Annotation of OpenXM_contrib2/asir2018/builtin/gf.c, Revision 1.2
1.1 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
26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
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: *
1.2 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2018/builtin/gf.c,v 1.1 2018/09/19 05:45:06 noro Exp $
1.1 noro 49: */
50: #include "ca.h"
51: #include "parse.h"
52:
53: struct resf_dlist {
54: int ib,id;
55: };
56:
57: int resf_degtest(int,int *,int,struct resf_dlist *);
58: void uhensel(P,NODE,int,int,NODE *);
59: void uhensel_incremental(P,NODE,int,int,int,NODE *);
60: void resf_hensel(int,P,int,P *,ML *);
61: void resf_dtest(P,ML,int,int *,int *,DCP *);
62: void resf_dtest_special(P,ML,int,int *,int *,DCP *);
63: void dtest_special(P,ML,P *);
64: void hensel_special(int,int,P,P *,ML *);
65:
66: void nullspace(UM **,UM,int,int,int *);
67: void nullspace_lm(LM **,int,int *);
68: void nullspace_gf2n(GF2N **,int,int *);
69: void nullspace_gfpn(GFPN **,int,int *);
70: void nullspace_gfs(GFS **,int,int *);
71: void nullspace_gfsn(GFSN **,int,int *);
72: void null_to_sol(int **,int *,int,int,UM *);
73:
74: void showgfmat(UM **,int);
75: void pwr_mod(P,P,V,P,int,Z,P *);
76: void rem_mod(P,P,V,P,int,P *);
77:
78: void Pnullspace(),Pgcda_mod(),Pftest(),Presfmain(),Ppwr_mod(),Puhensel();
79: void Puhensel_incremental();
80: void Psfuhensel();
81:
82: void Pnullspace_ff();
83:
84: void Psolve_linear_equation_gf2n();
85: void Plinear_form_to_vect(),Pvect_to_linear_form();
86:
87: void solve_linear_equation_gf2n(GF2N **,int,int,int *);
88: void linear_form_to_array(P,VL,int,Num *);
89: void array_to_linear_form(Num *,VL,int,P *);
90: void sfuhensel(P,NODE,GFS,int,NODE *);
91:
92: extern int current_ff;
93:
94: struct ftab gf_tab[] = {
95: {"solve_linear_equation_gf2n",Psolve_linear_equation_gf2n,1},
96: {"nullspace",Pnullspace,3},
97: {"nullspace_ff",Pnullspace_ff,1},
98: /* {"gcda_mod",Pgcda_mod,5}, */
99: {"ftest",Pftest,2},
100: {"resfmain",Presfmain,4},
101: {"pwr_mod",Ppwr_mod,6},
102: {"uhensel",Puhensel,4},
103: {"uhensel_incremental",Puhensel_incremental,5},
104: {"sfuhensel",Psfuhensel,4},
105: {0,0,0},
106: };
107:
108: int resf_degtest(int k,int *in,int nb,struct resf_dlist *dlist)
109: {
110: int i,d0,d;
111: int dl_i;
112: struct resf_dlist *t;
113:
114: if ( k < nb )
115: return 0;
116: if ( nb == 1 )
117: return 1;
118: d0 = 0; d = 0; dl_i = 0;
119: for ( i = 0; i < k; i++ ) {
120: t = &dlist[in[i]];
121: if ( t->ib > dl_i + 1 )
122: return 0;
123: else if ( t->ib == dl_i )
124: d += t->id;
125: else if ( !d || (dl_i && d0 != d) )
126: return 0;
127: else {
128: d0 = d; dl_i++; d = t->id;
129: }
130: }
131: if ( dl_i != nb - 1 || d0 != d )
132: return 0;
133: else
134: return 1;
135: }
136:
137: void Puhensel(NODE arg,LIST *rp)
138: {
139: P f;
140: NODE mfl,r;
141: int mod,bound;
142:
143: f = (P)ARG0(arg);
144: mfl = BDY((LIST)ARG1(arg));
1.2 ! noro 145: mod = ZTOS((Q)ARG2(arg));
! 146: bound = ZTOS((Q)ARG3(arg));
1.1 noro 147: uhensel(f,mfl,mod,bound,&r);
148: MKLIST(*rp,r);
149: }
150:
151: void Puhensel_incremental(NODE arg,LIST *rp)
152: {
153: P f;
154: NODE mfl,r;
155: int mod,bound,start;
156:
157: f = (P)ARG0(arg);
158: mfl = BDY((LIST)ARG1(arg));
1.2 ! noro 159: mod = ZTOS((Q)ARG2(arg));
! 160: start = ZTOS((Q)ARG3(arg));
! 161: bound = ZTOS((Q)ARG4(arg));
1.1 noro 162: uhensel_incremental(f,mfl,mod,start,bound,&r);
163: MKLIST(*rp,r);
164: }
165:
166: void uhensel(P f,NODE mfl,int mod,int bound,NODE *rp)
167: {
168: ML blist,clist,rlist;
169: LUM fl;
170: int nf,i;
171: P s;
172: V v;
173: NODE t,top;
174:
175: nf = length(mfl);
176: blist = MLALLOC(nf); blist->n = nf; blist->mod = mod;
177: for ( i = 0, t = mfl; i < nf; i++, t = NEXT(t) ) {
178: blist->c[i] = (pointer)UMALLOC(UDEG((P)BDY(t)));
179: ptoum(mod,(P)BDY(t),blist->c[i]);
180: }
181: gcdgen(f,blist,&clist);
182: blist->bound = clist->bound = bound;
183: W_LUMALLOC((int)UDEG(f),bound,fl);
184: ptolum(mod,bound,f,fl);
185: henmain(fl,blist,clist,&rlist);
186: v = VR(f);
187: for ( i = nf-1, top = 0; i >= 0; i-- ) {
188: lumtop(v,mod,bound,rlist->c[i],&s);
189: MKNODE(t,s,top); top = t;
190: }
191: *rp = top;
192: }
193:
194: void uhensel_incremental(P f,NODE mfl,int mod,int start,int bound,NODE *rp)
195: {
196: ML blist,clist,rlist;
197: LUM fl;
198: LUM *lblist;
199: int nf,i,j,k;
200: int **p;
201: P s;
202: V v;
203: NODE t,top;
204:
205: nf = length(mfl);
206: blist = MLALLOC(nf); blist->n = nf; blist->mod = mod;
207: lblist = (LUM *)MALLOC(nf*sizeof(LUM));
208: for ( i = 0, t = mfl; i < nf; i++, t = NEXT(t) ) {
209: blist->c[i] = (pointer)UMALLOC(UDEG((P)BDY(t)));
210: ptoum(mod,(P)BDY(t),blist->c[i]);
211: W_LUMALLOC((int)UDEG((P)BDY(t)),bound,lblist[i]);
212: ptolum(mod,start,(P)BDY(t),lblist[i]);
213: p = lblist[i]->c;
214: for ( j = DEG(lblist[i]); j >= 0; j-- )
215: for ( k = start; k < bound; k++ )
216: p[j][k] = 0;
217: }
218: gcdgen(f,blist,&clist);
219: clist->bound = bound;
220: W_LUMALLOC((int)UDEG(f),bound,fl);
221: ptolum(mod,bound,f,fl);
222: henmain_incremental(fl,lblist,clist,nf,mod,start,bound);
223: v = VR(f);
224: for ( i = nf-1, top = 0; i >= 0; i-- ) {
225: lumtop_unsigned(v,mod,bound,lblist[i],&s);
226: MKNODE(t,s,top); top = t;
227: }
228: *rp = top;
229: }
230:
231: void Psfuhensel(NODE arg,LIST *rp)
232: {
233: P f;
234: int bound;
235: NODE r,mfl;
236: GFS ev;
237:
238: f = (P)ARG0(arg);
239: mfl = BDY((LIST)ARG1(arg));
240: ev = (GFS)ARG2(arg);
1.2 ! noro 241: bound = ZTOS((Q)ARG3(arg));
1.1 noro 242: sfuhensel(f,mfl,ev,bound,&r);
243: MKLIST(*rp,r);
244: }
245:
246: void sfuhensel(P f,NODE mfl,GFS ev,int bound,NODE *rp)
247: {
248: BM fl;
249: BM *r;
250: VL vl,nvl;
251: int i,fn,dx,dy,d;
252: NODE t,top;
253: UM fm,hm,q;
254: UM *gm;
255: V x,y;
256: P g,s,u;
257:
258: clctv(CO,f,&vl);
259: if ( !vl || !vl->next || vl->next->next )
260: error("sfuhensel : f must be a bivariate poly");
261:
262: for ( i = 0, t = mfl; t; i++, t = NEXT(t) );
263: fn = i;
264:
265: gm = (UM *)MALLOC(fn*sizeof(UM));
266:
267: /* XXX : more severe check is necessary */
268: x = VR((P)BDY(mfl));
269: y = vl->v == x ? vl->next->v : vl->v;
270:
271: for ( i = 0, t = mfl, d = 0; i < fn; i++, t = NEXT(t) ) {
272: gm[i] = (pointer)UMALLOC(getdeg(x,(P)BDY(t)));
273: ptosfum((P)BDY(t),gm[i]);
274: d += DEG(gm[i]);
275: }
276:
277: /* reorder f if necessary */
278: if ( vl->v != x ) {
279: reordvar(vl,x,&nvl); reorderp(nvl,vl,f,&g);
280: vl = nvl; f = g;
281: }
282: dx = getdeg(x,f);
283: if ( dx != d )
284: error("sfuhensel : product of factors has incompatible degree");
285:
286: dy = getdeg(y,f);
287: dy = MAX(dy,bound);
288: fl = BMALLOC(dx,dy);
289: ptosfbm(dy,f,fl);
290: if ( ev ) shiftsfbm(fl,FTOIF(CONT(ev)));
291:
292: /* fm = fl mod y */
293: fm = W_UMALLOC(dx);
294: cpyum(COEF(fl)[0],fm);
295: hm = W_UMALLOC(dx);
296:
297: q = W_UMALLOC(dx);
298: r = (BM *)MLALLOC(fn*sizeof(BM));
299: for ( i = 0; i < fn-1; i++ ) {
300: /* fl = gm[i]*hm mod y */
301: divsfum(fm,gm[i],hm);
302: /* fl is replaced by the cofactor of gk mod y^bound */
303: /* r[i] = gk */
304: sfhenmain2(fl,gm[i],hm,bound,r+i);
305: cpyum(hm,fm);
306: }
307: /* finally, fl must be the lift of gm[fn-1] */
308: r[i] = fl;
309:
310: for ( i = fn-1, top = 0; i >= 0; i-- ) {
311: sfbmtop(r[i],x,y,&s);
312: reorderp(CO,vl,s,&u);
313: MKNODE(t,u,top); top = t;
314: }
315: *rp = top;
316: }
317:
318: void Presfmain(NODE arg,LIST *rp)
319: {
320: P f;
321: int mod,n,nb,i,j,k;
322: int *nf,*md;
323: P *mf;
324: NODE mfl,mdl,t,s,u;
325: ML list;
326: DCP dc;
327: int sflag;
328:
329: f = (P)ARG0(arg);
1.2 ! noro 330: mod = ZTOS((Q)ARG1(arg));
1.1 noro 331: mfl = BDY((LIST)ARG2(arg));
332: mdl = BDY((LIST)ARG3(arg));
333: for ( n = nb = 0, t = mfl; t; nb++, t = NEXT(t) )
334: for ( s = BDY((LIST)BDY(t)); s; n++, s = NEXT(s) );
335: if ( n == nb ) {
336: /* f must be irreducible! */
337: NEWDC(dc);
338: dc->c = f; dc->d = ONE;
339: } else {
340: nf = W_ALLOC(nb); md = W_ALLOC(nb); mf = (P *)ALLOCA(n*sizeof(P));
341: for ( k = i = 0, t = mfl, u = mdl, sflag = 1; t;
342: i++, t = NEXT(t), u = NEXT(u) ) {
343: if ( sflag && length(BDY((LIST)BDY(t))) != 2 )
344: sflag = 0;
345: for ( j = 0, s = BDY((LIST)BDY(t)); s; j++, s = NEXT(s) )
346: mf[k++] = (P)BDY(s);
1.2 ! noro 347: nf[i] = j; md[i] = ZTOS((Q)BDY(u));
1.1 noro 348: }
349: resf_hensel(mod,f,n,mf,&list);
350: if ( sflag )
351: resf_dtest_special(f,list,nb,nf,md,&dc);
352: else
353: resf_dtest(f,list,nb,nf,md,&dc);
354: }
355: dcptolist(dc,rp);
356: }
357:
358: void resf_hensel(int mod,P f,int nf,P *mfl,ML *listp)
359: {
360: register int i,j;
361: int q,n,bound,inv,lc;
362: int *p;
363: int **pp;
364: ML blist,clist,bqlist,cqlist,rlist;
365: UM *b;
366: LUM fl,tl;
367: LUM *l;
368: UM w;
369:
370: w = W_UMALLOC(UDEG(f));
371: blist = MLALLOC(nf); blist->n = nf; blist->mod = mod;
372:
373: /* c[0] must have lc(f) */
374: blist->c[0] = (pointer)UMALLOC(UDEG(mfl[0]));
375: ptoum(mod,mfl[0],w);
376: inv = invm(w->c[UDEG(mfl[0])],mod);
377: lc = remqi((Q)LC(f),mod);
378: lc = dmar(inv,lc,0,mod);
379: if ( lc == 1 )
380: copyum(w,blist->c[0]);
381: else
382: mulsum(mod,w,lc,blist->c[0]);
383:
384: /* c[i] (i=1,...,nf-1) must be monic */
385: for ( i = 1; i < nf; i++ ) {
386: blist->c[i] = (pointer)UMALLOC(UDEG(mfl[i]));
387: ptoum(mod,mfl[i],w);
388: inv = invm(w->c[UDEG(mfl[i])],mod);
389: if ( inv == 1 )
390: copyum(w,blist->c[i]);
391: else
392: mulsum(mod,w,inv,blist->c[i]);
393: }
394:
395: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
396: n = bqlist->n; q = bqlist->mod;
397: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
398: if ( bound == 1 ) {
399: *listp = rlist = MLALLOC(n);
400: rlist->n = n; rlist->mod = q; rlist->bound = bound;
401: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
402: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
403: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
404: pp[j][0] = p[j];
405: }
406: } else {
407: W_LUMALLOC((int)UDEG(f),bound,fl);
408: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
409: }
410: }
411:
412: void resf_dtest(P f,ML list,int nb,int *nfl,int *mdl,DCP *dcp)
413: {
414: int n,np,bound,q;
415: int i,j,k;
416: int *win;
417: P g,factor,cofactor;
418: Q csum,csumt;
419: DCP dcf,dcf0;
420: LUM *c;
421: ML wlist;
422: struct resf_dlist *dlist;
423: int z;
424:
425: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
426: win = W_ALLOC(np+1);
427: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
428: wlist = W_MLALLOC(np); wlist->n = list->n;
429: wlist->mod = list->mod; wlist->bound = list->bound;
430: c = (LUM *)COEF(wlist);
431: bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
432: dlist = (struct resf_dlist *)ALLOCA(np*sizeof(struct resf_dlist));
433: for ( i = 0, j = 0; j < nb; j++ )
434: for ( k = 0; k < nfl[j]; k++, i++ ) {
435: dlist[i].ib = j; dlist[i].id = DEG(c[i])/mdl[j];
436: }
437: k = nb;
438: for ( i = 0; i < nb; i++ )
439: win[i] = i+1;
440: for ( g = f, dcf = dcf0 = 0, --np, z = 0; ; ) {
441: #if 0
442: if ( !(z++ % 10000) )
443: fputc('.',stderr);
444: #endif
445: if ( resf_degtest(k,win,nb,dlist) &&
446: dtestmain(g,csum,wlist,k,win,&factor,&cofactor) ) {
447: NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = factor;
448: g = cofactor;
449: ucsump(g,&csum); mulq(csum,(Q)COEF(DC(g)),&csumt); csum = csumt;
450: for ( i = 0; i < k - 1; i++ )
451: for ( j = win[i] + 1; j < win[i + 1]; j++ ) {
452: c[j-i-1] = c[j];
453: dlist[j-i-1] = dlist[j];
454: }
455: for ( j = win[k-1] + 1; j <= np; j++ ) {
456: c[j-k] = c[j];
457: dlist[j-k] = dlist[j];
458: }
459: if ( ( np -= k ) < k )
460: break;
461: if ( np - win[0] + 1 < k )
462: if ( ++k > np )
463: break;
464: else
465: for ( i = 0; i < k; i++ )
466: win[i] = i + 1;
467: else
468: for ( i = 1; i < k; i++ )
469: win[i] = win[0] + i;
470: } else if ( !ncombi(1,np,k,win) )
471: if ( k == np )
472: break;
473: else
474: for ( i = 0, ++k; i < k; i++ )
475: win[i] = i + 1;
476: }
477: NEXTDC(dcf0,dcf); COEF(dcf) = g;
478: DEG(dcf) = ONE; NEXT(dcf) = 0;*dcp = dcf0;
479: }
480:
481: void resf_dtest_special(P f,ML list,int nb,int *nfl,int *mdl,DCP *dcp)
482: {
483: int n,np,bound,q;
484: int i,j;
485: int *win;
486: P g,factor,cofactor;
487: Q csum,csumt;
488: DCP dcf,dcf0;
489: LUM *c;
490: ML wlist;
491: int max;
492:
493: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
494: win = W_ALLOC(np+1);
495: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
496: wlist = W_MLALLOC(np); wlist->n = list->n;
497: wlist->mod = list->mod; wlist->bound = list->bound;
498: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
499: max = 1<<nb;
500: for ( g = f, dcf = dcf0 = 0, i = 0; i < max; i++ ) {
501: #if 0
502: if ( !(i % 1000) )
503: fprintf(stderr,"i=%d\n",i);
504: #endif
505: for ( j = 0; j < nb; j++ )
506: win[j] = (i&(1<<j)) ? 2*j+1 : 2*j;
507: if ( dtestmain(g,csum,wlist,nb,win,&factor,&cofactor) ) {
508: #if 0
509: fprintf(stderr,"success : i=%d\n",i);
510: #endif
511: NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = factor;
512: NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = cofactor;
513: NEXT(dcf) = 0;*dcp = dcf0;
514: return;
515: }
516: }
517: NEXTDC(dcf0,dcf); COEF(dcf) = g;
518: DEG(dcf) = ONE; NEXT(dcf) = 0;*dcp = dcf0;
519: }
520:
521: #if 0
522: void Pftest(arg,rp)
523: NODE arg;
524: P *rp;
525: {
526: ML list;
527: DCP dc;
528: P p;
529: P *mfl;
530:
531: p = (P)ARG0(arg); mfl = (P *)(((VECT)ARG1(arg))->body);
532: hensel_special(4,1,p,mfl,&list);
533: dtest_special(p,list,rp);
534: }
535:
536: void dtest_special(f,list,pr)
537: P f;
538: ML list;
539: P *pr;
540: {
541: int n,np,bound,q;
542: int i,j,k;
543: int *win;
544: P g,factor,cofactor;
545: Q csum,csumt;
546: DCP dc,dcf,dcf0;
547: LUM *c;
548: ML wlist;
549:
550: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
551: win = W_ALLOC(np+1);
552: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
553: wlist = W_MLALLOC(np); wlist->n = list->n;
554: wlist->mod = list->mod; wlist->bound = list->bound;
555: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
556: for ( g = f, i = 130000; i < (1<<20); i++ ) {
557: #if 0
558: if ( !(i % 1000) )
559: fprintf(stderr,"i=%d\n",i);
560: #endif
561: for ( j = 0; j < 20; j++ )
562: win[j] = (i&(1<<j)) ? 2*j+1 : 2*j;
563: if ( dtestmain(g,csum,wlist,20,win,&factor,&cofactor) ) {
564: #if 0
565: fprintf(stderr,"success : i=%d\n",i);
566: #endif
567: *pr = factor; return;
568: }
569: }
570: }
571:
572: void hensel_special(index,count,f,mfl,listp)
573: int index,count;
574: P f;
575: P *mfl;
576: ML *listp;
577: {
578: register int i,j;
579: int q,n,t,d,r,u,br,tmp,bound;
580: int *c,*p,*m,*w;
581: int **pp;
582: DCP dc;
583: ML blist,clist,bqlist,cqlist,rlist;
584: UM *b;
585: LUM fl,tl;
586: LUM *l;
587:
588: blist = MLALLOC(40); blist->n = 40; blist->mod = 11;
589: for ( i = 0; i < 40; i++ ) {
590: blist->c[i] = (pointer)UMALLOC(6);
591: ptoum(11,mfl[i],blist->c[i]);
592: }
593: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
594: n = bqlist->n; q = bqlist->mod;
595: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
596: if ( bound == 1 ) {
597: *listp = rlist = MLALLOC(n);
598: rlist->n = n; rlist->mod = q; rlist->bound = bound;
599: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
600: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
601: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
602: pp[j][0] = p[j];
603: }
604: } else {
605: W_LUMALLOC(UDEG(f),bound,fl);
606: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
607: }
608: }
609: #endif
610:
611: #if 0
612: void Pftest(arg,rp)
613: NODE arg;
614: P *rp;
615: {
616: ML list;
617: DCP dc;
618: P p;
619: P *mfl;
620:
621: p = (P)ARG0(arg); mfl = (P *)(((VECT)ARG1(arg))->body);
622: hensel_special(2,1,p,mfl,&list);
623: dtest_special(p,list,rp);
624: }
625:
626: void dtest_special(f,list,pr)
627: P f;
628: ML list;
629: P *pr;
630: {
631: int n,np,bound,q;
632: int i,j,k,t,b0;
633: int *win;
634: P g,factor,cofactor;
635: Q csum,csumt;
636: DCP dc,dcf,dcf0;
637: LUM *c;
638: ML wlist;
639: static int nbits[16] = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4};
640:
641: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
642: win = W_ALLOC(np+1);
643: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
644: wlist = W_MLALLOC(np); wlist->n = list->n;
645: wlist->mod = list->mod; wlist->bound = list->bound;
646: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
647: for ( g = f, i = 0; i < (1<<23); i++ ) {
648: #if 0
649: if ( !(i % 1000) )
650: fprintf(stderr,"i=%d\n",i);
651: #endif
652: t = i>>20; b0 = nbits[t];
653: if ( !b0 )
654: continue;
655: for ( j = 1; j < 6; j++ ) {
656: t = (i>>(20-4*j))&0xf;
657: if ( nbits[t] != b0 )
658: break;
659: }
660: if ( j != 6 )
661: continue;
662: for ( j = k = 0; j < 24; j++ )
663: if ( i & (1<<(23-j)) )
664: win[k++] = j;
665: if ( dtestmain(g,csum,wlist,k,win,&factor,&cofactor) ) {
666: #if 0
667: fprintf(stderr,"success : i=%d\n",i);
668: #endif
669: *pr = factor; return;
670: }
671: }
672: *pr = f;
673: }
674:
675: void hensel_special(index,count,f,mfl,listp)
676: int index,count;
677: P f;
678: P *mfl;
679: ML *listp;
680: {
681: register int i,j;
682: int q,n,t,d,r,u,br,tmp,bound;
683: int *c,*p,*m,*w;
684: int **pp;
685: DCP dc;
686: ML blist,clist,bqlist,cqlist,rlist;
687: UM *b;
688: LUM fl,tl;
689: LUM *l;
690:
691: blist = MLALLOC(24); blist->n = 24; blist->mod = 5;
692: for ( i = 0; i < 24; i++ ) {
693: blist->c[i] = (pointer)UMALLOC(7);
694: ptoum(5,mfl[i],blist->c[i]);
695: }
696: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
697: n = bqlist->n; q = bqlist->mod;
698: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
699: if ( bound == 1 ) {
700: *listp = rlist = MLALLOC(n);
701: rlist->n = n; rlist->mod = q; rlist->bound = bound;
702: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
703: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
704: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
705: pp[j][0] = p[j];
706: }
707: } else {
708: W_LUMALLOC(UDEG(f),bound,fl);
709: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
710: }
711: }
712: #endif
713:
714: void Pftest(NODE arg,P *rp)
715: {
716: ML list;
717: P p;
718: P *mfl;
719:
720: p = (P)ARG0(arg); mfl = (P *)(((VECT)ARG1(arg))->body);
721: hensel_special(5,1,p,mfl,&list);
722: dtest_special(p,list,rp);
723: }
724:
725: int nbits(int a)
726: {
727: int i,s;
728:
729: for ( i = 0, s = 0; a && (i < 20); i++, a >>= 1 )
730: if ( a & 1 ) s++;
731: return s;
732: }
733:
734: void dtest_special(P f,ML list,P *pr)
735: {
736: int n,np,bound,q;
737: int i,j,k,b0;
738: int *win;
739: P g,factor,cofactor;
740: Q csum,csumt;
741: LUM *c;
742: ML wlist;
743:
744: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
745: win = W_ALLOC(np+1);
746: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
747: wlist = W_MLALLOC(np); wlist->n = list->n;
748: wlist->mod = list->mod; wlist->bound = list->bound;
749: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
750: for ( g = f, i = 0; i < (1<<19); i++ ) {
751: #if 0
752: if ( !(i % 10000) )
753: fprintf(stderr,"i=%d\n",i);
754: #endif
755: b0 = nbits(i>>10);
756: if ( !b0 || (nbits(i&0x3ff) != b0) )
757: continue;
758: for ( j = k = 0; j < 20; j++ )
759: if ( i & (1<<(19-j)) )
760: win[k++] = j;
761: if ( dtestmain(g,csum,wlist,k,win,&factor,&cofactor) ) {
762: #if 0
763: fprintf(stderr,"success : i=%d\n",i);
764: #endif
765: *pr = factor; return;
766: }
767: }
768: *pr = f;
769: }
770:
771: void hensel_special(int index,int count,P f,P *mfl,ML *listp)
772: {
773: register int i,j;
774: int q,n,bound;
775: int *p;
776: int **pp;
777: ML blist,clist,bqlist,cqlist,rlist;
778: UM *b;
779: LUM fl,tl;
780: LUM *l;
781:
782: blist = MLALLOC(20); blist->n = 20; blist->mod = 11;
783: for ( i = 0; i < 20; i++ ) {
784: blist->c[i] = (pointer)UMALLOC(10);
785: ptoum(11,mfl[i],blist->c[i]);
786: }
787: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
788: n = bqlist->n; q = bqlist->mod;
789: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
790: if ( bound == 1 ) {
791: *listp = rlist = MLALLOC(n);
792: rlist->n = n; rlist->mod = q; rlist->bound = bound;
793: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
794: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
795: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
796: pp[j][0] = p[j];
797: }
798: } else {
799: W_LUMALLOC((int)UDEG(f),bound,fl);
800: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
801: }
802: }
803:
804: void Pnullspace(NODE arg,LIST *rp)
805: {
806: int i,j,n,mod;
807: MAT mat,r;
808: VECT u;
809: V v;
810: P p,z;
811: Z q;
812: UM **w;
813: UM mp;
814: P *t;
815: UM *s;
816: int *ind;
817: NODE n0,n1;
818:
819: mat = (MAT)ARG0(arg);
820: p = (P)ARG1(arg);
821: v = VR(p);
1.2 ! noro 822: mod = ZTOS((Q)ARG2(arg));
1.1 noro 823: n = mat->row;
824: w = (UM **)almat_pointer(n,n);
825: for ( i = 0; i < n; i++ )
826: for ( j = 0, t = (P *)mat->body[i], s = w[i]; j < n; j++ ) {
827: ptomp(mod,t[j],&z);
828: s[j] = W_UMALLOC((z&&!NUM(z))?UDEG(z):0);
829: mptoum(z,s[j]);
830: }
831: mp = W_UMALLOC(UDEG(p)); ptoum(mod,p,mp);
832: ind = (int *)ALLOCA(n*sizeof(int));
833: nullspace(w,mp,mod,n,ind);
834: MKMAT(r,n,n);
835: for ( i = 0; i < n; i++ )
836: for ( j = 0, t = (P *)r->body[i], s = w[i]; j < n; j++ )
837: umtop(v,s[j],&t[j]);
838: MKVECT(u,n);
839: for ( i = 0; i < n; i++ ) {
1.2 ! noro 840: STOZ(ind[i],q); u->body[i] = (pointer)q;
1.1 noro 841: }
842: MKNODE(n1,u,0); MKNODE(n0,r,n1); MKLIST(*rp,n0);
843: }
844:
845: void nullspace(UM **mat,UM p,int mod,int n,int *ind)
846: {
847: int i,j,l,s,d;
848: UM q,w,w1,h,inv;
849: UM *t,*u;
850:
851: d = DEG(p); inv = W_UMALLOC(d); q = W_UMALLOC(2*d);
852: w = W_UMALLOC(2*d); w1 = W_UMALLOC(2*d); h = W_UMALLOC(d);
853: bzero(ind,n*sizeof(int));
854: ind[0] = 0;
855: for ( i = j = 0; j < n; i++, j++ ) {
856: for ( ; j < n; j++ ) {
857: for ( l = i; l < n; l++ )
858: if ( DEG(mat[l][j])>=0 )
859: break;
860: if ( l < n ) {
861: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
862: } else
863: ind[j] = 1;
864: }
865: if ( j == n )
866: break;
867: invum(mod,p,mat[i][j],inv);
868: for ( s = j, t = mat[i]; s < n; s++ ) {
869: mulum(mod,t[s],inv,w);
870: DEG(w) = divum(mod,w,p,q);
871: cpyum(w,t[s]);
872: }
873: for ( l = 0; l < n; l++ ) {
874: if ( l == i )
875: continue;
876: u = mat[l]; DEG(w) = -1; subum(mod,w,u[j],h);
877: for ( s = j; s < n; s++ ) {
878: mulum(mod,h,t[s],w); addum(mod,w,u[s],w1);
879: DEG(w1) = divum(mod,w1,p,q); cpyum(w1,u[s]);
880: }
881: }
882: }
883: }
884:
885: void Pnullspace_ff(NODE arg,LIST *rp)
886: {
887: int i,j,n;
888: MAT mat,r;
889: VECT u;
890: Z q;
891: Obj **w;
892: Obj *t;
893: Obj *s;
894: int *ind;
895: NODE n0,n1;
896:
897: mat = (MAT)ARG0(arg);
898: n = mat->row;
899: w = (Obj **)almat_pointer(n,n);
900: for ( i = 0; i < n; i++ )
901: for ( j = 0, t = (Obj *)mat->body[i], s = w[i]; j < n; j++ )
902: s[j] = t[j];
903: ind = (int *)ALLOCA(n*sizeof(int));
904: switch ( current_ff ) {
905: case FF_GFP:
906: nullspace_lm((LM **)w,n,ind); break;
907: case FF_GF2N:
908: nullspace_gf2n((GF2N **)w,n,ind); break;
909: case FF_GFPN:
910: nullspace_gfpn((GFPN **)w,n,ind); break;
911: case FF_GFS:
912: nullspace_gfs((GFS **)w,n,ind); break;
913: case FF_GFSN:
914: nullspace_gfsn((GFSN **)w,n,ind); break;
915: default:
916: error("nullspace_ff : current_ff is not set");
917: }
918: MKMAT(r,n,n);
919: for ( i = 0; i < n; i++ )
920: for ( j = 0, t = (Obj *)r->body[i], s = w[i]; j < n; j++ )
921: t[j] = s[j];
922: MKVECT(u,n);
923: for ( i = 0; i < n; i++ ) {
1.2 ! noro 924: STOZ(ind[i],q); u->body[i] = (pointer)q;
1.1 noro 925: }
926: MKNODE(n1,u,0); MKNODE(n0,r,n1); MKLIST(*rp,n0);
927: }
928:
929: void nullspace_lm(LM **mat,int n,int *ind)
930: {
931: int i,j,l,s;
932: Z q,z,mod;
933: LM w,w1,h,inv;
934: LM *t,*u;
935:
936: getmod_lm(&mod);
937:
938: bzero(ind,n*sizeof(int));
939: ind[0] = 0;
940: for ( i = j = 0; j < n; i++, j++ ) {
941: for ( ; j < n; j++ ) {
942: for ( l = i; l < n; l++ ) {
943: simplm(mat[l][j],&w); mat[l][j] = w;
944: if ( mat[l][j] )
945: break;
946: }
947: if ( l < n ) {
948: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
949: } else
950: ind[j] = 1;
951: }
952: if ( j == n )
953: break;
954: lmtolf(mat[i][j],&q); invz(q,mod,&z); MKLM(BDY(z),inv);
955: for ( s = j, t = mat[i]; s < n; s++ ) {
956: mullm(t[s],inv,&w); t[s] = w;
957: }
958: for ( l = 0; l < n; l++ ) {
959: if ( l == i )
960: continue;
961: u = mat[l]; chsgnlm(u[j],&h);
962: for ( s = j; s < n; s++ ) {
963: mullm(h,t[s],&w); addlm(w,u[s],&w1); u[s] = w1;
964: }
965: }
966: }
967: }
968:
969: void nullspace_gf2n(GF2N **mat,int n,int *ind)
970: {
971: int i,j,l,s;
972: GF2N w,w1,h,inv;
973: GF2N *t,*u;
974: extern int gf2n_lazy;
975:
976: bzero(ind,n*sizeof(int));
977: ind[0] = 0;
978: for ( i = j = 0; j < n; i++, j++ ) {
979: for ( ; j < n; j++ ) {
980: for ( l = i; l < n; l++ ) {
981: simpgf2n(mat[l][j],&w); mat[l][j] = w;
982: if ( mat[l][j] )
983: break;
984: }
985: if ( l < n ) {
986: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
987: } else
988: ind[j] = 1;
989: }
990: if ( j == n )
991: break;
992: invgf2n(mat[i][j],&inv);
993: for ( s = j, t = mat[i]; s < n; s++ ) {
994: mulgf2n(t[s],inv,&w); t[s] = w;
995: }
996: for ( l = 0; l < n; l++ ) {
997: if ( l == i )
998: continue;
999: u = mat[l]; h = u[j];
1000: for ( s = j; s < n; s++ ) {
1001: mulgf2n(h,t[s],&w); addgf2n(w,u[s],&w1); u[s] = w1;
1002: }
1003: }
1004: }
1005: }
1006:
1007: void nullspace_gfpn(GFPN **mat,int n,int *ind)
1008: {
1009: int i,j,l,s;
1010: GFPN w,w1,h,inv;
1011: GFPN *t,*u;
1012:
1013: bzero(ind,n*sizeof(int));
1014: ind[0] = 0;
1015: for ( i = j = 0; j < n; i++, j++ ) {
1016: for ( ; j < n; j++ ) {
1017: for ( l = i; l < n; l++ ) {
1018: simpgfpn(mat[l][j],&w); mat[l][j] = w;
1019: if ( mat[l][j] )
1020: break;
1021: }
1022: if ( l < n ) {
1023: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1024: } else
1025: ind[j] = 1;
1026: }
1027: if ( j == n )
1028: break;
1029: divgfpn((GFPN)ONE,(GFPN)mat[i][j],&inv);
1030: for ( s = j, t = mat[i]; s < n; s++ ) {
1031: mulgfpn(t[s],inv,&w); t[s] = w;
1032: }
1033: for ( l = 0; l < n; l++ ) {
1034: if ( l == i )
1035: continue;
1036: u = mat[l]; chsgngfpn(u[j],&h);
1037: for ( s = j; s < n; s++ ) {
1038: mulgfpn(h,t[s],&w); addgfpn(w,u[s],&w1); u[s] = w1;
1039: }
1040: }
1041: }
1042: }
1043:
1044: void nullspace_gfs(GFS **mat,int n,int *ind)
1045: {
1046: int i,j,l,s;
1047: GFS w,w1,h,inv;
1048: GFS *t,*u;
1049: GFS one;
1050:
1051: bzero(ind,n*sizeof(int));
1052: ind[0] = 0;
1053: mqtogfs(ONEM,&one);
1054:
1055: for ( i = j = 0; j < n; i++, j++ ) {
1056: for ( ; j < n; j++ ) {
1057: for ( l = i; l < n; l++ )
1058: if ( mat[l][j] )
1059: break;
1060: if ( l < n ) {
1061: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1062: } else
1063: ind[j] = 1;
1064: }
1065: if ( j == n )
1066: break;
1067: divgfs(one,mat[i][j],&inv);
1068: for ( s = j, t = mat[i]; s < n; s++ ) {
1069: mulgfs(t[s],inv,&w); t[s] = w;
1070: }
1071: for ( l = 0; l < n; l++ ) {
1072: if ( l == i )
1073: continue;
1074: u = mat[l];
1075: chsgngfs(u[j],&h);
1076: for ( s = j; s < n; s++ ) {
1077: mulgfs(h,t[s],&w); addgfs(w,u[s],&w1); u[s] = w1;
1078: }
1079: }
1080: }
1081: }
1082:
1083: void nullspace_gfsn(GFSN **mat,int n,int *ind)
1084: {
1085: int i,j,l,s;
1086: GFSN w,w1,h,inv;
1087: GFSN *t,*u;
1088:
1089: bzero(ind,n*sizeof(int));
1090: ind[0] = 0;
1091:
1092: for ( i = j = 0; j < n; i++, j++ ) {
1093: for ( ; j < n; j++ ) {
1094: for ( l = i; l < n; l++ )
1095: if ( mat[l][j] )
1096: break;
1097: if ( l < n ) {
1098: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1099: } else
1100: ind[j] = 1;
1101: }
1102: if ( j == n )
1103: break;
1104: invgfsn(mat[i][j],&inv);
1105: for ( s = j, t = mat[i]; s < n; s++ ) {
1106: mulgfsn(t[s],inv,&w); t[s] = w;
1107: }
1108: for ( l = 0; l < n; l++ ) {
1109: if ( l == i )
1110: continue;
1111: u = mat[l];
1112: chsgngfsn(u[j],&h);
1113: for ( s = j; s < n; s++ ) {
1114: mulgfsn(h,t[s],&w); addgfsn(w,u[s],&w1); u[s] = w1;
1115: }
1116: }
1117: }
1118: }
1119:
1120: /* p = a(0)vl[0]+a(1)vl[1]+...+a(m-1)vl[m-1]+a(m) -> array = [a(0) a(1) ... a(m)] */
1121:
1122: void linear_form_to_array(P p,VL vl,int m,Num *array)
1123: {
1124: int i;
1125: DCP dc;
1126:
1127: bzero((char *)array,(m+1)*sizeof(Num *));
1128: for ( i = 0; p && vl; vl = NEXT(vl), i++ ) {
1129: if ( ID(p) == O_N )
1130: break;
1131: else if ( VR(p) == vl->v ) {
1132: dc = DC(p);
1133: array[i] = (Num)COEF(dc);
1134: dc = NEXT(dc);
1135: p = dc ? COEF(dc) : 0;
1136: }
1137: }
1138: array[m] = (Num)p;
1139: }
1140:
1141: void array_to_linear_form(Num *array,VL vl,int m,P *r)
1142: {
1143: P t;
1144: DCP dc0,dc1;
1145:
1146: if ( !m )
1147: *r = (P)array[0];
1148: else {
1149: array_to_linear_form(array+1,NEXT(vl),m-1,&t);
1150: if ( !array[0] )
1151: *r = t;
1152: else {
1153: NEWDC(dc0); DEG(dc0) = ONE; COEF(dc0) = (P)array[0];
1154: if ( !t )
1155: NEXT(dc0) = 0;
1156: else {
1157: NEWDC(dc1); DEG(dc1) = 0; COEF(dc1) = t;
1158: NEXT(dc1) = 0;
1159: NEXT(dc0) = dc1;
1160: }
1161: MKP(vl->v,dc0,*r);
1162: }
1163: }
1164: }
1165:
1166: void Psolve_linear_equation_gf2n(NODE arg,LIST *rp)
1167: {
1168: NODE eqs,tn;
1169: VL vars,tvl;
1170: int i,j,n,m,dim,codim;
1171: GF2N **w;
1172: int *ind;
1173: NODE n0,n1;
1174:
1175: get_vars(ARG0(arg),&vars);
1176: eqs = BDY((LIST)ARG0(arg));
1177: for ( n = 0, tn = eqs; tn; tn = NEXT(tn), n++);
1178: for ( m = 0, tvl = vars; tvl; tvl = NEXT(tvl), m++);
1179: w = (GF2N **)almat_pointer(n,m+1);
1180: for ( i = 0, tn = eqs; i < n; i++, tn = NEXT(tn) )
1181: linear_form_to_array(BDY(tn),vars,m,(Num *)w[i]);
1182: ind = (int *)ALLOCA(m*sizeof(int));
1183: solve_linear_equation_gf2n(w,n,m,ind);
1184: for ( j = 0, dim = 0; j < m; j++ )
1185: if ( ind[j] )
1186: dim++;
1187: codim = m-dim;
1188: for ( i = codim; i < n; i++ )
1189: if ( w[i][m] ) {
1190: MKLIST(*rp,0); return;
1191: }
1192: for ( i = 0, n0 = 0; i < codim; i++ ) {
1193: NEXTNODE(n0,n1);
1194: array_to_linear_form((Num *)w[i],vars,m,(P *)&BDY(n1));
1195: }
1196: if ( n0 )
1197: NEXT(n1) = 0;
1198: MKLIST(*rp,n0);
1199: }
1200:
1201: void solve_linear_equation_gf2n(GF2N **mat,int n,int m,int *ind)
1202: {
1203: int i,j,l,s;
1204: GF2N w,w1,h,inv;
1205: GF2N *t,*u;
1206: extern int gf2n_lazy;
1207:
1208: bzero(ind,m*sizeof(int));
1209: ind[0] = 0;
1210: for ( i = j = 0; j < m; i++, j++ ) {
1211: for ( ; j < m; j++ ) {
1212: for ( l = i; l < n; l++ ) {
1213: simpgf2n(mat[l][j],&w); mat[l][j] = w;
1214: if ( mat[l][j] )
1215: break;
1216: }
1217: if ( l < n ) {
1218: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1219: } else
1220: ind[j] = 1;
1221: }
1222: if ( j == m )
1223: break;
1224: invgf2n(mat[i][j],&inv);
1225: for ( s = j, t = mat[i]; s <= m; s++ ) {
1226: mulgf2n(t[s],inv,&w); t[s] = w;
1227: }
1228: for ( l = 0; l < n; l++ ) {
1229: if ( l == i )
1230: continue;
1231: u = mat[l]; h = u[j];
1232: for ( s = j; s <= m; s++ ) {
1233: mulgf2n(h,t[s],&w); addgf2n(w,u[s],&w1); u[s] = w1;
1234: }
1235: }
1236: }
1237: }
1238:
1239: /*
1240: void null_to_sol(mat,ind,mod,n,r)
1241: int **mat;
1242: int *ind;
1243: int mod,n;
1244: UM *r;
1245: {
1246: int i,j,k,l;
1247: int *c;
1248: UM w;
1249:
1250: for ( i = 0, l = 0; i < n; i++ ) {
1251: if ( !ind[i] )
1252: continue;
1253: w = UMALLOC(n);
1254: for ( j = k = 0, c = COEF(w); j < n; j++ )
1255: if ( ind[j] )
1256: c[j] = 0;
1257: else
1258: c[j] = mat[k++][i];
1259: c[i] = mod-1;
1260: for ( j = n; j >= 0; j-- )
1261: if ( c[j] )
1262: break;
1263: DEG(w) = j;
1264: r[l++] = w;
1265: }
1266: }
1267: */
1268:
1269: void showgfmat(UM **mat,int n)
1270: {
1271: int i,j,k;
1272: int *c;
1273: UM p;
1274:
1275: for ( i = 0; i < n; i++ ) {
1276: for ( j = 0; j < n; j++ ) {
1277: p = mat[i][j];
1278: if ( DEG(p) < 0 )
1279: fprintf(asir_out,"0");
1280: else
1281: for ( p = mat[i][j], k = DEG(p), c = COEF(p); k >= 0; k-- ) {
1282: if ( c[k] )
1283: fprintf(asir_out,"+%d",c[k]);
1284: if ( k > 1 )
1285: fprintf(asir_out,"a^%d",k);
1286: else if ( k == 1 )
1287: fprintf(asir_out,"a",k);
1288: }
1289: fprintf(asir_out," ");
1290: }
1291: fprintf(asir_out,"\n");
1292: }
1293: }
1294:
1295: #if 0
1296: void Pgcda_mod(arg,rp)
1297: NODE arg;
1298: P *rp;
1299: {
1300: p1 = (P)ARG0(arg);
1301: p2 = (P)ARG1(arg);
1302: v = VR((P)ARG2(arg));
1303: d = (P)ARG3(arg);
1.2 ! noro 1304: m = ZTOS((Q)ARG4(arg));
1.1 noro 1305: reordvar(CO,v,&vl);
1306: reorderp(vl,CO,p1,&t); ptomp(m,t,&m1);
1307: reorderp(vl,CO,p2,&t); ptomp(m,t,&m2);
1308: if ( NUM(m1) || NUM(m2) || VR(m1) != v || VR(m2) != v ) {
1309: *rp = ONE; return;
1310: }
1311: if ( deg(v,m1) >= deg(v,m2) ) {
1312: t = m1; m1 = m2; m2 = t;
1313: }
1314: while ( 1 ) {
1315: inva_mod(COEF(DC(m2)),d,m,&inv);
1316: NEWDC(dc); NEXT(dc) = 0; MKP(v,dc,h);
1.2 ! noro 1317: d0 = deg(v,m1)-deg(v,m2); STOZ(d0,DEG(dc));
1.1 noro 1318: mulgq(m,d,inv,COEF(DC(m1)),&COEF(dc));
1319: mulgp(vl,m,d,m2,h,&t); subgp(vl,m,d,m1,t,&s);
1320: }
1321: }
1322: #endif
1323:
1324: void Ppwr_mod(NODE arg,P *rp)
1325: {
1326: P p,a,d,r;
1327: int m;
1328: Z n;
1329:
1.2 ! noro 1330: m = ZTOS((Q)ARG4(arg)); n = (Z)ARG5(arg);
1.1 noro 1331: ptomp(m,(P)ARG0(arg),&p); ptomp(m,(P)ARG1(arg),&a);
1332: ptomp(m,(P)ARG3(arg),&d);
1333: pwr_mod(p,a,VR((P)ARG2(arg)),d,m,n,&r);
1334: mptop(r,rp);
1335: }
1336:
1337: void pwr_mod(P p,P a,V v,P d,int m,Z n,P *rp)
1338: {
1339: P t,s,r;
1340: Z n1,two,b;
1341:
1342: if ( !n )
1343: *rp = (P)ONEM;
1344: else if ( UNIZ(n) )
1345: *rp = p;
1346: else {
1.2 ! noro 1347: STOZ(2,two);
1.1 noro 1348: divqrz(n,two,&n1,&b);
1349: pwr_mod(p,a,v,d,m,n1,&t);
1350: mulmp(CO,m,t,t,&s); rem_mod(s,a,v,d,m,&r);
1351: if ( b ) {
1352: mulmp(CO,m,r,p,&t); rem_mod(t,a,v,d,m,rp);
1353: } else
1354: *rp = r;
1355: }
1356: }
1357:
1358: void rem_mod(P p,P a,V v,P d,int m,P *rp)
1359: {
1360: P tmp,r1,r2;
1361:
1362: divsrmp(CO,m,p,d,&tmp,&r1);
1363: divsrmp(CO,m,r1,a,&tmp,&r2);
1364: divsrmp(CO,m,r2,d,&tmp,rp);
1365: }
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to gf.c CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM_contrib2 / asir2018 / builtin