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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: *
1.15 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/gf.c,v 1.14 2001/10/09 01:36:06 noro Exp $
1.3 noro 49: */
1.1 noro 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 *);
1.15 ! noro 59: void uhensel_incremental(P,NODE,int,int,int,NODE *);
1.1 noro 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 *);
1.5 noro 70: void nullspace_gfs(GFS **,int,int *);
1.12 noro 71: void nullspace_gfsn(GFSN **,int,int *);
1.1 noro 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,N,P *);
76: void rem_mod(P,P,V,P,int,P *);
77:
78: void Pnullspace(),Pgcda_mod(),Pftest(),Presfmain(),Ppwr_mod(),Puhensel();
1.15 ! noro 79: void Puhensel_incremental();
1.6 noro 80: void Psfuhensel();
1.1 noro 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 *);
1.9 noro 90: void sfuhensel(P,NODE,GFS,int,NODE *);
1.1 noro 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},
1.15 ! noro 103: {"uhensel_incremental",Puhensel_incremental,5},
1.9 noro 104: {"sfuhensel",Psfuhensel,4},
1.1 noro 105: {0,0,0},
106: };
107:
108: int resf_degtest(k,in,nb,dlist)
109: int k;
110: int *in;
111: int nb;
112: struct resf_dlist *dlist;
113: {
114: int i,d0,d;
115: int dl_i;
116: struct resf_dlist *t;
117:
118: if ( k < nb )
119: return 0;
120: if ( nb == 1 )
121: return 1;
122: d0 = 0; d = 0; dl_i = 0;
123: for ( i = 0; i < k; i++ ) {
124: t = &dlist[in[i]];
125: if ( t->ib > dl_i + 1 )
126: return 0;
127: else if ( t->ib == dl_i )
128: d += t->id;
129: else if ( !d || (dl_i && d0 != d) )
130: return 0;
131: else {
132: d0 = d; dl_i++; d = t->id;
133: }
134: }
135: if ( dl_i != nb - 1 || d0 != d )
136: return 0;
137: else
138: return 1;
139: }
140:
141: void Puhensel(arg,rp)
142: NODE arg;
143: LIST *rp;
144: {
145: P f;
146: NODE mfl,r;
147: int mod,bound;
148:
149: f = (P)ARG0(arg);
150: mfl = BDY((LIST)ARG1(arg));
151: mod = QTOS((Q)ARG2(arg));
152: bound = QTOS((Q)ARG3(arg));
153: uhensel(f,mfl,mod,bound,&r);
154: MKLIST(*rp,r);
155: }
156:
1.15 ! noro 157: void Puhensel_incremental(arg,rp)
! 158: NODE arg;
! 159: LIST *rp;
! 160: {
! 161: P f;
! 162: NODE mfl,r;
! 163: int mod,bound,start;
! 164:
! 165: f = (P)ARG0(arg);
! 166: mfl = BDY((LIST)ARG1(arg));
! 167: mod = QTOS((Q)ARG2(arg));
! 168: start = QTOS((Q)ARG3(arg));
! 169: bound = QTOS((Q)ARG4(arg));
! 170: uhensel_incremental(f,mfl,mod,start,bound,&r);
! 171: MKLIST(*rp,r);
! 172: }
! 173:
1.1 noro 174: void uhensel(f,mfl,mod,bound,rp)
175: P f;
176: NODE mfl;
177: int mod,bound;
178: NODE *rp;
179: {
180: ML blist,clist,rlist;
181: LUM fl;
182: int nf,i;
183: P s;
184: V v;
185: NODE t,top;
186:
187: nf = length(mfl);
188: blist = MLALLOC(nf); blist->n = nf; blist->mod = mod;
189: for ( i = 0, t = mfl; i < nf; i++, t = NEXT(t) ) {
190: blist->c[i] = (pointer)UMALLOC(UDEG((P)BDY(t)));
191: ptoum(mod,(P)BDY(t),blist->c[i]);
192: }
193: gcdgen(f,blist,&clist);
194: blist->bound = clist->bound = bound;
195: W_LUMALLOC((int)UDEG(f),bound,fl);
196: ptolum(mod,bound,f,fl);
197: henmain(fl,blist,clist,&rlist);
198: v = VR(f);
199: for ( i = nf-1, top = 0; i >= 0; i-- ) {
200: lumtop(v,mod,bound,rlist->c[i],&s);
1.15 ! noro 201: MKNODE(t,s,top); top = t;
! 202: }
! 203: *rp = top;
! 204: }
! 205:
! 206: void uhensel_incremental(f,mfl,mod,start,bound,rp)
! 207: P f;
! 208: NODE mfl;
! 209: int mod,start,bound;
! 210: NODE *rp;
! 211: {
! 212: ML blist,clist,rlist;
! 213: LUM fl;
! 214: LUM *lblist;
! 215: int nf,i,j,k;
! 216: int **p;
! 217: P s;
! 218: V v;
! 219: NODE t,top;
! 220:
! 221: nf = length(mfl);
! 222: blist = MLALLOC(nf); blist->n = nf; blist->mod = mod;
! 223: lblist = (LUM *)MALLOC(nf*sizeof(LUM));
! 224: for ( i = 0, t = mfl; i < nf; i++, t = NEXT(t) ) {
! 225: blist->c[i] = (pointer)UMALLOC(UDEG((P)BDY(t)));
! 226: ptoum(mod,(P)BDY(t),blist->c[i]);
! 227: W_LUMALLOC((int)UDEG((P)BDY(t)),bound,lblist[i]);
! 228: ptolum(mod,start,(P)BDY(t),lblist[i]);
! 229: p = lblist[i]->c;
! 230: for ( j = DEG(lblist[i]); j >= 0; j-- )
! 231: for ( k = start; k < bound; k++ )
! 232: p[j][k] = 0;
! 233: }
! 234: gcdgen(f,blist,&clist);
! 235: clist->bound = bound;
! 236: W_LUMALLOC((int)UDEG(f),bound,fl);
! 237: ptolum(mod,bound,f,fl);
! 238: henmain_incremental(fl,lblist,clist,nf,mod,start,bound);
! 239: v = VR(f);
! 240: for ( i = nf-1, top = 0; i >= 0; i-- ) {
! 241: lumtop_unsigned(v,mod,bound,lblist[i],&s);
1.1 noro 242: MKNODE(t,s,top); top = t;
1.6 noro 243: }
244: *rp = top;
245: }
246:
247: void Psfuhensel(arg,rp)
248: NODE arg;
249: LIST *rp;
250: {
251: P f;
1.9 noro 252: int bound;
253: NODE r,mfl;
1.8 noro 254: GFS ev;
1.6 noro 255:
256: f = (P)ARG0(arg);
1.9 noro 257: mfl = BDY((LIST)ARG1(arg));
258: ev = (GFS)ARG2(arg);
259: bound = QTOS((Q)ARG3(arg));
260: sfuhensel(f,mfl,ev,bound,&r);
261: MKLIST(*rp,r);
1.6 noro 262: }
263:
1.9 noro 264: void sfuhensel(f,mfl,ev,bound,rp)
1.6 noro 265: P f;
1.9 noro 266: NODE mfl;
267: GFS ev;
268: int bound;
1.6 noro 269: NODE *rp;
270: {
1.9 noro 271: BM fl;
272: BM *r;
273: VL vl,nvl;
1.13 noro 274: int i,fn,dx,dy,d;
1.6 noro 275: NODE t,top;
1.9 noro 276: UM fm,hm,q;
277: UM *gm;
278: V x,y;
279: P g,s,u;
280:
281: clctv(CO,f,&vl);
282: if ( !vl || !vl->next || vl->next->next )
283: error("sfuhensel : f must be a bivariate poly");
1.8 noro 284:
1.9 noro 285: for ( i = 0, t = mfl; t; i++, t = NEXT(t) );
286: fn = i;
1.8 noro 287:
1.9 noro 288: gm = (UM *)MALLOC(fn*sizeof(UM));
289:
290: /* XXX : more severe check is necessary */
291: x = VR((P)BDY(mfl));
292: y = vl->v == x ? vl->next->v : vl->v;
293:
1.13 noro 294: for ( i = 0, t = mfl, d = 0; i < fn; i++, t = NEXT(t) ) {
1.9 noro 295: gm[i] = (pointer)UMALLOC(getdeg(x,(P)BDY(t)));
296: ptosfum((P)BDY(t),gm[i]);
1.13 noro 297: d += DEG(gm[i]);
1.9 noro 298: }
299:
300: /* reorder f if necessary */
301: if ( vl->v != x ) {
302: reordvar(vl,x,&nvl); reorderp(nvl,vl,f,&g);
303: vl = nvl; f = g;
304: }
305: dx = getdeg(x,f);
1.13 noro 306: if ( dx != d )
307: error("sfuhensel : product of factors has incompatible degree");
308:
1.9 noro 309: dy = getdeg(y,f);
1.10 noro 310: dy = MAX(dy,bound);
311: fl = BMALLOC(dx,dy);
312: ptosfbm(dy,f,fl);
1.11 noro 313: if ( ev ) shiftsfbm(fl,FTOIF(CONT(ev)));
1.9 noro 314:
315: /* fm = fl mod y */
316: fm = W_UMALLOC(dx);
317: cpyum(COEF(fl)[0],fm);
318: hm = W_UMALLOC(dx);
319:
320: q = W_UMALLOC(dx);
321: r = (BM *)MLALLOC(fn*sizeof(BM));
322: for ( i = 0; i < fn-1; i++ ) {
323: /* fl = gm[i]*hm mod y */
324: divsfum(fm,gm[i],hm);
325: /* fl is replaced by the cofactor of gk mod y^bound */
326: /* r[i] = gk */
327: sfhenmain2(fl,gm[i],hm,bound,r+i);
328: cpyum(hm,fm);
329: }
330: /* finally, fl must be the lift of gm[fn-1] */
331: r[i] = fl;
1.6 noro 332:
1.9 noro 333: for ( i = fn-1, top = 0; i >= 0; i-- ) {
1.10 noro 334: sfbmtop(r[i],x,y,&s);
1.9 noro 335: reorderp(CO,vl,s,&u);
1.8 noro 336: MKNODE(t,u,top); top = t;
1.1 noro 337: }
338: *rp = top;
339: }
340:
341: void Presfmain(arg,rp)
342: NODE arg;
343: LIST *rp;
344: {
345: P f;
346: int mod,n,nb,i,j,k;
347: int *nf,*md;
348: P *mf;
349: NODE mfl,mdl,t,s,u;
350: ML list;
351: DCP dc;
352: int sflag;
353:
354: f = (P)ARG0(arg);
355: mod = QTOS((Q)ARG1(arg));
356: mfl = BDY((LIST)ARG2(arg));
357: mdl = BDY((LIST)ARG3(arg));
358: for ( n = nb = 0, t = mfl; t; nb++, t = NEXT(t) )
359: for ( s = BDY((LIST)BDY(t)); s; n++, s = NEXT(s) );
360: if ( n == nb ) {
361: /* f must be irreducible! */
362: NEWDC(dc);
363: dc->c = f; dc->d = ONE;
364: } else {
365: nf = W_ALLOC(nb); md = W_ALLOC(nb); mf = (P *)ALLOCA(n*sizeof(P));
366: for ( k = i = 0, t = mfl, u = mdl, sflag = 1; t;
367: i++, t = NEXT(t), u = NEXT(u) ) {
368: if ( sflag && length(BDY((LIST)BDY(t))) != 2 )
369: sflag = 0;
370: for ( j = 0, s = BDY((LIST)BDY(t)); s; j++, s = NEXT(s) )
371: mf[k++] = (P)BDY(s);
372: nf[i] = j; md[i] = QTOS((Q)BDY(u));
373: }
374: resf_hensel(mod,f,n,mf,&list);
375: if ( sflag )
376: resf_dtest_special(f,list,nb,nf,md,&dc);
377: else
378: resf_dtest(f,list,nb,nf,md,&dc);
379: }
380: dcptolist(dc,rp);
381: }
382:
383: void resf_hensel(mod,f,nf,mfl,listp)
384: int mod;
385: P f;
386: int nf;
387: P *mfl;
388: ML *listp;
389: {
390: register int i,j;
1.2 noro 391: int q,n,bound,inv,lc;
1.1 noro 392: int *p;
393: int **pp;
394: ML blist,clist,bqlist,cqlist,rlist;
395: UM *b;
396: LUM fl,tl;
397: LUM *l;
1.2 noro 398: UM w;
1.1 noro 399:
1.2 noro 400: w = W_UMALLOC(UDEG(f));
1.1 noro 401: blist = MLALLOC(nf); blist->n = nf; blist->mod = mod;
1.2 noro 402:
403: /* c[0] must have lc(f) */
404: blist->c[0] = (pointer)UMALLOC(UDEG(mfl[0]));
405: ptoum(mod,mfl[0],w);
406: inv = invm(w->c[UDEG(mfl[0])],mod);
407: lc = rem(NM((Q)LC(f)),mod);
408: if ( SGN((Q)LC(f)) < 0 )
409: lc = (mod-lc)%mod;
410: lc = dmar(inv,lc,0,mod);
411: if ( lc == 1 )
412: copyum(w,blist->c[0]);
413: else
414: mulsum(mod,w,lc,blist->c[0]);
415:
416: /* c[i] (i=1,...,nf-1) must be monic */
417: for ( i = 1; i < nf; i++ ) {
1.1 noro 418: blist->c[i] = (pointer)UMALLOC(UDEG(mfl[i]));
1.2 noro 419: ptoum(mod,mfl[i],w);
420: inv = invm(w->c[UDEG(mfl[i])],mod);
421: if ( inv == 1 )
422: copyum(w,blist->c[i]);
423: else
424: mulsum(mod,w,inv,blist->c[i]);
1.1 noro 425: }
1.2 noro 426:
1.1 noro 427: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
428: n = bqlist->n; q = bqlist->mod;
429: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
430: if ( bound == 1 ) {
431: *listp = rlist = MLALLOC(n);
432: rlist->n = n; rlist->mod = q; rlist->bound = bound;
433: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
434: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
435: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
436: pp[j][0] = p[j];
437: }
438: } else {
439: W_LUMALLOC((int)UDEG(f),bound,fl);
440: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
441: }
442: }
443:
444: void resf_dtest(f,list,nb,nfl,mdl,dcp)
445: P f;
446: ML list;
447: int nb;
448: int *nfl,*mdl;
449: DCP *dcp;
450: {
451: int n,np,bound,q;
452: int i,j,k;
453: int *win;
454: P g,factor,cofactor;
455: Q csum,csumt;
456: DCP dcf,dcf0;
457: LUM *c;
458: ML wlist;
459: struct resf_dlist *dlist;
460: int z;
461:
462: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
463: win = W_ALLOC(np+1);
464: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
465: wlist = W_MLALLOC(np); wlist->n = list->n;
466: wlist->mod = list->mod; wlist->bound = list->bound;
467: c = (LUM *)COEF(wlist);
468: bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
469: dlist = (struct resf_dlist *)ALLOCA(np*sizeof(struct resf_dlist));
470: for ( i = 0, j = 0; j < nb; j++ )
471: for ( k = 0; k < nfl[j]; k++, i++ ) {
472: dlist[i].ib = j; dlist[i].id = DEG(c[i])/mdl[j];
473: }
474: k = nb;
475: for ( i = 0; i < nb; i++ )
476: win[i] = i+1;
477: for ( g = f, dcf = dcf0 = 0, --np, z = 0; ; ) {
478: #if 0
479: if ( !(z++ % 10000) )
480: fputc('.',stderr);
481: #endif
482: if ( resf_degtest(k,win,nb,dlist) &&
483: dtestmain(g,csum,wlist,k,win,&factor,&cofactor) ) {
484: NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = factor;
485: g = cofactor;
486: ucsump(g,&csum); mulq(csum,(Q)COEF(DC(g)),&csumt); csum = csumt;
487: for ( i = 0; i < k - 1; i++ )
488: for ( j = win[i] + 1; j < win[i + 1]; j++ ) {
489: c[j-i-1] = c[j];
490: dlist[j-i-1] = dlist[j];
491: }
492: for ( j = win[k-1] + 1; j <= np; j++ ) {
493: c[j-k] = c[j];
494: dlist[j-k] = dlist[j];
495: }
496: if ( ( np -= k ) < k )
497: break;
498: if ( np - win[0] + 1 < k )
499: if ( ++k > np )
500: break;
501: else
502: for ( i = 0; i < k; i++ )
503: win[i] = i + 1;
504: else
505: for ( i = 1; i < k; i++ )
506: win[i] = win[0] + i;
507: } else if ( !ncombi(1,np,k,win) )
508: if ( k == np )
509: break;
510: else
511: for ( i = 0, ++k; i < k; i++ )
512: win[i] = i + 1;
513: }
514: NEXTDC(dcf0,dcf); COEF(dcf) = g;
515: DEG(dcf) = ONE; NEXT(dcf) = 0;*dcp = dcf0;
516: }
517:
518: void resf_dtest_special(f,list,nb,nfl,mdl,dcp)
519: P f;
520: ML list;
521: int nb;
522: int *nfl,*mdl;
523: DCP *dcp;
524: {
525: int n,np,bound,q;
526: int i,j;
527: int *win;
528: P g,factor,cofactor;
529: Q csum,csumt;
530: DCP dcf,dcf0;
531: LUM *c;
532: ML wlist;
533: int max;
534:
535: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
536: win = W_ALLOC(np+1);
537: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
538: wlist = W_MLALLOC(np); wlist->n = list->n;
539: wlist->mod = list->mod; wlist->bound = list->bound;
540: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
541: max = 1<<nb;
542: for ( g = f, dcf = dcf0 = 0, i = 0; i < max; i++ ) {
543: #if 0
544: if ( !(i % 1000) )
545: fprintf(stderr,"i=%d\n",i);
546: #endif
547: for ( j = 0; j < nb; j++ )
548: win[j] = (i&(1<<j)) ? 2*j+1 : 2*j;
549: if ( dtestmain(g,csum,wlist,nb,win,&factor,&cofactor) ) {
550: #if 0
551: fprintf(stderr,"success : i=%d\n",i);
552: #endif
553: NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = factor;
554: NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = cofactor;
555: NEXT(dcf) = 0;*dcp = dcf0;
556: return;
557: }
558: }
559: NEXTDC(dcf0,dcf); COEF(dcf) = g;
560: DEG(dcf) = ONE; NEXT(dcf) = 0;*dcp = dcf0;
561: }
562:
563: #if 0
564: void Pftest(arg,rp)
565: NODE arg;
566: P *rp;
567: {
568: ML list;
569: DCP dc;
570: P p;
571: P *mfl;
572:
573: p = (P)ARG0(arg); mfl = (P *)(((VECT)ARG1(arg))->body);
574: hensel_special(4,1,p,mfl,&list);
575: dtest_special(p,list,rp);
576: }
577:
578: void dtest_special(f,list,pr)
579: P f;
580: ML list;
581: P *pr;
582: {
583: int n,np,bound,q;
584: int i,j,k;
585: int *win;
586: P g,factor,cofactor;
587: Q csum,csumt;
588: DCP dc,dcf,dcf0;
589: LUM *c;
590: ML wlist;
591:
592: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
593: win = W_ALLOC(np+1);
594: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
595: wlist = W_MLALLOC(np); wlist->n = list->n;
596: wlist->mod = list->mod; wlist->bound = list->bound;
597: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
598: for ( g = f, i = 130000; i < (1<<20); i++ ) {
599: #if 0
600: if ( !(i % 1000) )
601: fprintf(stderr,"i=%d\n",i);
602: #endif
603: for ( j = 0; j < 20; j++ )
604: win[j] = (i&(1<<j)) ? 2*j+1 : 2*j;
605: if ( dtestmain(g,csum,wlist,20,win,&factor,&cofactor) ) {
606: #if 0
607: fprintf(stderr,"success : i=%d\n",i);
608: #endif
609: *pr = factor; return;
610: }
611: }
612: }
613:
614: void hensel_special(index,count,f,mfl,listp)
615: int index,count;
616: P f;
617: P *mfl;
618: ML *listp;
619: {
620: register int i,j;
621: int q,n,t,d,r,u,br,tmp,bound;
622: int *c,*p,*m,*w;
623: int **pp;
624: DCP dc;
625: ML blist,clist,bqlist,cqlist,rlist;
626: UM *b;
627: LUM fl,tl;
628: LUM *l;
629:
630: blist = MLALLOC(40); blist->n = 40; blist->mod = 11;
631: for ( i = 0; i < 40; i++ ) {
632: blist->c[i] = (pointer)UMALLOC(6);
633: ptoum(11,mfl[i],blist->c[i]);
634: }
635: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
636: n = bqlist->n; q = bqlist->mod;
637: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
638: if ( bound == 1 ) {
639: *listp = rlist = MLALLOC(n);
640: rlist->n = n; rlist->mod = q; rlist->bound = bound;
641: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
642: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
643: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
644: pp[j][0] = p[j];
645: }
646: } else {
647: W_LUMALLOC(UDEG(f),bound,fl);
648: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
649: }
650: }
651: #endif
652:
653: #if 0
654: void Pftest(arg,rp)
655: NODE arg;
656: P *rp;
657: {
658: ML list;
659: DCP dc;
660: P p;
661: P *mfl;
662:
663: p = (P)ARG0(arg); mfl = (P *)(((VECT)ARG1(arg))->body);
664: hensel_special(2,1,p,mfl,&list);
665: dtest_special(p,list,rp);
666: }
667:
668: void dtest_special(f,list,pr)
669: P f;
670: ML list;
671: P *pr;
672: {
673: int n,np,bound,q;
674: int i,j,k,t,b0;
675: int *win;
676: P g,factor,cofactor;
677: Q csum,csumt;
678: DCP dc,dcf,dcf0;
679: LUM *c;
680: ML wlist;
681: static int nbits[16] = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4};
682:
683: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
684: win = W_ALLOC(np+1);
685: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
686: wlist = W_MLALLOC(np); wlist->n = list->n;
687: wlist->mod = list->mod; wlist->bound = list->bound;
688: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
689: for ( g = f, i = 0; i < (1<<23); i++ ) {
690: #if 0
691: if ( !(i % 1000) )
692: fprintf(stderr,"i=%d\n",i);
693: #endif
694: t = i>>20; b0 = nbits[t];
695: if ( !b0 )
696: continue;
697: for ( j = 1; j < 6; j++ ) {
698: t = (i>>(20-4*j))&0xf;
699: if ( nbits[t] != b0 )
700: break;
701: }
702: if ( j != 6 )
703: continue;
704: for ( j = k = 0; j < 24; j++ )
705: if ( i & (1<<(23-j)) )
706: win[k++] = j;
707: if ( dtestmain(g,csum,wlist,k,win,&factor,&cofactor) ) {
708: #if 0
709: fprintf(stderr,"success : i=%d\n",i);
710: #endif
711: *pr = factor; return;
712: }
713: }
714: *pr = f;
715: }
716:
717: void hensel_special(index,count,f,mfl,listp)
718: int index,count;
719: P f;
720: P *mfl;
721: ML *listp;
722: {
723: register int i,j;
724: int q,n,t,d,r,u,br,tmp,bound;
725: int *c,*p,*m,*w;
726: int **pp;
727: DCP dc;
728: ML blist,clist,bqlist,cqlist,rlist;
729: UM *b;
730: LUM fl,tl;
731: LUM *l;
732:
733: blist = MLALLOC(24); blist->n = 24; blist->mod = 5;
734: for ( i = 0; i < 24; i++ ) {
735: blist->c[i] = (pointer)UMALLOC(7);
736: ptoum(5,mfl[i],blist->c[i]);
737: }
738: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
739: n = bqlist->n; q = bqlist->mod;
740: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
741: if ( bound == 1 ) {
742: *listp = rlist = MLALLOC(n);
743: rlist->n = n; rlist->mod = q; rlist->bound = bound;
744: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
745: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
746: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
747: pp[j][0] = p[j];
748: }
749: } else {
750: W_LUMALLOC(UDEG(f),bound,fl);
751: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
752: }
753: }
754: #endif
755:
756: void Pftest(arg,rp)
757: NODE arg;
758: P *rp;
759: {
760: ML list;
761: P p;
762: P *mfl;
763:
764: p = (P)ARG0(arg); mfl = (P *)(((VECT)ARG1(arg))->body);
765: hensel_special(5,1,p,mfl,&list);
766: dtest_special(p,list,rp);
767: }
768:
769: int nbits(a)
770: int a;
771: {
772: int i,s;
773:
774: for ( i = 0, s = 0; a && (i < 20); i++, a >>= 1 )
775: if ( a & 1 ) s++;
776: return s;
777: }
778:
779: void dtest_special(f,list,pr)
780: P f;
781: ML list;
782: P *pr;
783: {
784: int n,np,bound,q;
785: int i,j,k,b0;
786: int *win;
787: P g,factor,cofactor;
788: Q csum,csumt;
789: LUM *c;
790: ML wlist;
791:
792: n = UDEG(f); np = list->n; bound = list->bound; q = list->mod;
793: win = W_ALLOC(np+1);
794: ucsump(f,&csum); mulq(csum,(Q)COEF(DC(f)),&csumt); csum = csumt;
795: wlist = W_MLALLOC(np); wlist->n = list->n;
796: wlist->mod = list->mod; wlist->bound = list->bound;
797: c = (LUM *)COEF(wlist); bcopy((char *)COEF(list),(char *)c,(int)(sizeof(LUM)*np));
798: for ( g = f, i = 0; i < (1<<19); i++ ) {
799: #if 0
800: if ( !(i % 10000) )
801: fprintf(stderr,"i=%d\n",i);
802: #endif
803: b0 = nbits(i>>10);
804: if ( !b0 || (nbits(i&0x3ff) != b0) )
805: continue;
806: for ( j = k = 0; j < 20; j++ )
807: if ( i & (1<<(19-j)) )
808: win[k++] = j;
809: if ( dtestmain(g,csum,wlist,k,win,&factor,&cofactor) ) {
810: #if 0
811: fprintf(stderr,"success : i=%d\n",i);
812: #endif
813: *pr = factor; return;
814: }
815: }
816: *pr = f;
817: }
818:
819: void hensel_special(index,count,f,mfl,listp)
820: int index,count;
821: P f;
822: P *mfl;
823: ML *listp;
824: {
825: register int i,j;
826: int q,n,bound;
827: int *p;
828: int **pp;
829: ML blist,clist,bqlist,cqlist,rlist;
830: UM *b;
831: LUM fl,tl;
832: LUM *l;
833:
834: blist = MLALLOC(20); blist->n = 20; blist->mod = 11;
835: for ( i = 0; i < 20; i++ ) {
836: blist->c[i] = (pointer)UMALLOC(10);
837: ptoum(11,mfl[i],blist->c[i]);
838: }
839: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
840: n = bqlist->n; q = bqlist->mod;
841: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
842: if ( bound == 1 ) {
843: *listp = rlist = MLALLOC(n);
844: rlist->n = n; rlist->mod = q; rlist->bound = bound;
845: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
846: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
847: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
848: pp[j][0] = p[j];
849: }
850: } else {
851: W_LUMALLOC((int)UDEG(f),bound,fl);
852: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
853: }
854: }
855:
856: void Pnullspace(arg,rp)
857: NODE arg;
858: LIST *rp;
859: {
860: int i,j,n,mod;
861: MAT mat,r;
862: VECT u;
863: V v;
864: P p,z;
865: Q q;
866: UM **w;
867: UM mp;
868: P *t;
869: UM *s;
870: int *ind;
871: NODE n0,n1;
872:
873: mat = (MAT)ARG0(arg);
874: p = (P)ARG1(arg);
875: v = VR(p);
876: mod = QTOS((Q)ARG2(arg));
877: n = mat->row;
878: w = (UM **)almat_pointer(n,n);
879: for ( i = 0; i < n; i++ )
880: for ( j = 0, t = (P *)mat->body[i], s = w[i]; j < n; j++ ) {
881: ptomp(mod,t[j],&z);
882: s[j] = W_UMALLOC((z&&!NUM(z))?UDEG(z):0);
883: mptoum(z,s[j]);
884: }
885: mp = W_UMALLOC(UDEG(p)); ptoum(mod,p,mp);
886: ind = (int *)ALLOCA(n*sizeof(int));
887: nullspace(w,mp,mod,n,ind);
888: MKMAT(r,n,n);
889: for ( i = 0; i < n; i++ )
890: for ( j = 0, t = (P *)r->body[i], s = w[i]; j < n; j++ )
891: umtop(v,s[j],&t[j]);
892: MKVECT(u,n);
893: for ( i = 0; i < n; i++ ) {
894: STOQ(ind[i],q); u->body[i] = (pointer)q;
895: }
896: MKNODE(n1,u,0); MKNODE(n0,r,n1); MKLIST(*rp,n0);
897: }
898:
899: void nullspace(mat,p,mod,n,ind)
900: UM **mat;
901: UM p;
902: int mod,n;
903: int *ind;
904: {
905: int i,j,l,s,d;
906: UM q,w,w1,h,inv;
907: UM *t,*u;
908:
909: d = DEG(p); inv = W_UMALLOC(d); q = W_UMALLOC(2*d);
910: w = W_UMALLOC(2*d); w1 = W_UMALLOC(2*d); h = W_UMALLOC(d);
911: bzero(ind,n*sizeof(int));
912: ind[0] = 0;
913: for ( i = j = 0; j < n; i++, j++ ) {
914: for ( ; j < n; j++ ) {
915: for ( l = i; l < n; l++ )
916: if ( DEG(mat[l][j])>=0 )
917: break;
918: if ( l < n ) {
919: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
920: } else
921: ind[j] = 1;
922: }
923: if ( j == n )
924: break;
925: invum(mod,p,mat[i][j],inv);
926: for ( s = j, t = mat[i]; s < n; s++ ) {
927: mulum(mod,t[s],inv,w);
928: DEG(w) = divum(mod,w,p,q);
929: cpyum(w,t[s]);
930: }
931: for ( l = 0; l < n; l++ ) {
932: if ( l == i )
933: continue;
934: u = mat[l]; DEG(w) = -1; subum(mod,w,u[j],h);
935: for ( s = j; s < n; s++ ) {
936: mulum(mod,h,t[s],w); addum(mod,w,u[s],w1);
937: DEG(w1) = divum(mod,w1,p,q); cpyum(w1,u[s]);
938: }
939: }
940: }
941: }
942:
943: void Pnullspace_ff(arg,rp)
944: NODE arg;
945: LIST *rp;
946: {
947: int i,j,n;
948: MAT mat,r;
949: VECT u;
950: Q q;
951: Obj **w;
952: Obj *t;
953: Obj *s;
954: int *ind;
955: NODE n0,n1;
956:
957: mat = (MAT)ARG0(arg);
958: n = mat->row;
959: w = (Obj **)almat_pointer(n,n);
960: for ( i = 0; i < n; i++ )
961: for ( j = 0, t = (Obj *)mat->body[i], s = w[i]; j < n; j++ )
962: s[j] = t[j];
963: ind = (int *)ALLOCA(n*sizeof(int));
964: switch ( current_ff ) {
965: case FF_GFP:
966: nullspace_lm((LM **)w,n,ind); break;
967: case FF_GF2N:
968: nullspace_gf2n((GF2N **)w,n,ind); break;
969: case FF_GFPN:
970: nullspace_gfpn((GFPN **)w,n,ind); break;
1.5 noro 971: case FF_GFS:
972: nullspace_gfs((GFS **)w,n,ind); break;
1.12 noro 973: case FF_GFSN:
974: nullspace_gfsn((GFSN **)w,n,ind); break;
1.1 noro 975: default:
976: error("nullspace_ff : current_ff is not set");
977: }
978: MKMAT(r,n,n);
979: for ( i = 0; i < n; i++ )
980: for ( j = 0, t = (Obj *)r->body[i], s = w[i]; j < n; j++ )
981: t[j] = s[j];
982: MKVECT(u,n);
983: for ( i = 0; i < n; i++ ) {
984: STOQ(ind[i],q); u->body[i] = (pointer)q;
985: }
986: MKNODE(n1,u,0); MKNODE(n0,r,n1); MKLIST(*rp,n0);
987: }
988:
989: void nullspace_lm(mat,n,ind)
990: LM **mat;
991: int n;
992: int *ind;
993: {
994: int i,j,l,s;
995: Q q,mod;
996: N lm;
997: LM w,w1,h,inv;
998: LM *t,*u;
999:
1000: getmod_lm(&lm); NTOQ(lm,1,mod);
1001:
1002: bzero(ind,n*sizeof(int));
1003: ind[0] = 0;
1004: for ( i = j = 0; j < n; i++, j++ ) {
1005: for ( ; j < n; j++ ) {
1006: for ( l = i; l < n; l++ ) {
1007: simplm(mat[l][j],&w); mat[l][j] = w;
1008: if ( mat[l][j] )
1009: break;
1010: }
1011: if ( l < n ) {
1012: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1013: } else
1014: ind[j] = 1;
1015: }
1016: if ( j == n )
1017: break;
1018: NTOQ(mat[i][j]->body,1,q); invl(q,mod,(Q *)&inv);
1019: for ( s = j, t = mat[i]; s < n; s++ ) {
1020: mullm(t[s],inv,&w); t[s] = w;
1021: }
1022: for ( l = 0; l < n; l++ ) {
1023: if ( l == i )
1024: continue;
1025: u = mat[l]; chsgnlm(u[j],&h);
1026: for ( s = j; s < n; s++ ) {
1027: mullm(h,t[s],&w); addlm(w,u[s],&w1); u[s] = w1;
1028: }
1029: }
1030: }
1031: }
1032:
1033: void nullspace_gf2n(mat,n,ind)
1034: GF2N **mat;
1035: int n;
1036: int *ind;
1037: {
1038: int i,j,l,s;
1039: GF2N w,w1,h,inv;
1040: GF2N *t,*u;
1041: extern gf2n_lazy;
1042:
1043: bzero(ind,n*sizeof(int));
1044: ind[0] = 0;
1045: for ( i = j = 0; j < n; i++, j++ ) {
1046: for ( ; j < n; j++ ) {
1047: for ( l = i; l < n; l++ ) {
1048: simpgf2n(mat[l][j],&w); mat[l][j] = w;
1049: if ( mat[l][j] )
1050: break;
1051: }
1052: if ( l < n ) {
1053: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1054: } else
1055: ind[j] = 1;
1056: }
1057: if ( j == n )
1058: break;
1059: invgf2n(mat[i][j],&inv);
1060: for ( s = j, t = mat[i]; s < n; s++ ) {
1061: mulgf2n(t[s],inv,&w); t[s] = w;
1062: }
1063: for ( l = 0; l < n; l++ ) {
1064: if ( l == i )
1065: continue;
1066: u = mat[l]; h = u[j];
1067: for ( s = j; s < n; s++ ) {
1068: mulgf2n(h,t[s],&w); addgf2n(w,u[s],&w1); u[s] = w1;
1069: }
1070: }
1071: }
1072: }
1073:
1074: void nullspace_gfpn(mat,n,ind)
1075: GFPN **mat;
1076: int n;
1077: int *ind;
1078: {
1079: int i,j,l,s;
1080: GFPN w,w1,h,inv;
1081: GFPN *t,*u;
1082:
1083: bzero(ind,n*sizeof(int));
1084: ind[0] = 0;
1085: for ( i = j = 0; j < n; i++, j++ ) {
1086: for ( ; j < n; j++ ) {
1087: for ( l = i; l < n; l++ ) {
1088: simpgfpn(mat[l][j],&w); mat[l][j] = w;
1089: if ( mat[l][j] )
1090: break;
1091: }
1092: if ( l < n ) {
1093: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1094: } else
1095: ind[j] = 1;
1096: }
1097: if ( j == n )
1098: break;
1099: divgfpn((GFPN)ONE,(GFPN)mat[i][j],&inv);
1100: for ( s = j, t = mat[i]; s < n; s++ ) {
1101: mulgfpn(t[s],inv,&w); t[s] = w;
1102: }
1103: for ( l = 0; l < n; l++ ) {
1104: if ( l == i )
1105: continue;
1106: u = mat[l]; chsgngfpn(u[j],&h);
1107: for ( s = j; s < n; s++ ) {
1108: mulgfpn(h,t[s],&w); addgfpn(w,u[s],&w1); u[s] = w1;
1109: }
1110: }
1111: }
1112: }
1.5 noro 1113:
1114: void nullspace_gfs(mat,n,ind)
1115: GFS **mat;
1116: int n;
1117: int *ind;
1118: {
1119: int i,j,l,s;
1120: GFS w,w1,h,inv;
1121: GFS *t,*u;
1122: GFS one;
1123:
1124: bzero(ind,n*sizeof(int));
1125: ind[0] = 0;
1126: mqtogfs(ONEM,&one);
1127:
1128: for ( i = j = 0; j < n; i++, j++ ) {
1129: for ( ; j < n; j++ ) {
1130: for ( l = i; l < n; l++ )
1131: if ( mat[l][j] )
1132: break;
1133: if ( l < n ) {
1134: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1135: } else
1136: ind[j] = 1;
1137: }
1138: if ( j == n )
1139: break;
1140: divgfs(one,mat[i][j],&inv);
1141: for ( s = j, t = mat[i]; s < n; s++ ) {
1142: mulgfs(t[s],inv,&w); t[s] = w;
1143: }
1144: for ( l = 0; l < n; l++ ) {
1145: if ( l == i )
1146: continue;
1147: u = mat[l];
1148: chsgngfs(u[j],&h);
1149: for ( s = j; s < n; s++ ) {
1150: mulgfs(h,t[s],&w); addgfs(w,u[s],&w1); u[s] = w1;
1.12 noro 1151: }
1152: }
1153: }
1154: }
1155:
1156: void nullspace_gfsn(mat,n,ind)
1157: GFSN **mat;
1158: int n;
1159: int *ind;
1160: {
1161: int i,j,l,s;
1162: GFSN w,w1,h,inv;
1163: GFSN *t,*u;
1164:
1165: bzero(ind,n*sizeof(int));
1166: ind[0] = 0;
1167:
1168: for ( i = j = 0; j < n; i++, j++ ) {
1169: for ( ; j < n; j++ ) {
1170: for ( l = i; l < n; l++ )
1171: if ( mat[l][j] )
1172: break;
1173: if ( l < n ) {
1174: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1175: } else
1176: ind[j] = 1;
1177: }
1178: if ( j == n )
1179: break;
1180: invgfsn(mat[i][j],&inv);
1181: for ( s = j, t = mat[i]; s < n; s++ ) {
1182: mulgfsn(t[s],inv,&w); t[s] = w;
1183: }
1184: for ( l = 0; l < n; l++ ) {
1185: if ( l == i )
1186: continue;
1187: u = mat[l];
1188: chsgngfsn(u[j],&h);
1189: for ( s = j; s < n; s++ ) {
1190: mulgfsn(h,t[s],&w); addgfsn(w,u[s],&w1); u[s] = w1;
1.5 noro 1191: }
1192: }
1193: }
1194: }
1195:
1.1 noro 1196: /* p = a(0)vl[0]+a(1)vl[1]+...+a(m-1)vl[m-1]+a(m) -> array = [a(0) a(1) ... a(m)] */
1197:
1198: void linear_form_to_array(p,vl,m,array)
1199: P p;
1200: VL vl;
1201: int m;
1202: Num *array;
1203: {
1204: int i;
1205: DCP dc;
1206:
1207: bzero((char *)array,(m+1)*sizeof(Num *));
1208: for ( i = 0; p && vl; vl = NEXT(vl), i++ ) {
1209: if ( ID(p) == O_N )
1210: break;
1211: else if ( VR(p) == vl->v ) {
1212: dc = DC(p);
1213: array[i] = (Num)COEF(dc);
1214: dc = NEXT(dc);
1215: p = dc ? COEF(dc) : 0;
1216: }
1217: }
1218: array[m] = (Num)p;
1219: }
1220:
1221: void array_to_linear_form(array,vl,m,r)
1222: Num *array;
1223: VL vl;
1224: int m;
1225: P *r;
1226: {
1227: P t;
1228: DCP dc0,dc1;
1229:
1230: if ( !m )
1231: *r = (P)array[0];
1232: else {
1233: array_to_linear_form(array+1,NEXT(vl),m-1,&t);
1234: if ( !array[0] )
1235: *r = t;
1236: else {
1237: NEWDC(dc0); DEG(dc0) = ONE; COEF(dc0) = (P)array[0];
1238: if ( !t )
1239: NEXT(dc0) = 0;
1240: else {
1241: NEWDC(dc1); DEG(dc1) = 0; COEF(dc1) = t;
1242: NEXT(dc1) = 0;
1243: NEXT(dc0) = dc1;
1244: }
1245: MKP(vl->v,dc0,*r);
1246: }
1247: }
1248: }
1249:
1250: void Psolve_linear_equation_gf2n(arg,rp)
1251: NODE arg;
1252: LIST *rp;
1253: {
1254: NODE eqs,tn;
1255: VL vars,tvl;
1256: int i,j,n,m,dim,codim;
1257: GF2N **w;
1258: int *ind;
1259: NODE n0,n1;
1260:
1261: get_vars(ARG0(arg),&vars);
1262: eqs = BDY((LIST)ARG0(arg));
1263: for ( n = 0, tn = eqs; tn; tn = NEXT(tn), n++);
1264: for ( m = 0, tvl = vars; tvl; tvl = NEXT(tvl), m++);
1265: w = (GF2N **)almat_pointer(n,m+1);
1266: for ( i = 0, tn = eqs; i < n; i++, tn = NEXT(tn) )
1267: linear_form_to_array(BDY(tn),vars,m,(Num *)w[i]);
1268: ind = (int *)ALLOCA(m*sizeof(int));
1269: solve_linear_equation_gf2n(w,n,m,ind);
1270: for ( j = 0, dim = 0; j < m; j++ )
1271: if ( ind[j] )
1272: dim++;
1273: codim = m-dim;
1274: for ( i = codim; i < n; i++ )
1275: if ( w[i][m] ) {
1276: MKLIST(*rp,0); return;
1277: }
1278: for ( i = 0, n0 = 0; i < codim; i++ ) {
1279: NEXTNODE(n0,n1);
1280: array_to_linear_form((Num *)w[i],vars,m,(P *)&BDY(n1));
1281: }
1282: if ( n0 )
1283: NEXT(n1) = 0;
1284: MKLIST(*rp,n0);
1285: }
1286:
1287: void solve_linear_equation_gf2n(mat,n,m,ind)
1288: GF2N **mat;
1289: int n;
1290: int *ind;
1291: {
1292: int i,j,l,s;
1293: GF2N w,w1,h,inv;
1294: GF2N *t,*u;
1295: extern gf2n_lazy;
1296:
1297: bzero(ind,m*sizeof(int));
1298: ind[0] = 0;
1299: for ( i = j = 0; j < m; i++, j++ ) {
1300: for ( ; j < m; j++ ) {
1301: for ( l = i; l < n; l++ ) {
1302: simpgf2n(mat[l][j],&w); mat[l][j] = w;
1303: if ( mat[l][j] )
1304: break;
1305: }
1306: if ( l < n ) {
1307: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1308: } else
1309: ind[j] = 1;
1310: }
1311: if ( j == m )
1312: break;
1313: invgf2n(mat[i][j],&inv);
1314: for ( s = j, t = mat[i]; s <= m; s++ ) {
1315: mulgf2n(t[s],inv,&w); t[s] = w;
1316: }
1317: for ( l = 0; l < n; l++ ) {
1318: if ( l == i )
1319: continue;
1320: u = mat[l]; h = u[j];
1321: for ( s = j; s <= m; s++ ) {
1322: mulgf2n(h,t[s],&w); addgf2n(w,u[s],&w1); u[s] = w1;
1323: }
1324: }
1325: }
1326: }
1327:
1328: /*
1329: void null_to_sol(mat,ind,mod,n,r)
1330: int **mat;
1331: int *ind;
1332: int mod,n;
1333: UM *r;
1334: {
1335: int i,j,k,l;
1336: int *c;
1337: UM w;
1338:
1339: for ( i = 0, l = 0; i < n; i++ ) {
1340: if ( !ind[i] )
1341: continue;
1342: w = UMALLOC(n);
1343: for ( j = k = 0, c = COEF(w); j < n; j++ )
1344: if ( ind[j] )
1345: c[j] = 0;
1346: else
1347: c[j] = mat[k++][i];
1348: c[i] = mod-1;
1349: for ( j = n; j >= 0; j-- )
1350: if ( c[j] )
1351: break;
1352: DEG(w) = j;
1353: r[l++] = w;
1354: }
1355: }
1356: */
1357:
1358: void showgfmat(mat,n)
1359: UM **mat;
1360: int n;
1361: {
1362: int i,j,k;
1363: int *c;
1364: UM p;
1365:
1366: for ( i = 0; i < n; i++ ) {
1367: for ( j = 0; j < n; j++ ) {
1368: p = mat[i][j];
1369: if ( DEG(p) < 0 )
1370: fprintf(asir_out,"0");
1371: else
1372: for ( p = mat[i][j], k = DEG(p), c = COEF(p); k >= 0; k-- ) {
1373: if ( c[k] )
1374: fprintf(asir_out,"+%d",c[k]);
1375: if ( k > 1 )
1376: fprintf(asir_out,"a^%d",k);
1377: else if ( k == 1 )
1378: fprintf(asir_out,"a",k);
1379: }
1380: fprintf(asir_out," ");
1381: }
1382: fprintf(asir_out,"\n");
1383: }
1384: }
1385:
1386: #if 0
1387: void Pgcda_mod(arg,rp)
1388: NODE arg;
1389: P *rp;
1390: {
1391: p1 = (P)ARG0(arg);
1392: p2 = (P)ARG1(arg);
1393: v = VR((P)ARG2(arg));
1394: d = (P)ARG3(arg);
1395: m = QTOS((Q)ARG4(arg));
1396: reordvar(CO,v,&vl);
1397: reorderp(vl,CO,p1,&t); ptomp(m,t,&m1);
1398: reorderp(vl,CO,p2,&t); ptomp(m,t,&m2);
1399: if ( NUM(m1) || NUM(m2) || VR(m1) != v || VR(m2) != v ) {
1400: *rp = ONE; return;
1401: }
1402: if ( deg(v,m1) >= deg(v,m2) ) {
1403: t = m1; m1 = m2; m2 = t;
1404: }
1405: while ( 1 ) {
1406: inva_mod(COEF(DC(m2)),d,m,&inv);
1407: NEWDC(dc); NEXT(dc) = 0; MKP(v,dc,h);
1408: d0 = deg(v,m1)-deg(v,m2); STOQ(d0,DEG(dc));
1409: mulgq(m,d,inv,COEF(DC(m1)),&COEF(dc));
1410: mulgp(vl,m,d,m2,h,&t); subgp(vl,m,d,m1,t,&s);
1411: }
1412: }
1413: #endif
1414:
1415: void Ppwr_mod(arg,rp)
1416: NODE arg;
1417: P *rp;
1418: {
1419: P p,a,d,r;
1420: int m;
1421: Q q;
1422: N n;
1423:
1424: m = QTOS((Q)ARG4(arg)); q = (Q)ARG5(arg); n = q ? NM(q) : 0;
1425: ptomp(m,(P)ARG0(arg),&p); ptomp(m,(P)ARG1(arg),&a);
1426: ptomp(m,(P)ARG3(arg),&d);
1427: pwr_mod(p,a,VR((P)ARG2(arg)),d,m,n,&r);
1428: mptop(r,rp);
1429: }
1430:
1431: void pwr_mod(p,a,v,d,m,n,rp)
1432: P p,a,d;
1433: V v;
1434: int m;
1435: N n;
1436: P *rp;
1437: {
1438: int b;
1439: P t,s,r;
1440: N n1;
1441:
1442: if ( !n )
1443: *rp = (P)ONEM;
1444: else if ( UNIN(n) )
1445: *rp = p;
1446: else {
1447: b = divin(n,2,&n1);
1448: pwr_mod(p,a,v,d,m,n1,&t);
1449: mulmp(CO,m,t,t,&s); rem_mod(s,a,v,d,m,&r);
1450: if ( b ) {
1451: mulmp(CO,m,r,p,&t); rem_mod(t,a,v,d,m,rp);
1452: } else
1453: *rp = r;
1454: }
1455: }
1456:
1457: void rem_mod(p,a,v,d,m,rp)
1458: P p,a,d;
1459: V v;
1460: int m;
1461: P *rp;
1462: {
1463: P tmp,r1,r2;
1464:
1465: divsrmp(CO,m,p,d,&tmp,&r1);
1466: divsrmp(CO,m,r1,a,&tmp,&r2);
1467: divsrmp(CO,m,r2,d,&tmp,rp);
1468: }