DEG(dc))-1)*UDEG(COEF(dc));
878:
879: if ( d1 == 0 ) {
880: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = g; NEXT(dc) = 0;
881: if ( !dcr0 )
882: dcr0 = dc;
883: else
884: NEXT(dcr) = dc;
885: *dcp = dcr0;
886: return;
887: }
888:
889: if ( d < d1 )
890: goto END;
891: if ( d > d1 ) {
892: d = d1;
893: found = 1;
894: bcopy((char *)vn1,(char *)svn1,(int)(sizeof(struct oVN)*nv));
895: sp0 = p0; sdc0 = dc0;
896: goto END;
897: }
898: /* d1 == d */
899: if ( found ) {
900: found = 0;
901: #if 0
902: if ( d > d1 ) {
903: d = d1;
904: /*} */
905: #endif
906: msqfrmainmain(nvl,g,svn1,sp0,sdc0,&dc,&gg); g = gg;
907: if ( dc ) {
908: if ( !dcr0 )
909: dcr0 = dc;
910: else
911: NEXT(dcr) = dc;
912: for ( dcr = dc; NEXT(dcr); dcr = NEXT(dcr) );
913: if ( NUM(g) ) {
914: NEXT(dcr) = 0; *dcp = dcr0;
915: return;
916: }
917: d = deg(VR(g),g);
918: }
919: }
920: }
921: END:
922: if ( nextbin(vnt,j) )
923: break;
924: }
925: next(vn);
926: }
927: }
928:
929: void msqfrmainmain(vl,p,vn,p0,dc0,dcp,pp)
930: VL vl;
931: P p;
932: VN vn;
933: P p0;
934: DCP dc0;
935: DCP *dcp;
936: P *pp;
937: {
938: int i,j,k,np;
939: DCP *a;
940: DCP dc,dcr,dcr0,dct;
941: P g,t,s,u,t0,f,f0,d,d0,g0,h0,x,xx;
942: Q q;
943: V v;
944:
945: for ( np = 0, dc = dc0; dc; dc = NEXT(dc), np++ );
946: a = (DCP *)ALLOCA((np + 1)*sizeof(DCP));
947: for ( i = 0, dc = dc0; dc; i++, dc = NEXT(dc) )
948: a[np-i-1] = dc;
949:
950: for ( i = 0, dcr0 = 0, f = p, f0 = p0, v = VR(p);
951: i < np; i++ ) {
952: if ( (i == (np-1))&&UNIQ(DEG(a[i])) ) {
953: NEXTDC(dcr0,dcr);
954: DEG(dcr) = DEG(a[i]);
955: COEF(dcr) = f;
956: f = (P)ONE;
957: } else if ( (i == (np-1))&&UNIQ(DEG(DC(COEF(a[i])))) ) {
958: diffp(vl,f,v,&s); pcp(vl,s,&t,&u);
959: if ( divtpz(vl,f,t,&s) ) {
960: NEXTDC(dcr0,dcr);
961: DEG(dcr) = DEG(a[i]);
962: COEF(dcr) = s;
963: f = (P)ONE;
964: } else
965: break;
966: } else {
967: for ( t = f, t0 = f0,
968: j = 0, k = QTOS(DEG(a[i]))-1; j < k; j++ ) {
969: diffp(vl,t,v,&s); t = s;
970: diffp(vl,t0,v,&s); t0 = s;
971: }
972: factorial(k,&q);
973: divsp(vl,t,(P)q,&s);
974: for ( dct = DC(s); NEXT(dct); dct = NEXT(dct) );
975: if ( DEG(dct) ) {
976: MKV(VR(s),x); pwrp(vl,x,DEG(dct),&xx);
977: divsp(vl,s,xx,&d);
978: } else {
979: xx = (P)ONE; d = s;
980: }
981: divsp(vl,t0,xx,&t);
982: divsp(vl,t,(P)q,&s);
983: ptozp(s,1,(Q *)&t,&d0);
984:
985: for ( dct = DC(COEF(a[i])); NEXT(dct); dct = NEXT(dct) );
986: if ( DEG(dct) )
987: divsp(vl,COEF(a[i]),xx,&g0);
988: else {
989: xx = (P)ONE; g0 = COEF(a[i]);
990: }
991:
992: pcp(vl,d,&t,&u); d = t;
993: ptozp(g0,1,(Q *)&u,&t); g0 = t;
994:
995: {
996: DCP dca,dcb;
997:
998: fctrp(vl,LC(d),&dca);
999: for ( dcb = dca, u = (P)ONE; dcb; dcb = NEXT(dcb) ) {
1000: if ( NUM(COEF(dcb)) ) {
1001: mulp(vl,u,COEF(dcb),&t); u = t;
1002: } else {
1003: Q qq;
1004: P tt;
1005:
1006: pwrp(vl,COEF(dcb),DEG(a[i]),&s);
1007: for ( t = LC(f), j = 0; divtpz(vl,t,s,&tt); j++, t = tt );
1008: STOQ(j,qq);
1009: if ( cmpq(qq,DEG(dcb)) > 0 )
1010: qq = DEG(dcb);
1011: pwrp(vl,COEF(dcb),qq,&t); mulp(vl,u,t,&s); u = s;
1012: }
1013: }
1014: divsp(vl,d0,g0,&h0);
1015: }
1016: mfctrhen2(vl,vn,d,d0,g0,h0,u,LC(d),&s);
1017: if ( s ) {
1018: mulp(vl,s,xx,&g);
1019: pwrp(vl,g,DEG(a[i]),&t);
1020: if ( divtpz(vl,f,t,&s) ) {
1021: NEXTDC(dcr0,dcr);
1022: DEG(dcr) = DEG(a[i]); COEF(dcr) = g;
1023: f = s; substvp(vl,f,vn,&f0);
1024: } else
1025: break;
1026: } else
1027: break;
1028: }
1029: }
1030: *pp = f;
1031: if ( dcr0 )
1032: NEXT(dcr) = 0;
1033: *dcp = dcr0;
1034: }
1035:
1036: void mfctrhen2(vl,vn,f,f0,g0,h0,lcg,lch,gp)
1037: VL vl;
1038: VN vn;
1039: P f;
1040: P f0,g0,h0,lcg,lch;
1041: P *gp;
1042: {
1043: V v;
1044: P f1,lc,lc0,lcg0,lch0;
1045: P m,ff0,gg0,hh0,gk,hk,ggg,gggr,hhh,ak,bk,tmp;
1046: Q bb,qk,s;
1047: Q cbd;
1048: int dbd;
1049: int d;
1050:
1051: if ( NUM(g0) ) {
1052: *gp = (P)ONE;
1053: return;
1054: }
1055:
1056: v = VR(f); d = deg(v,f);
1057: if ( d == deg(v,g0) ) {
1058: pcp(vl,f,gp,&tmp);
1059: return;
1060: }
1061:
1062: mulp(vl,lcg,lch,&lc);
1063: if ( !divtpz(vl,lc,LC(f),(P *)&s) ) {
1064: *gp = 0;
1065: return;
1066: }
1067: mulp(vl,(P)s,f,&f1);
1068: dbd = dbound(VR(f1),f1) + 1; cbound(vl,f1,&cbd);
1069:
1070: substvp(vl,lc,vn,&lc0);
1071: divq((Q)lc0,(Q)LC(f0),(Q *)&m); mulp(vl,f0,m,&ff0);
1072: substvp(vl,lcg,vn,&lcg0);
1073: divq((Q)lcg0,(Q)LC(g0),(Q *)&m); mulp(vl,g0,m,&gg0);
1074: substvp(vl,lch,vn,&lch0);
1075: divq((Q)lch0,(Q)LC(h0),(Q *)&m); mulp(vl,h0,m,&hh0);
1076: addq(cbd,cbd,&bb);
1077: henzq1(gg0,hh0,bb,&bk,&ak,&qk); gk = gg0; hk = hh0;
1078: henmv(vl,vn,f1,gk,hk,ak,bk,
1079: lcg,lch,lcg0,lch0,qk,dbd,&ggg,&hhh);
1080:
1081: if ( divtpz(vl,f1,ggg,&gggr) )
1082: pcp(vl,ggg,gp,&tmp);
1083: else
1084: *gp = 0;
1085: }
1086:
1087: int sqfrchk(p)
1088: P p;
1089: {
1090: Q c;
1091: P f;
1092: DCP dc;
1093:
1094: ptozp(p,SGN((Q)UCOEF(p)),&c,&f); usqp(f,&dc);
1095: if ( NEXT(dc) || !UNIQ(DEG(dc)) )
1096: return ( 0 );
1097: else
1098: return ( 1 );
1099: }
1100:
1101: int cycchk(p)
1102: P p;
1103: {
1104: Q c;
1105: P f;
1106:
1107: ptozp(p,SGN((Q)UCOEF(p)),&c,&f);
1108: if ( iscycp(f) || iscycm(f) )
1109: return 0;
1110: else
1111: return 1;
1112: }
1113:
1114: int zerovpchk(vl,p,vn)
1115: VL vl;
1116: P p;
1117: VN vn;
1118: {
1119: P t;
1120:
1121: substvp(vl,p,vn,&t);
1122: if ( t )
1123: return ( 0 );
1124: else
1125: return ( 1 );
1126: }
1127:
1128: int valideval(vl,dc,vn)
1129: VL vl;
1130: DCP dc;
1131: VN vn;
1132: {
1133: DCP dct;
1134: Q *a;
1135: int i,j,n;
1136: N q,r;
1137:
1138: for ( dct = NEXT(dc), n = 0; dct; dct = NEXT(dct), n++ );
1139: W_CALLOC(n,Q,a);
1140: for ( dct = NEXT(dc), i = 0; dct; dct = NEXT(dct), i++ ) {
1141: substvp(vl,COEF(dct),vn,(P *)&a[i]);
1142: if ( !a[i] )
1143: return ( 0 );
1144:
1145: for ( j = 0; j < i; j++ ) {
1146: divn(NM(a[j]),NM(a[i]),&q,&r);
1147: if ( !r )
1148: return ( 0 );
1149: divn(NM(a[i]),NM(a[j]),&q,&r);
1150: if ( !r )
1151: return ( 0 );
1152: }
1153: }
1154: return ( 1 );
1155: }
1156:
1157: void estimatelc(vl,c,dc,vn,lcp)
1158: VL vl;
1159: Q c;
1160: DCP dc;
1161: VN vn;
1162: P *lcp;
1163: {
1164: int i;
1165: DCP dct;
1166: P r,s,t;
1167: Q c0,c1,c2;
1168:
1169: for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) {
1170: if ( NUM(COEF(dct)) ) {
1171: mulp(vl,r,COEF(dct),&s); r = s;
1172: } else {
1173: substvp(vl,COEF(dct),vn,(P *)&c0);
1174: for ( i = 0, c1 = c; i < (int)QTOS(DEG(dct)); i++ ) {
1175: divq(c1,c0,&c2);
1176: if ( !INT(c2) )
1177: break;
1178: else
1179: c1 = c2;
1180: }
1181: if ( i ) {
1182: STOQ(i,c1);
1183: pwrp(vl,COEF(dct),c1,&s); mulp(vl,r,s,&t); r = t;
1184: }
1185: }
1186: }
1187: *lcp = r;
1188: }
1189:
1190: void monomialfctr(vl,p,pr,dcp)
1191: VL vl;
1192: P p;
1193: P *pr;
1194: DCP *dcp;
1195: {
1196: VL nvl,avl;
1197: Q d;
1198: P f,t,s;
1199: DCP dc0,dc;
1200:
1201: clctv(vl,p,&nvl);
1202: for ( dc0 = 0, avl = nvl, f = p; avl; avl = NEXT(avl) ) {
1203: getmindeg(avl->v,f,&d);
1204: if ( d ) {
1205: MKV(avl->v,t); NEXTDC(dc0,dc); DEG(dc) = d; COEF(dc) = t;
1206: pwrp(vl,t,d,&s); divsp(vl,f,s,&t); f = t;
1207: }
1208: }
1209: if ( dc0 )
1210: NEXT(dc) = 0;
1211: *pr = f; *dcp = dc0;
1212: }
1213:
1214: void afctr(vl,p0,p,dcp)
1215: VL vl;
1216: P p,p0;
1217: DCP *dcp;
1218: {
1219: DCP dc,dc0,dcr,dct,dcs;
1220: P t;
1221: VL nvl;
1222:
1223: if ( VR(p) == VR(p0) ) {
1224: NEWDC(dc);
1225: DEG(dc) = ONE;
1226: COEF(dc) = p;
1227: NEXT(dc) = 0;
1228: *dcp = dc;
1229: return;
1230: }
1231:
1232: clctv(vl,p,&nvl);
1233: if ( !NEXT(nvl) )
1234: ufctr(p,1,&dc);
1235: else {
1236: sqa(vl,p0,p,&dc);
1237: for ( dct = dc; dct; dct = NEXT(dct) ) {
1238: pmonic(vl,p0,COEF(dct),&t); COEF(dct) = t;
1239: }
1240: }
1241: if ( NUM(COEF(dc)) )
1242: dcr = NEXT(dc);
1243: else
1244: dcr = dc;
1245: for ( dc0 = 0; dcr; dcr = NEXT(dcr) ) {
1246: afctrmain(vl,p0,COEF(dcr),1,&dcs);
1247:
1248: for ( dct = dcs; dct; dct = NEXT(dct) )
1249: DEG(dct) = DEG(dcr);
1250: if ( !dc0 )
1251: dc0 = dcs;
1252: else {
1253: for ( dct = dc0; NEXT(dct); dct = NEXT(dct) );
1254: NEXT(dct) = dcs;
1255: }
1256: }
1257: *dcp = dc0;
1258: }
1259:
1260: void afctrmain(vl,p0,p,init,dcp)
1261: VL vl;
1262: P p,p0;
1263: int init;
1264: DCP *dcp;
1265: {
1266: P x,y,s,m,a,t,u,pt,pt1,res,g;
1267: Q q;
1268: DCP dc,dc0,dcsq0,dcr0,dcr,dct,dcs;
1269: V v,v0;
1270:
1271: if ( !cmpq(DEG(DC(p)),ONE) ) {
1272: NEWDC(dc); DEG(dc) = ONE; NEXT(dc) = 0;
1273: pmonic(vl,p0,p,&COEF(dc)); *dcp = dc;
1274: return;
1275: }
1276:
1277: v = VR(p); MKV(v,x);
1278: v0 = VR(p0); MKV(v0,y);
1279: STOQ(init,q),s = (P)q;
1280: mulp(vl,s,y,&m); subp(vl,x,m,&t); addp(vl,x,m,&a);
1281: substp(vl,p,v,t,&pt);
1282: remsdcp(vl,pt,p0,&pt1);
1283:
1284: /*
1285: if ( ( deg(v0,p0) <= 3 ) || ( TCPQ(p0) <= 2 ) )
1286: resultp(vl,v0,p0,pt1,&res);
1287: else
1288: srcrnorm(vl,v0,pt1,p0,&res);
1289: */
1290: #if 0
1291: srcr(vl,v0,pt1,p0,&res);
1292: #endif
1293: resultp(vl,v0,p0,pt1,&res);
1294: usqp(res,&dcsq0);
1295: for ( dc0 = 0, dct = dcsq0; dct; dct = NEXT(dct) ) {
1296: if ( UNIQ(DEG(dct)) )
1297: ufctr(COEF(dct),deg(v0,p0),&dcs);
1298: else
1299: ufctr(COEF(dct),1,&dcs);
1300: for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
1301: DEG(dcr) = DEG(dct);
1302: if ( !dc0 ) {
1303: dc0 = NEXT(dcs);
1304: dc = dc0;
1305: } else {
1306: for ( ; NEXT(dc); dc = NEXT(dc) );
1307: NEXT(dc) = NEXT(dcs);
1308: }
1309: }
1310: sortfs(&dc0);
1311:
1312: for ( g = p, dcr = dcr0 = 0, dc = dc0; dc; dc = NEXT(dc) ) {
1313: if ( !UNIQ(DEG(dc)) ) {
1314: substp(vl,COEF(dc),v,a,&pt); remsdcp(vl,pt,p0,&s);
1315: gcda(vl,p0,s,g,&u);
1316: if ( !NUM(u) && (VR(u) == v)) {
1317: afctrmain(vl,p0,u,init+1,&dct);
1318: for ( dcs = dct, t = (P)ONE; dcs; dcs = NEXT(dcs) ) {
1319: mulp(vl,t,COEF(dcs),&s); remsdcp(vl,s,p0,&t);
1320: }
1321: pdiva(vl,p0,g,t,&s); g = s;
1322: if ( !dcr0 )
1323: dcr0 = dct;
1324: else
1325: NEXT(dcr) = dct;
1326: for ( dcr = dct; NEXT(dcr); dcr = NEXT(dcr) );
1327: }
1328: } else {
1329: substp(vl,COEF(dc),v,a,&pt); remsdcp(vl,pt,p0,&s);
1330: gcda(vl,p0,s,g,&u);
1331: if ( !NUM(u) && (VR(u) == v)) {
1332: NEXTDC(dcr0,dcr);
1333: DEG(dcr) = ONE;
1334: COEF(dcr) = u;
1335: pdiva(vl,p0,g,u,&t); g = t;
1336: }
1337: }
1338: }
1339: if ( dcr0 )
1340: NEXT(dcr) = 0;
1341: *dcp = dcr0;
1342: }