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1.15 ! noro 1: /* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.14 2002/12/18 06:15:40 noro Exp $ */
1.1 noro 2:
3: #include "ca.h"
4:
1.3 noro 5: void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp);
6: void gcdsf_main(VL vl,P *pa,int m,P *r);
7: void ugcdsf(P *pa,int m,P *r);
1.10 noro 8: void head_monomial(VL vl,V v,P p,P *coef,P *term);
1.4 noro 9: void sqfrsfmain(VL vl,P f,DCP *dcp);
10: void pthrootsf(P f,Q m,P *r);
11: void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp);
12: void gcdsf(VL vl,P *pa,int k,P *r);
1.5 noro 13: void mfctrsfmain(VL vl, P f, DCP *dcp);
1.7 noro 14: void next_evaluation_point(int *mev,int n);
1.12 noro 15: void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp);
16: void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,int *mev,P *up);
1.7 noro 17: void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r);
18: void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r);
1.12 noro 19: void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,int *mev,P *r);
1.8 noro 20: void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv);
1.7 noro 21: void poly_to_gfsn_poly(VL vl,P f,V v,P *r);
22: void gfsn_poly_to_poly(VL vl,P f,V v,P *r);
1.8 noro 23: void poly_to_gfsn_poly_main(P f,V v,P *r);
24: void gfsn_poly_to_poly_main(P f,V v,P *r);
25: void gfsn_univariate_to_sfbm(P f,int dy,BM *r);
26: void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r);
1.4 noro 27:
28: void lex_lc(P f,P *c)
29: {
30: if ( !f || NUM(f) )
31: *c = f;
32: else
33: lex_lc(COEF(DC(f)),c);
34: }
35:
36: DCP append_dc(DCP dc,DCP dct)
37: {
38: DCP dcs;
39:
40: if ( !dc )
41: return dct;
42: else {
43: for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) );
44: NEXT (dcs) = dct;
45: return dc;
46: }
47: }
48:
49: void sqfrsf(VL vl, P f, DCP *dcp)
50: {
51: DCP dc,dct;
52: Obj obj;
1.14 noro 53: P t,s,c,cont;
1.13 noro 54: VL tvl,onevl;
1.4 noro 55:
56: simp_ff((Obj)f,&obj); f = (P)obj;
57: lex_lc(f,&c); divsp(vl,f,c,&t); f = t;
58: monomialfctr(vl,f,&t,&dc); f = t;
59: clctv(vl,f,&tvl); vl = tvl;
1.13 noro 60: NEWVL(onevl); NEXT(onevl)=0;
1.4 noro 61: if ( !vl )
62: ;
63: else if ( !NEXT(vl) ) {
64: sfusqfr(f,&dct);
65: dc = append_dc(dc,NEXT(dct));
66: } else {
67: t = f;
68: for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
1.13 noro 69: onevl->v = tvl->v;
1.14 noro 70: cont_pp_mv_sf(vl,onevl,t,&cont,&s); t = s;
71: sqfrsf(vl,cont,&dct);
1.4 noro 72: dc = append_dc(dc,NEXT(dct));
73: }
74: sqfrsfmain(vl,t,&dct);
75: dc = append_dc(dc,dct);
76: }
77: NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc;
78: *dcp = dct;
79: }
80:
81: void sqfrsfmain(VL vl,P f,DCP *dcp)
82: {
83: VL tvl;
84: DCP dc,dct,dcs;
85: P t,s;
86: Q m,m1;
87: V v;
88:
89: clctv(vl,f,&tvl); vl = tvl;
90: dc = 0;
91: t = f;
92: for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
93: v = tvl->v;
94: partial_sqfrsf(vl,v,t,&s,&dct); t = s;
95: dc = append_dc(dc,dct);
96: }
97: if ( !NUM(t) ) {
98: STOQ(characteristic_sf(),m);
99: pthrootsf(t,m,&s);
100: sqfrsfmain(vl,s,&dct);
101: for ( dcs = dct; dcs; dcs = NEXT(dcs) ) {
102: mulq(DEG(dcs),m,&m1); DEG(dcs) = m1;
103: }
104: dc = append_dc(dc,dct);
105: }
106: *dcp = dc;
107: }
108:
109: void pthrootsf(P f,Q m,P *r)
110: {
111: DCP dc,dc0,dct;
112: N qn,rn;
113:
114: if ( NUM(f) )
115: pthrootgfs(f,r);
116: else {
117: dc = DC(f);
118: dc0 = 0;
119: for ( dc0 = 0; dc; dc = NEXT(dc) ) {
120: NEXTDC(dc0,dct);
121: pthrootsf(COEF(dc),m,&COEF(dct));
122: if ( DEG(dc) ) {
123: divn(NM(DEG(dc)),NM(m),&qn,&rn);
124: if ( rn )
125: error("pthrootsf : cannot happen");
126: NTOQ(qn,1,DEG(dct));
127: } else
128: DEG(dct) = 0;
129: }
130: NEXT(dct) = 0;
131: MKP(VR(f),dc0,*r);
132: }
133: }
134:
135: void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp)
136: {
137: P ps[2];
138: DCP dc0,dc;
139: int m;
140: P t,flat,flat1,g,df,q;
141:
142: diffp(vl,f,v,&df);
143: if ( !df ) {
144: *dcp = 0;
145: *r = f;
146: return;
147: }
148: ps[0] = f; ps[1] = df;
149: gcdsf(vl,ps,2,&g);
150: divsp(vl,f,g,&flat);
151: m = 0;
152: t = f;
153: dc0 = 0;
154: while ( !NUM(flat) ) {
155: while ( divtp(vl,t,flat,&q) ) {
156: t = q; m++;
157: }
158: ps[0] = t; ps[1] = flat;
159: gcdsf(vl,ps,2,&flat1);
160: divsp(vl,flat,flat1,&g);
161: flat = flat1;
162: NEXTDC(dc0,dc);
163: COEF(dc) = g;
164: STOQ(m,DEG(dc));
165: }
166: NEXT(dc) = 0;
167: *dcp = dc0;
168: *r = t;
169: }
1.1 noro 170:
171: void gcdsf(VL vl,P *pa,int k,P *r)
172: {
1.3 noro 173: P *ps,*pl,*pm;
174: P **cp;
1.1 noro 175: int *cn;
176: DCP *ml;
177: Obj obj;
178: int i,j,l,m;
179: P mg,mgsf,t;
180: VL avl,nvl,tvl,svl;
181:
182: ps = (P *)ALLOCA(k*sizeof(P));
183: for ( i = 0, m = 0; i < k; i++ ) {
184: simp_ff((Obj)pa[i],&obj);
185: if ( obj )
1.3 noro 186: ps[m++] = (P)obj;
1.1 noro 187: }
188: if ( !m ) {
189: *r = 0;
190: return;
191: }
192: if ( m == 1 ) {
1.3 noro 193: *r = ps[0];
1.1 noro 194: return;
195: }
196: pl = (P *)ALLOCA(m*sizeof(P));
197: ml = (DCP *)ALLOCA(m*sizeof(DCP));
198: for ( i = 0; i < m; i++ )
199: monomialfctr(vl,ps[i],&pl[i],&ml[i]);
1.3 noro 200: gcdmonomial(vl,ml,m,&mg); simp_ff((Obj)mg,&obj); mgsf = (P)obj;
1.1 noro 201: for ( i = 0, nvl = vl, avl = 0; nvl && i < m; i++ ) {
202: clctv(vl,pl[i],&tvl);
203: intersectv(nvl,tvl,&svl); nvl = svl;
204: mergev(vl,avl,tvl,&svl); avl = svl;
205: }
206: if ( !nvl ) {
207: *r = mgsf;
208: return;
209: }
210: if ( !NEXT(avl) ) {
211: ugcdsf(pl,m,&t);
212: mulp(vl,mgsf,t,r);
213: return;
214: }
215: for ( tvl = nvl, i = 0; tvl; tvl = NEXT(tvl), i++ );
216: for ( tvl = avl, j = 0; tvl; tvl = NEXT(tvl), j++ );
217: if ( i == j ) {
218: /* all the pl[i]'s have the same variables */
219: gcdsf_main(avl,pl,m,&t);
220: } else {
221: cp = (P **)ALLOCA(m*sizeof(P *));
222: cn = (int *)ALLOCA(m*sizeof(int));
223: for ( i = 0; i < m; i++ ) {
224: cp[i] = (P *)ALLOCA(lengthp(pl[i])*sizeof(P));
225: cn[i] = pcoef(vl,nvl,pl[i],cp[i]);
226: }
227: for ( i = j = 0; i < m; i++ )
228: j += cn[i];
229: pm = (P *)ALLOCA(j*sizeof(P));
230: for ( i = l = 0; i < m; i++ )
231: for ( j = 0; j < cn[i]; j++ )
232: pm[l++] = cp[i][j];
233: gcdsf(vl,pm,l,&t);
234: }
235: mulp(vl,mgsf,t,r);
236: }
237:
238: /* univariate gcd */
239:
240: void ugcdsf(P *pa,int m,P *r)
241: {
1.3 noro 242: P *ps;
1.1 noro 243: int i;
244: UM w1,w2,w3,w;
245: int d;
246: V v;
247:
248: if ( m == 1 ) {
249: *r = pa[0];
250: return;
251: }
1.3 noro 252: for ( i = 0; i < m; i++ )
253: if ( NUM(pa[i]) ) {
254: itogfs(1,r);
255: return;
256: }
1.1 noro 257: ps = (P *)ALLOCA(m*sizeof(P));
258: sort_by_deg(m,pa,ps);
1.3 noro 259: v = VR(ps[m-1]);
260: d = getdeg(v,ps[m-1]);
1.1 noro 261: w1 = W_UMALLOC(d);
262: w2 = W_UMALLOC(d);
263: w3 = W_UMALLOC(d);
264: ptosfum(ps[0],w1);
265: for ( i = 1; i < m; i++ ) {
266: ptosfum(ps[i],w2);
267: gcdsfum(w1,w2,w3);
268: w = w1; w1 = w3; w3 = w;
269: if ( !DEG(w1) ) {
1.3 noro 270: itogfs(1,r);
1.1 noro 271: return;
272: }
273: }
274: sfumtop(v,w1,r);
275: }
276:
1.4 noro 277: /* deg(HT(p),v), where p is considered as distributed poly over F[v] */
278: int gethdeg(VL vl,V v,P p)
279: {
280: DCP dc;
281: Q dmax;
282: P cmax;
283:
284: if ( !p )
285: return -1;
286: else if ( NUM(p) )
287: return 0;
288: else if ( VR(p) != v )
289: /* HT(p) = HT(lc(p))*x^D */
290: return gethdeg(vl,v,COEF(DC(p)));
291: else {
292: /* VR(p) = v */
293: dc = DC(p); dmax = DEG(dc); cmax = COEF(dc);
294: for ( dc = NEXT(dc); dc; dc = NEXT(dc) )
295: if ( compp(vl,COEF(dc),cmax) > 0 ) {
296: dmax = DEG(dc); cmax = COEF(dc);
297: }
298: return QTOS(dmax);
299: }
300: }
1.1 noro 301:
302: /* all the pa[i]'s have the same variables (=vl) */
303:
304: void gcdsf_main(VL vl,P *pa,int m,P *r)
305: {
1.3 noro 306: int nv,i,i0,imin,d,d0,d1,d2,dmin,index;
307: V v,v0,vmin;
1.2 noro 308: VL tvl,nvl,rvl,nvl0,rvl0;
1.3 noro 309: P *pc, *ps, *ph,*lps;
310: P x,t,cont,hg,g,hm,mod,s;
311: P hge,ge,ce,he,u,cof1e,mode,mod1,adj,cof1,coadj,q;
312: GFS sf;
1.2 noro 313:
1.1 noro 314: for ( nv = 0, tvl = vl; tvl; tvl = NEXT(tvl), nv++);
315: if ( nv == 1 ) {
316: ugcdsf(pa,m,r);
317: return;
318: }
1.4 noro 319: /* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */
1.1 noro 320: tvl = vl;
321: do {
322: v = tvl->v;
323: i = 0;
324: do {
1.4 noro 325: d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]);
1.1 noro 326: if ( i == 0 || (d < d0) ) {
327: d0 = d; i0 = i; v0 = v;
328: }
329: } while ( ++i < m );
330: if ( tvl == vl || (d0 < dmin) ) {
331: dmin = d0; imin = i0; vmin = v0;
332: }
333: } while ( tvl = NEXT(tvl) );
334:
335: /* reorder variables so that vmin is the last variable */
336: for ( nvl0 = 0, rvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) )
337: if ( tvl->v != vmin ) {
338: NEXTVL(nvl0,nvl); nvl->v = tvl->v;
339: NEXTVL(rvl0,rvl); rvl->v = tvl->v;
340: }
341: /* rvl = remaining variables */
1.3 noro 342: NEXT(rvl) = 0; rvl = rvl0;
1.1 noro 343: /* nvl = ...,vmin */
1.3 noro 344: NEXTVL(nvl0,nvl); nvl->v = vmin; NEXT(nvl) = 0; nvl = nvl0;
1.2 noro 345: MKV(vmin,x);
1.1 noro 346:
347: /* for content and primitive part */
348: pc = (P *)ALLOCA(m*sizeof(P));
349: ps = (P *)ALLOCA(m*sizeof(P));
350: ph = (P *)ALLOCA(m*sizeof(P));
351: /* separate the contents */
352: for ( i = 0; i < m; i++ ) {
1.3 noro 353: reorderp(nvl,vl,pa[i],&t);
1.1 noro 354: cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]);
1.10 noro 355: head_monomial(nvl,vmin,ps[i],&ph[i],&t);
1.1 noro 356: }
357: ugcdsf(pc,m,&cont);
358: ugcdsf(ph,m,&hg);
359:
360: /* for hg*pp (used in check phase) */
361: lps = (P *)ALLOCA(m*sizeof(P));
362: for ( i = 0; i < m; i++ )
363: mulp(nvl,hg,ps[i],&lps[i]);
364:
365: while ( 1 ) {
366: g = 0;
1.3 noro 367: cof1 = 0;
1.1 noro 368: hm = 0;
1.3 noro 369: itogfs(1,&mod);
1.1 noro 370: index = 0;
1.3 noro 371: for ( index = 0; getdeg(vmin,mod) <= d+1; index++ ) {
1.1 noro 372: /* evaluation pt */
1.3 noro 373: indextogfs(index,&s);
1.1 noro 374: substp(nvl,hg,vmin,s,&hge);
375: if ( !hge )
376: continue;
377: for ( i = 0; i < m; i++ )
378: substp(nvl,ps[i],vmin,s,&ph[i]);
379: /* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */
380: gcdsf(nvl,ph,m,&ge);
1.10 noro 381: head_monomial(nvl,vmin,ge,&ce,&he);
1.3 noro 382: if ( NUM(he) ) {
1.1 noro 383: *r = cont;
384: return;
385: }
1.3 noro 386: divgfs((GFS)hge,(GFS)ce,&sf); t = (P)sf;
387: mulp(nvl,t,ge,&u); ge = u;
1.1 noro 388: divsp(nvl,ph[imin],ge,&t); mulp(nvl,hge,t,&cof1e);
1.2 noro 389: /* hm=0 : reset; he==hm : lucky */
1.3 noro 390: if ( !hm || !compp(nvl,he,hm) ) {
1.2 noro 391: substp(nvl,mod,vmin,s,&mode); divsp(nvl,mod,mode,&mod1);
392: /* adj = mod/(mod|x=s)*(ge-g|x=s) */
393: substp(nvl,g,vmin,s,&t);
394: subp(nvl,ge,t,&u); mulp(nvl,mod1,u,&adj);
395: /* coadj = mod/(mod|vmin=s)*(cof1e-cof1e|vmin=s) */
396: substp(nvl,cof1,vmin,s,&t);
1.3 noro 397: subp(nvl,cof1e,t,&u); mulp(nvl,mod1,u,&coadj);
1.2 noro 398: if ( !adj ) {
399: /* adj == gcd ? */
400: for ( i = 0; i < m; i++ )
1.3 noro 401: if ( !divtp(nvl,lps[i],g,&t) )
1.2 noro 402: break;
403: if ( i == m ) {
1.3 noro 404: cont_pp_mv_sf(nvl,rvl,g,&t,&u);
1.2 noro 405: mulp(nvl,cont,u,&t);
1.3 noro 406: reorderp(vl,nvl,t,r);
1.2 noro 407: return;
408: }
409: } else if ( !coadj ) {
1.3 noro 410: /* ps[imin]/coadj == gcd ? */
411: if ( divtp(nvl,lps[imin],cof1,&q) ) {
1.2 noro 412: for ( i = 0; i < m; i++ )
413: if ( !divtp(nvl,lps[i],q,&t) )
414: break;
415: if ( i == m ) {
416: cont_pp_mv_sf(nvl,rvl,q,&t,&u);
417: mulp(nvl,cont,u,&t);
1.3 noro 418: reorderp(vl,nvl,t,r);
1.2 noro 419: return;
420: }
421: }
422: }
423: addp(nvl,g,adj,&t); g = t;
424: addp(nvl,cof1,coadj,&t); cof1 = t;
425: subp(nvl,x,s,&t); mulp(nvl,mod,t,&u); mod = u;
426: hm = he;
427: } else {
428: d1 = homdeg(hm); d2 = homdeg(he);
429: if ( d1 < d2 ) /* we use current hm */
430: continue;
431: else if ( d1 > d2 ) {
432: /* use he */
433: g = ge;
434: cof1 = cof1e;
435: hm = he;
436: subp(nvl,x,s,&mod);
437: } else {
438: /* d1==d2, but hm!=he => both are unlucky */
439: g = 0;
440: cof1 = 0;
1.3 noro 441: itogfs(1,&mod);
1.2 noro 442: }
1.1 noro 443: }
444: }
445: }
446: }
447:
1.10 noro 448: void head_monomial(VL vl,V v,P p,P *coef,P *term)
1.1 noro 449: {
450: P t,s,u;
451: DCP dc;
452: GFS one;
453:
1.3 noro 454: itogfs(1,&one);
455: t = (P)one;
1.1 noro 456: while ( 1 ) {
457: if ( NUM(p) || VR(p) == v ) {
458: *coef = p;
459: *term = t;
460: return;
461: } else {
1.3 noro 462: NEWDC(dc);
463: COEF(dc) = (P)one; DEG(dc) = DEG(DC(p));
1.1 noro 464: MKP(VR(p),dc,s);
465: mulp(vl,t,s,&u); t = u;
466: p = COEF(DC(p));
467: }
468: }
469: }
470:
471: void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)
472: {
473: DP dp;
474: MP t;
475: int i,m;
476: P *ps;
1.15 ! noro 477: struct order_spec spec;
1.1 noro 478:
1.15 ! noro 479: create_order_spec(0,&spec);
! 480: initd(&spec);
1.1 noro 481: ptod(vl,rvl,p,&dp);
482: for ( t = BDY(dp), m = 0; t; t = NEXT(t), m++ );
483: ps = (P *)ALLOCA(m*sizeof(P));
1.3 noro 484: for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ )
1.1 noro 485: ps[i] = C(t);
1.10 noro 486: gcdsf(vl,ps,m,c);
1.3 noro 487: divsp(vl,p,*c,pp);
1.5 noro 488: }
489:
490: void mfctrsf(VL vl, P f, DCP *dcp)
491: {
492: DCP dc0,dc,dct,dcs,dcr;
493: Obj obj;
494:
495: simp_ff((Obj)f,&obj); f = (P)obj;
496: sqfrsf(vl,f,&dct);
497: dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0;
498: for ( ; dct; dct = NEXT(dct) ) {
499: mfctrsfmain(vl,COEF(dct),&dcs);
500: for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
501: DEG(dcr) = DEG(dct);
502: for ( ; NEXT(dc); dc = NEXT(dc) );
503: NEXT(dc) = dcs;
504: }
505: *dcp = dc0;
506: }
507:
508: /* f : sqfr, non const */
509:
510: void mfctrsfmain(VL vl, P f, DCP *dcp)
511: {
1.6 noro 512: VL tvl,nvl,rvl;
1.7 noro 513: DCP dc,dc0,dc1,dc2,dct,lcfdc,dcs;
514: int imin,inext,i,j,n,k,np;
1.5 noro 515: int *da;
516: V vx,vy;
517: V *va;
1.7 noro 518: P *l,*tl;
1.5 noro 519: P gcd,g,df,dfmin;
520: P pa[2];
1.10 noro 521: P f0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s;
1.12 noro 522: P ype,yme,fin;
1.6 noro 523: GFS ev,evy;
524: P *fp0;
525: int *mev,*win;
1.5 noro 526:
527: clctv(vl,f,&tvl); vl = tvl;
528: if ( !vl )
529: error("mfctrsfmain : cannot happen");
530: if ( !NEXT(vl) ) {
531: /* univariate */
532: ufctrsf(f,&dc);
533: /* remove lc */
534: *dcp = NEXT(dc);
535: return;
536: }
537: for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ );
538: va = (V *)ALLOCA(n*sizeof(int));
539: da = (int *)ALLOCA(n*sizeof(int));
540: /* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */
541: imin = -1;
542: for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) {
543: va[i] = tvl->v;
544: da[i] = getdeg(va[i],f);
545: diffp(vl,f,va[i],&df);
546: if ( !df )
547: continue;
548: if ( imin < 0 || da[i] < da[imin] ) {
549: dfmin = df;
550: imin = i;
551: }
552: }
553: /* find v1 neq v s.t. deg(f,v) is minimal */
554: inext = -1;
555: for ( i = 0; i < n; i++ ) {
556: if ( i == imin )
557: continue;
558: if ( inext < 0 || da[i] < da[inext] )
559: inext = i;
560: }
561: pa[0] = f;
562: pa[1] = dfmin;
1.11 noro 563: gcdsf(vl,pa,2,&gcd);
1.5 noro 564: if ( !NUM(gcd) ) {
565: /* f = gcd * f/gcd */
566: mfctrsfmain(vl,gcd,&dc1);
567: divsp(vl,f,gcd,&g);
568: mfctrsfmain(vl,g,&dc2);
569: for ( dct = dc1; NEXT(dct); dct = NEXT(dct) );
570: NEXT(dct) = dc2;
571: *dcp = dc1;
572: return;
573: }
574: /* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */
575: nvl = 0;
576: NEXTVL(nvl,tvl); tvl->v = va[imin];
577: NEXTVL(nvl,tvl); tvl->v = va[inext];
578: for ( i = 0; i < n; i++ ) {
579: if ( i == imin || i == inext )
580: continue;
581: NEXTVL(nvl,tvl); tvl->v = va[i];
582: }
583: NEXT(tvl) = 0;
584:
1.12 noro 585: fin = f;
1.10 noro 586: reorderp(nvl,vl,f,&g); f = g;
1.5 noro 587: vx = nvl->v;
588: vy = NEXT(nvl)->v;
1.6 noro 589: MKV(vx,x);
590: MKV(vy,y);
591: /* remaining variables */
592: rvl = NEXT(NEXT(nvl));
593: if ( !rvl ) {
1.5 noro 594: /* bivariate */
1.10 noro 595: sfbfctr(f,vx,vy,getdeg(vx,f),&dc1);
1.5 noro 596: for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) {
597: NEXTDC(dc0,dc);
598: DEG(dc) = ONE;
599: reorderp(vl,nvl,COEF(dc1),&COEF(dc));
600: }
601: NEXT(dc) = 0;
602: *dcp = dc0;
603: return;
604: }
1.6 noro 605: /* n >= 3; nvl = (vx,vy,X) */
606: /* find good evaluation pt for X */
607: mev = (int *)CALLOC(n-2,sizeof(int));
608: while ( 1 ) {
1.10 noro 609: /* lcf(mev)=0 => invalid */
610: substvp_sf(nvl,rvl,COEF(DC(f)),mev,&t);
611: if ( t ) {
612: substvp_sf(nvl,rvl,f,mev,&f0);
613: pa[0] = f0;
614: diffp(nvl,f0,vx,&pa[1]);
615: if ( pa[1] ) {
616: gcdsf(nvl,pa,2,&gcd);
1.6 noro 617: /* XXX maybe we have to accept the case where gcd is a poly of y */
1.10 noro 618: if ( NUM(gcd) )
619: break;
620: }
1.6 noro 621: }
1.7 noro 622: /* XXX if generated indices exceed q of GF(q) => error in indextogfs */
623: next_evaluation_point(mev,n-2);
1.6 noro 624: }
1.10 noro 625: /* f0 = f(x,y,mev) */
626: /* separate content; f0 may have the content wrt x */
627: cont_pp_sfp(nvl,f0,&c0,&pp0);
1.6 noro 628:
1.7 noro 629: /* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */
630: sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0;
1.6 noro 631:
632: if ( !NEXT(dc) ) {
633: /* f is irreducible */
1.12 noro 634: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = fin; NEXT(dc) = 0;
1.6 noro 635: *dcp = dc;
636: return;
637: }
1.7 noro 638: /* ype = y+evy, yme = y-evy */
639: addp(nvl,y,(P)evy,&ype); subp(nvl,y,(P)evy,&yme);
640:
1.6 noro 641: /* shift c0; c0 <- c0(y+evy) */
1.7 noro 642: substp(nvl,c0,vy,ype,&s); c0 = s;
643:
644: /* shift f; f <- f(y+evy) */
645: substp(nvl,f,vy,ype,&s); f = s;
646:
647: /* now f(x,0,mev) = c0 * prod dc */
1.6 noro 648:
649: /* factorize lc_x(f) */
650: lcf = COEF(DC(f));
1.7 noro 651: mfctrsf(nvl,lcf,&dct);
652: /* skip the first element (= a number) */
1.12 noro 653: lcfdc = NEXT(dct);
1.6 noro 654:
655: /* np = number of bivariate factors */
656: for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ );
657: fp0 = (P *)ALLOCA((np+1)*sizeof(P));
658: for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ )
659: fp0[i] = COEF(dct);
660: fp0[np] = 0;
1.7 noro 661: l = tl = (P *)ALLOCA((np+1)*sizeof(P));
1.6 noro 662: win = W_ALLOC(np+1);
1.7 noro 663:
1.6 noro 664: for ( k = 1, win[0] = 1, --np; ; ) {
665: itogfs(1,&u0);
666: /* u0 = product of selected factors */
667: for ( i = 0; i < k; i++ ) {
668: mulp(nvl,u0,fp0[win[i]],&t); u0 = t;
669: }
670: /* we have to consider the content */
1.10 noro 671: /* f0 = c0*u0*v0 */
1.12 noro 672: mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcu);
1.6 noro 673: divsp(nvl,pp0,u0,&v0);
1.12 noro 674: mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcv);
675: mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,mev,&u);
1.7 noro 676: if ( u ) {
677: /* save the factor */
678: reorderp(vl,nvl,u,&t);
1.12 noro 679: /* y -> y-evy */
680: substp(vl,t,vy,yme,tl++);
1.7 noro 681:
682: /* update f,pp0 */
683: divsp(nvl,f,u,&t); f = t;
684: divsp(nvl,pp0,u0,&t); pp0 = t;
685: /* update win, fp0 */
686: for ( i = 0; i < k-1; i++ )
687: for ( j = win[i]+1; j < win[i+1]; j++ )
688: fp0[j-i-1] = fp0[j];
689: for ( j = win[k-1]+1; j <= np; j++ )
690: fp0[j-k] = fp0[j];
691: if ( ( np -= k ) < k ) break;
692: if ( np-win[0]+1 < k )
693: if ( ++k <= np ) {
694: for ( i = 0; i < k; i++ )
695: win[i] = i + 1;
696: continue;
697: } else
698: break;
699: else
700: for ( i = 1; i < k; i++ )
701: win[i] = win[0] + i;
702: } else {
703: if ( ncombi(1,np,k,win) == 0 )
704: if ( k == np ) break;
705: else
706: for ( i = 0, ++k; i < k; i++ )
707: win[i] = i + 1;
708: }
1.6 noro 709: }
1.10 noro 710: reorderp(vl,nvl,f,&t);
1.12 noro 711: /* y -> y-evy */
712: substp(vl,t,vy,yme,tl++);
1.10 noro 713: *tl = 0;
714: for ( dc0 = 0, i = 0; l[i]; i++ ) {
715: NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = l[i];
716: }
717: NEXT(dc) = 0; *dcp = dc0;
1.6 noro 718: }
719:
1.7 noro 720: void next_evaluation_point(int *e,int n)
721: {
722: int i,t,j;
723:
724: for ( i = n-1; i >= 0; i-- )
725: if ( e[i] ) break;
726: if ( i < 0 ) e[n-1] = 1;
727: else if ( i == 0 ) {
728: t = e[0]; e[0] = 0; e[n-1] = t+1;
729: } else {
730: e[i-1]++; t = e[i];
731: for ( j = i; j < n-1; j++ )
732: e[j] = 0;
733: e[n-1] = t-1;
734: }
735: }
736:
737: /*
738: * dc : f1^E1*...*fk^Ek
1.12 noro 739: * find e1,...,ek s.t. fi(mev)^ei | c
1.7 noro 740: * and return f1^e1*...*fk^ek
741: * vl = (vx,vy,rvl)
742: */
743:
1.12 noro 744: void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp)
1.7 noro 745: {
746: DCP dct;
747: P r,c1,c2,t,s,f;
748: int i,d;
749: Q q;
750:
751: for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) {
752: if ( NUM(COEF(dct)) )
753: continue;
754: /* constant part */
1.12 noro 755: substvp_sf(vl,rvl,COEF(dct),mev,&f);
1.7 noro 756: d = QTOS(DEG(dct));
757: for ( i = 0, c1 = c; i < d; i++ )
758: if ( !divtp(vl,c1,f,&c2) )
759: break;
760: else
761: c1 = c2;
762: if ( i ) {
763: STOQ(i,q);
764: pwrp(vl,COEF(dct),q,&s); mulp(vl,r,s,&t); r = t;
765: }
766: }
767: *lcp = r;
768: }
769:
770: void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r)
771: {
772: int i;
773: VL tvl;
774: P g,t;
775: GFS ev;
776:
777: for ( g = f, i = 0, tvl = rvl; tvl; tvl = NEXT(tvl), i++ ) {
778: if ( !mev )
779: ev = 0;
780: else
781: indextogfs(mev[i],&ev);
782: substp(vl,g,tvl->v,(P)ev,&t); g = t;
783: }
784: *r = g;
785: }
786:
787: /*
788: * f <- f(X+sgn*mev)
789: */
790:
791: void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r)
792: {
793: VL tvl;
794: int i;
795: P x,g,t,s;
796: GFS ev;
797:
798: for ( g = f, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) {
799: if ( !mev[i] )
800: continue;
801: indextogfs(mev[i],&ev);
802: MKV(tvl->v,x);
803: if ( sgn > 0 )
804: addp(vl,x,(P)ev,&t);
805: else
806: subp(vl,x,(P)ev,&t);
807: substp(vl,g,tvl->v,t,&s); g = s;
808: }
809: *r = g;
810: }
811:
812: /*
813: * pp(f(0)) = u0*v0
814: */
815:
1.12 noro 816: void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,int *mev,P *up)
1.7 noro 817: {
818: VL tvl,onevl;
819: P t,s,w,u,v,ff,si,wu,wv,fj,cont;
820: UM ydy;
821: V vx,vy;
822: int dy,n,i,dbd,nv,j;
823: int *md;
824: P *uh,*vh;
1.12 noro 825: P x,du0,dv0,m,q,r,fin;
1.7 noro 826: P *cu,*cv;
827: GFSN inv;
828:
1.13 noro 829: /* check the validity of lc's and adjust coeffs */
830: /* f -> lcu*lcv*x^(m+l)+... */
831: mulp(vl,lcu,lcv,&t);
832: if ( !divtp(vl,t,LC(f),&m) ) {
833: *up = 0; return;
834: }
835: mulp(vl,m,f,&t); f = t;
1.12 noro 836: /* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(mev)/am)*x^(m-1)+... */
837: /* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(mev)/bl)*x^(l-1)+... */
838: adjust_coef_sf(vl,rvl,lcu,u0,mev,&u);
839: adjust_coef_sf(vl,rvl,lcv,v0,mev,&v);
1.10 noro 840:
1.12 noro 841: /* f <- f(X+mev), u <- u(X+mev), v <- v(X+mev) */
842: fin = f;
843: shift_sf(vl,rvl,f,mev,1,&s); f = s;
844: shift_sf(vl,rvl,u,mev,1,&s); u = s;
845: shift_sf(vl,rvl,v,mev,1,&s); v = s;
846:
1.7 noro 847: vx = vl->v; vy = NEXT(vl)->v;
848: n = getdeg(vx,f);
849: dy = getdeg(vy,f)+1;
850: MKV(vx,x);
851: cu = (P *)ALLOCA((n+1)*sizeof(P));
852: cv = (P *)ALLOCA((n+1)*sizeof(P));
853:
854: /* ydy = y^dy */
1.10 noro 855: ydy = C_UMALLOC(dy); DEG(ydy) = dy; COEF(ydy)[dy] = _onesf();
1.7 noro 856: setmod_gfsn(ydy);
857:
858: /* (R[y]/(y^dy))[x,X] */
1.10 noro 859: poly_to_gfsn_poly(vl,f,vy,&ff);
1.7 noro 860: poly_to_gfsn_poly(vl,u,vy,&t); u = t;
861: poly_to_gfsn_poly(vl,v,vy,&t); v = t;
862: substvp_sf(vl,rvl,u,0,&u0);
863: substvp_sf(vl,rvl,v,0,&v0);
864:
865: /* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */
1.8 noro 866: extended_gcd_modyk(u0,v0,vx,vy,dy,&cu[0],&cv[0]);
1.7 noro 867:
868: /* dv0 = LC(v0)^(-1)*v0 mod y^dy */
869: invgfsn((GFSN)LC(v0),&inv); mulp(vl,v0,(P)inv,&dv0);
870:
871: /* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */
1.10 noro 872: /* (x*cu[i])*u0+(x*cv[i])*v0 = x^(i+1) */
873: /* x*cu[i] = q*dv0+r => cu[i+1] = r */
874: /* cv[i+1]*v0 = x*cv[i]*v0+q*u0*dv0 = (x*cv[i]+q*u0*inv)*v0 */
1.7 noro 875: for ( i = 1; i <= n; i++ ) {
876: mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]);
1.10 noro 877: mulp(vl,x,cv[i-1],&m); mulp(vl,q,(P)inv,&t);
878: mulp(vl,t,u0,&s);
879: addp(vl,m,s,&cv[i]);
880: }
881:
882: #if 0
883: /* XXX : check */
884: for ( i = 0; i <= n; i++ ) {
885: mulp(vl,cu[i],u0,&m); mulp(vl,cv[i],v0,&s);
886: addp(vl,m,s,&w);
887: printexpr(vl,w);
888: fprintf(asir_out,"\n");
1.7 noro 889: }
1.10 noro 890: #endif
891:
1.7 noro 892: dbd = dbound(vx,f)+1;
893:
894: /* extract homogeneous parts */
895: W_CALLOC(dbd,P,uh); W_CALLOC(dbd,P,vh);
896: for ( i = 0; i <= dbd; i++ ) {
897: exthpc(vl,vx,u,i,&uh[i]); exthpc(vl,vx,v,i,&vh[i]);
898: }
899:
900: /* register degrees in each variables */
901: for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ );
902: md = (int *)ALLOCA(nv*sizeof(int));
903: for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
1.10 noro 904: md[i] = getdeg(tvl->v,f);
1.7 noro 905:
906: /* XXX for removing content of factor wrt vx */
907: NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0;
908:
909: for ( j = 1; j <= dbd; j++ ) {
910: for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
911: if ( getdeg(tvl->v,u)+getdeg(tvl->v,v) > md[i] ) {
912: *up = 0;
913: return;
914: }
915: for ( i = 0, t = 0; i <= j; i++ ) {
916: mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w;
917: }
1.10 noro 918:
1.7 noro 919: /* s = degree j part of (f-uv) */
920: exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s);
921: for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) {
1.10 noro 922: if ( !s )
1.7 noro 923: si = 0;
924: else if ( VR(s) == vx )
925: coefp(s,i,&si);
926: else if ( i == 0 )
927: si = s;
928: else
929: si = 0;
930: if ( si ) {
1.10 noro 931: mulp(vl,si,cv[i],&m); addp(vl,wu,m,&t); wu = t;
932: mulp(vl,si,cu[i],&m); addp(vl,wv,m,&t); wv = t;
1.7 noro 933: }
934: }
935: if ( !wu ) {
1.10 noro 936: gfsn_poly_to_poly(vl,u,vy,&t);
1.12 noro 937: shift_sf(vl,rvl,t,mev,-1,&s);
938: if ( divtp(vl,fin,s,&q) ) {
939: cont_pp_mv_sf(vl,onevl,s,&cont,up);
1.7 noro 940: return;
941: }
942: }
943: if ( !wv ) {
1.10 noro 944: gfsn_poly_to_poly(vl,v,vy,&t);
1.12 noro 945: shift_sf(vl,rvl,t,mev,-1,&s);
946: if ( divtp(vl,fin,s,&q) ) {
1.7 noro 947: cont_pp_mv_sf(vl,onevl,q,&cont,up);
948: return;
949: }
950: }
951: addp(vl,u,wu,&t); u = t;
952: addp(vl,uh[j],wu,&t); uh[j] = t;
953: addp(vl,v,wv,&t); v = t;
954: addp(vl,vh[j],wv,&t); vh[j] = t;
955: }
956: }
957:
1.12 noro 958: void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,int *mev,P *r)
1.7 noro 959: {
960: P lcu0,cu;
961: DCP dc0,dcu,dc;
962:
1.12 noro 963: substvp_sf(vl,rvl,lcu,mev,&lcu0);
1.7 noro 964: divsp(vl,lcu0,LC(u0),&cu);
965: for ( dc0 = 0, dcu = DC(u0); dcu; dcu = NEXT(dcu) ) {
966: if ( !dc0 ) {
967: NEXTDC(dc0,dc);
968: COEF(dc) = lcu;
969: } else {
970: NEXTDC(dc0,dc);
971: mulp(vl,cu,COEF(dcu),&COEF(dc));
972: }
973: DEG(dc) = DEG(dcu);
974: }
975: NEXT(dc) = 0;
976: MKP(VR(u0),dc0,*r);
977: }
978:
1.8 noro 979: void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv)
1.6 noro 980: {
1.8 noro 981: BM g,h,a,b;
982:
983: gfsn_univariate_to_sfbm(u0,dy,&g);
984: gfsn_univariate_to_sfbm(v0,dy,&h);
985: sfexgcd_by_hensel(g,h,dy,&a,&b);
986: sfbm_to_gfsn_univariate(a,x,y,cu);
987: sfbm_to_gfsn_univariate(b,x,y,cv);
988: }
989:
990: /* (F[y])[x] -> F[x][y] */
991:
992: void gfsn_univariate_to_sfbm(P f,int dy,BM *r)
993: {
994: int dx,d,i;
995: BM b;
996: UM cy;
997: DCP dc;
998:
999: dx = getdeg(VR(f),f);
1000: b = BMALLOC(dx,dy);
1001: DEG(b) = dy;
1002: for ( dc = DC(f); dc; dc = NEXT(dc) ) {
1003: /* d : degree in x, cy : poly in y */
1004: d = QTOS(DEG(dc));
1005: cy = BDY((GFSN)COEF(dc));
1006: for ( i = DEG(cy); i >= 0; i-- )
1007: COEF(COEF(b)[i])[d] = COEF(cy)[i];
1008: }
1.9 noro 1009: for ( i = 0; i <= dy; i++ )
1010: degum(COEF(b)[i],dx);
1.8 noro 1011: *r = b;
1012: }
1013:
1014: void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r)
1015: {
1016: P g;
1017: VL vl;
1018:
1019: sfbmtop(f,x,y,&g);
1020: NEWVL(vl); vl->v = x;
1021: NEWVL(NEXT(vl)); NEXT(vl)->v = y;
1022: NEXT(NEXT(vl)) = 0;
1023: poly_to_gfsn_poly(vl,g,y,r);
1.6 noro 1024: }
1025:
1.7 noro 1026: void poly_to_gfsn_poly(VL vl,P f,V v,P *r)
1.6 noro 1027: {
1.8 noro 1028: VL tvl,nvl0,nvl;
1029: P g;
1030:
1031: /* (x,y,...,v,...) -> (x,y,...,v) */
1032: for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
1033: if ( tvl->v != v ) {
1034: NEXTVL(nvl0,nvl);
1035: nvl->v = tvl->v;
1036: }
1037: }
1038: NEXTVL(nvl0,nvl);
1039: nvl->v = v;
1040: NEXT(nvl) = 0;
1041: reorderp(nvl0,vl,f,&g);
1042: poly_to_gfsn_poly_main(g,v,r);
1043: }
1044:
1045: void poly_to_gfsn_poly_main(P f,V v,P *r)
1046: {
1047: int d;
1048: UM u;
1049: GFSN g;
1050: DCP dc,dct,dc0;
1051:
1.9 noro 1052: if ( !f )
1.8 noro 1053: *r = f;
1.9 noro 1054: else if ( NUM(f) || VR(f) == v ) {
1.8 noro 1055: d = getdeg(v,f);
1056: u = UMALLOC(d);
1057: ptosfum(f,u);
1058: MKGFSN(u,g);
1059: *r = (P)g;
1060: } else {
1061: for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
1062: NEXTDC(dc0,dc);
1063: DEG(dc) = DEG(dct);
1064: poly_to_gfsn_poly_main(COEF(dct),v,&COEF(dc));
1065: }
1066: NEXT(dc) = 0;
1067: MKP(VR(f),dc0,*r);
1068: }
1.6 noro 1069: }
1070:
1.7 noro 1071: void gfsn_poly_to_poly(VL vl,P f,V v,P *r)
1.6 noro 1072: {
1.8 noro 1073: VL tvl,nvl0,nvl;
1074: P g;
1075:
1076: gfsn_poly_to_poly_main(f,v,&g);
1077: /* (x,y,...,v,...) -> (x,y,...,v) */
1078: for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
1079: if ( tvl->v != v ) {
1080: NEXTVL(nvl0,nvl);
1081: nvl->v = tvl->v;
1082: }
1083: }
1084: NEXTVL(nvl0,nvl);
1085: nvl->v = v;
1086: NEXT(nvl) = 0;
1087: reorderp(vl,nvl0,g,r);
1088: }
1089:
1090: void gfsn_poly_to_poly_main(P f,V v,P *r)
1091: {
1092: DCP dc,dc0,dct;
1093:
1094: if ( !f )
1095: *r = f;
1096: else if ( NUM(f) ) {
1097: if ( NID((Num)f) == N_GFSN )
1098: sfumtop(v,BDY((GFSN)f),r);
1099: else
1100: *r = f;
1101: } else {
1102: for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
1103: NEXTDC(dc0,dc);
1104: DEG(dc) = DEG(dct);
1105: gfsn_poly_to_poly_main(COEF(dct),v,&COEF(dc));
1106: }
1107: NEXT(dc) = 0;
1108: MKP(VR(f),dc0,*r);
1109: }
1.1 noro 1110: }
1.9 noro 1111:
1112: void printsfum(UM f)
1113: {
1114: int i;
1115:
1116: for ( i = DEG(f); i >= 0; i-- ) {
1117: printf("+(");
1118: printf("%d",IFTOF(COEF(f)[i]));
1119: printf(")*y^%d",i);
1120: }
1121: }
1122:
1123: void printsfbm(BM f)
1124: {
1125: int i;
1126:
1127: for ( i = DEG(f); i >= 0; i-- ) {
1128: printf("+(");
1129: printsfum(COEF(f)[i]);
1130: printf(")*y^%d",i);
1131: }
1132: }
1133: