Annotation of OpenXM_contrib2/asir2018/engine/Fgfs.c, Revision 1.1
1.1 ! noro 1: /* $OpenXM$ */
! 2:
! 3: #include "ca.h"
! 4:
! 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);
! 8: void head_monomial(VL vl,V v,P p,P *coef,P *term);
! 9: void sqfrsfmain(VL vl,P f,DCP *dcp);
! 10: void pthrootsf(P f,Z 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);
! 13: void mfctrsfmain(VL vl, P f, DCP *dcp);
! 14: void next_evaluation_point(int *mev,int n);
! 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);
! 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);
! 19: void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,int *mev,P *r);
! 20: void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv);
! 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);
! 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);
! 27:
! 28: void monomialfctr_sf(VL vl,P p,P *pr,DCP *dcp)
! 29: {
! 30: VL nvl,avl;
! 31: Z d;
! 32: P f,t,s;
! 33: DCP dc0,dc;
! 34: Obj obj;
! 35:
! 36: clctv(vl,p,&nvl);
! 37: for ( dc0 = 0, avl = nvl, f = p; avl; avl = NEXT(avl) ) {
! 38: getmindeg(avl->v,f,&d);
! 39: if ( d ) {
! 40: MKV(avl->v,t);
! 41: simp_ff((Obj)t,&obj); t = (P)obj;
! 42: NEXTDC(dc0,dc); DEG(dc) = d; COEF(dc) = t;
! 43: pwrp(vl,t,d,&s); divsp(vl,f,s,&t); f = t;
! 44: }
! 45: }
! 46: if ( dc0 )
! 47: NEXT(dc) = 0;
! 48: *pr = f; *dcp = dc0;
! 49: }
! 50:
! 51: void lex_lc(P f,P *c)
! 52: {
! 53: if ( !f || NUM(f) )
! 54: *c = f;
! 55: else
! 56: lex_lc(COEF(DC(f)),c);
! 57: }
! 58:
! 59: DCP append_dc(DCP dc,DCP dct)
! 60: {
! 61: DCP dcs;
! 62:
! 63: if ( !dc )
! 64: return dct;
! 65: else {
! 66: for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) );
! 67: NEXT (dcs) = dct;
! 68: return dc;
! 69: }
! 70: }
! 71:
! 72: void sqfrsf(VL vl, P f, DCP *dcp)
! 73: {
! 74: DCP dc,dct;
! 75: Obj obj;
! 76: P t,s,c,cont;
! 77: VL tvl,onevl;
! 78:
! 79: simp_ff((Obj)f,&obj); f = (P)obj;
! 80: lex_lc(f,&c); divsp(vl,f,c,&t); f = t;
! 81: monomialfctr_sf(vl,f,&t,&dc); f = t;
! 82: clctv(vl,f,&tvl); vl = tvl;
! 83: NEWVL(onevl); NEXT(onevl)=0;
! 84: if ( !vl )
! 85: ;
! 86: else if ( !NEXT(vl) ) {
! 87: sfusqfr(f,&dct);
! 88: dc = append_dc(dc,NEXT(dct));
! 89: } else {
! 90: t = f;
! 91: for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
! 92: onevl->v = tvl->v;
! 93: cont_pp_mv_sf(vl,onevl,t,&cont,&s); t = s;
! 94: sqfrsf(vl,cont,&dct);
! 95: dc = append_dc(dc,NEXT(dct));
! 96: }
! 97: sqfrsfmain(vl,t,&dct);
! 98: dc = append_dc(dc,dct);
! 99: }
! 100: NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc;
! 101: *dcp = dct;
! 102: }
! 103:
! 104: void sqfrsfmain(VL vl,P f,DCP *dcp)
! 105: {
! 106: VL tvl;
! 107: DCP dc,dct,dcs;
! 108: P t,s;
! 109: Z m,m1;
! 110: V v;
! 111:
! 112: clctv(vl,f,&tvl); vl = tvl;
! 113: dc = 0;
! 114: t = f;
! 115: for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
! 116: v = tvl->v;
! 117: partial_sqfrsf(vl,v,t,&s,&dct); t = s;
! 118: dc = append_dc(dc,dct);
! 119: }
! 120: if ( !NUM(t) ) {
! 121: STOQ(characteristic_sf(),m);
! 122: pthrootsf(t,m,&s);
! 123: sqfrsfmain(vl,s,&dct);
! 124: for ( dcs = dct; dcs; dcs = NEXT(dcs) ) {
! 125: mulz(DEG(dcs),m,&m1); DEG(dcs) = m1;
! 126: }
! 127: dc = append_dc(dc,dct);
! 128: }
! 129: *dcp = dc;
! 130: }
! 131:
! 132: void pthrootsf(P f,Z m,P *r)
! 133: {
! 134: DCP dc,dc0,dct;
! 135: Z qn,rn;
! 136:
! 137: if ( NUM(f) )
! 138: pthrootgfs((GFS)f,(GFS *)r);
! 139: else {
! 140: dc = DC(f);
! 141: dc0 = 0;
! 142: for ( dc0 = 0; dc; dc = NEXT(dc) ) {
! 143: NEXTDC(dc0,dct);
! 144: pthrootsf(COEF(dc),m,&COEF(dct));
! 145: if ( DEG(dc) ) {
! 146: divqrz(DEG(dc),m,&qn,&rn);
! 147: if ( rn )
! 148: error("pthrootsf : cannot happen");
! 149: DEG(dct) = qn;
! 150: } else
! 151: DEG(dct) = 0;
! 152: }
! 153: NEXT(dct) = 0;
! 154: MKP(VR(f),dc0,*r);
! 155: }
! 156: }
! 157:
! 158: void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp)
! 159: {
! 160: P ps[2];
! 161: DCP dc0,dc;
! 162: int m;
! 163: P t,flat,flat1,g,df,q;
! 164:
! 165: diffp(vl,f,v,&df);
! 166: if ( !df ) {
! 167: *dcp = 0;
! 168: *r = f;
! 169: return;
! 170: }
! 171: ps[0] = f; ps[1] = df;
! 172: gcdsf(vl,ps,2,&g);
! 173: divsp(vl,f,g,&flat);
! 174: m = 0;
! 175: t = f;
! 176: dc0 = 0;
! 177: while ( !NUM(flat) ) {
! 178: while ( divtp(vl,t,flat,&q) ) {
! 179: t = q; m++;
! 180: }
! 181: ps[0] = t; ps[1] = flat;
! 182: gcdsf(vl,ps,2,&flat1);
! 183: divsp(vl,flat,flat1,&g);
! 184: flat = flat1;
! 185: NEXTDC(dc0,dc);
! 186: COEF(dc) = g;
! 187: STOQ(m,DEG(dc));
! 188: }
! 189: NEXT(dc) = 0;
! 190: *dcp = dc0;
! 191: *r = t;
! 192: }
! 193:
! 194: void gcdsf(VL vl,P *pa,int k,P *r)
! 195: {
! 196: P *ps,*pl,*pm;
! 197: P **cp;
! 198: int *cn;
! 199: DCP *ml;
! 200: Obj obj;
! 201: int i,j,l,m;
! 202: P mg,mgsf,t;
! 203: VL avl,nvl,tvl,svl;
! 204:
! 205: ps = (P *)ALLOCA(k*sizeof(P));
! 206: for ( i = 0, m = 0; i < k; i++ ) {
! 207: simp_ff((Obj)pa[i],&obj);
! 208: if ( obj )
! 209: ps[m++] = (P)obj;
! 210: }
! 211: if ( !m ) {
! 212: *r = 0;
! 213: return;
! 214: }
! 215: if ( m == 1 ) {
! 216: *r = ps[0];
! 217: return;
! 218: }
! 219: pl = (P *)ALLOCA(m*sizeof(P));
! 220: ml = (DCP *)ALLOCA(m*sizeof(DCP));
! 221: for ( i = 0; i < m; i++ )
! 222: monomialfctr(vl,ps[i],&pl[i],&ml[i]);
! 223: gcdmonomial(vl,ml,m,&mg); simp_ff((Obj)mg,&obj); mgsf = (P)obj;
! 224: for ( i = 0, nvl = vl, avl = 0; nvl && i < m; i++ ) {
! 225: clctv(vl,pl[i],&tvl);
! 226: intersectv(nvl,tvl,&svl); nvl = svl;
! 227: mergev(vl,avl,tvl,&svl); avl = svl;
! 228: }
! 229: if ( !nvl ) {
! 230: *r = mgsf;
! 231: return;
! 232: }
! 233: if ( !NEXT(avl) ) {
! 234: ugcdsf(pl,m,&t);
! 235: mulp(vl,mgsf,t,r);
! 236: return;
! 237: }
! 238: for ( tvl = nvl, i = 0; tvl; tvl = NEXT(tvl), i++ );
! 239: for ( tvl = avl, j = 0; tvl; tvl = NEXT(tvl), j++ );
! 240: if ( i == j ) {
! 241: /* all the pl[i]'s have the same variables */
! 242: gcdsf_main(avl,pl,m,&t);
! 243: } else {
! 244: cp = (P **)ALLOCA(m*sizeof(P *));
! 245: cn = (int *)ALLOCA(m*sizeof(int));
! 246: for ( i = 0; i < m; i++ ) {
! 247: cp[i] = (P *)ALLOCA(lengthp(pl[i])*sizeof(P));
! 248: cn[i] = pcoef(vl,nvl,pl[i],cp[i]);
! 249: }
! 250: for ( i = j = 0; i < m; i++ )
! 251: j += cn[i];
! 252: pm = (P *)ALLOCA(j*sizeof(P));
! 253: for ( i = l = 0; i < m; i++ )
! 254: for ( j = 0; j < cn[i]; j++ )
! 255: pm[l++] = cp[i][j];
! 256: gcdsf(vl,pm,l,&t);
! 257: }
! 258: mulp(vl,mgsf,t,r);
! 259: }
! 260:
! 261: /* univariate gcd */
! 262:
! 263: void ugcdsf(P *pa,int m,P *r)
! 264: {
! 265: P *ps;
! 266: int i;
! 267: UM w1,w2,w3,w;
! 268: int d;
! 269: V v;
! 270:
! 271: if ( m == 1 ) {
! 272: *r = pa[0];
! 273: return;
! 274: }
! 275: for ( i = 0; i < m; i++ )
! 276: if ( NUM(pa[i]) ) {
! 277: itogfs(1,(GFS *)r);
! 278: return;
! 279: }
! 280: ps = (P *)ALLOCA(m*sizeof(P));
! 281: sort_by_deg(m,pa,ps);
! 282: v = VR(ps[m-1]);
! 283: d = getdeg(v,ps[m-1]);
! 284: w1 = W_UMALLOC(d);
! 285: w2 = W_UMALLOC(d);
! 286: w3 = W_UMALLOC(d);
! 287: ptosfum(ps[0],w1);
! 288: for ( i = 1; i < m; i++ ) {
! 289: ptosfum(ps[i],w2);
! 290: gcdsfum(w1,w2,w3);
! 291: w = w1; w1 = w3; w3 = w;
! 292: if ( !DEG(w1) ) {
! 293: itogfs(1,(GFS *)r);
! 294: return;
! 295: }
! 296: }
! 297: sfumtop(v,w1,r);
! 298: }
! 299:
! 300: /* deg(HT(p),v), where p is considered as distributed poly over F[v] */
! 301: int gethdeg(VL vl,V v,P p)
! 302: {
! 303: DCP dc;
! 304: Z dmax;
! 305: P cmax;
! 306:
! 307: if ( !p )
! 308: return -1;
! 309: else if ( NUM(p) )
! 310: return 0;
! 311: else if ( VR(p) != v )
! 312: /* HT(p) = HT(lc(p))*x^D */
! 313: return gethdeg(vl,v,COEF(DC(p)));
! 314: else {
! 315: /* VR(p) = v */
! 316: dc = DC(p); dmax = DEG(dc); cmax = COEF(dc);
! 317: for ( dc = NEXT(dc); dc; dc = NEXT(dc) )
! 318: if ( compp(vl,COEF(dc),cmax) > 0 ) {
! 319: dmax = DEG(dc); cmax = COEF(dc);
! 320: }
! 321: return QTOS(dmax);
! 322: }
! 323: }
! 324:
! 325: /* all the pa[i]'s have the same variables (=vl) */
! 326:
! 327: void gcdsf_main(VL vl,P *pa,int m,P *r)
! 328: {
! 329: int nv,i,i0,imin,d,d0,d1,d2,dmin,index;
! 330: V v,v0,vmin;
! 331: VL tvl,nvl,rvl,nvl0,rvl0;
! 332: P *pc, *ps, *ph,*lps;
! 333: P x,t,cont,hg,g,hm,mod,s;
! 334: P hge,ge,ce,he,u,cof1e,mode,mod1,adj,cof1,coadj,q;
! 335: GFS sf;
! 336:
! 337: for ( nv = 0, tvl = vl; tvl; tvl = NEXT(tvl), nv++);
! 338: if ( nv == 1 ) {
! 339: ugcdsf(pa,m,r);
! 340: return;
! 341: }
! 342: /* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */
! 343: tvl = vl;
! 344: do {
! 345: v = tvl->v;
! 346: i = 0;
! 347: do {
! 348: d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]);
! 349: if ( i == 0 || (d < d0) ) {
! 350: d0 = d; i0 = i; v0 = v;
! 351: }
! 352: } while ( ++i < m );
! 353: if ( tvl == vl || (d0 < dmin) ) {
! 354: dmin = d0; imin = i0; vmin = v0;
! 355: }
! 356: } while ( (tvl = NEXT(tvl)) != 0 );
! 357:
! 358: /* reorder variables so that vmin is the last variable */
! 359: for ( nvl0 = 0, rvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) )
! 360: if ( tvl->v != vmin ) {
! 361: NEXTVL(nvl0,nvl); nvl->v = tvl->v;
! 362: NEXTVL(rvl0,rvl); rvl->v = tvl->v;
! 363: }
! 364: /* rvl = remaining variables */
! 365: NEXT(rvl) = 0; rvl = rvl0;
! 366: /* nvl = ...,vmin */
! 367: NEXTVL(nvl0,nvl); nvl->v = vmin; NEXT(nvl) = 0; nvl = nvl0;
! 368: MKV(vmin,x);
! 369:
! 370: /* for content and primitive part */
! 371: pc = (P *)ALLOCA(m*sizeof(P));
! 372: ps = (P *)ALLOCA(m*sizeof(P));
! 373: ph = (P *)ALLOCA(m*sizeof(P));
! 374: /* separate the contents */
! 375: for ( i = 0; i < m; i++ ) {
! 376: reorderp(nvl,vl,pa[i],&t);
! 377: cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]);
! 378: head_monomial(nvl,vmin,ps[i],&ph[i],&t);
! 379: }
! 380: ugcdsf(pc,m,&cont);
! 381: ugcdsf(ph,m,&hg);
! 382:
! 383: /* for hg*pp (used in check phase) */
! 384: lps = (P *)ALLOCA(m*sizeof(P));
! 385: for ( i = 0; i < m; i++ )
! 386: mulp(nvl,hg,ps[i],&lps[i]);
! 387:
! 388: while ( 1 ) {
! 389: g = 0;
! 390: cof1 = 0;
! 391: hm = 0;
! 392: itogfs(1,(GFS *)&mod);
! 393: index = 0;
! 394: for ( index = 0; getdeg(vmin,mod) <= d+1; index++ ) {
! 395: /* evaluation pt */
! 396: indextogfs(index,(GFS *)&s);
! 397: substp(nvl,hg,vmin,s,&hge);
! 398: if ( !hge )
! 399: continue;
! 400: for ( i = 0; i < m; i++ )
! 401: substp(nvl,ps[i],vmin,s,&ph[i]);
! 402: /* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */
! 403: gcdsf(nvl,ph,m,&ge);
! 404: head_monomial(nvl,vmin,ge,&ce,&he);
! 405: if ( NUM(he) ) {
! 406: *r = cont;
! 407: return;
! 408: }
! 409: divgfs((GFS)hge,(GFS)ce,&sf); t = (P)sf;
! 410: mulp(nvl,t,ge,&u); ge = u;
! 411: divsp(nvl,ph[imin],ge,&t); mulp(nvl,hge,t,&cof1e);
! 412: /* hm=0 : reset; he==hm : lucky */
! 413: if ( !hm || !compp(nvl,he,hm) ) {
! 414: substp(nvl,mod,vmin,s,&mode); divsp(nvl,mod,mode,&mod1);
! 415: /* adj = mod/(mod|x=s)*(ge-g|x=s) */
! 416: substp(nvl,g,vmin,s,&t);
! 417: subp(nvl,ge,t,&u); mulp(nvl,mod1,u,&adj);
! 418: /* coadj = mod/(mod|vmin=s)*(cof1e-cof1e|vmin=s) */
! 419: substp(nvl,cof1,vmin,s,&t);
! 420: subp(nvl,cof1e,t,&u); mulp(nvl,mod1,u,&coadj);
! 421: if ( !adj ) {
! 422: /* adj == gcd ? */
! 423: for ( i = 0; i < m; i++ )
! 424: if ( !divtp(nvl,lps[i],g,&t) )
! 425: break;
! 426: if ( i == m ) {
! 427: cont_pp_mv_sf(nvl,rvl,g,&t,&u);
! 428: mulp(nvl,cont,u,&t);
! 429: reorderp(vl,nvl,t,r);
! 430: return;
! 431: }
! 432: } else if ( !coadj ) {
! 433: /* ps[imin]/coadj == gcd ? */
! 434: if ( divtp(nvl,lps[imin],cof1,&q) ) {
! 435: for ( i = 0; i < m; i++ )
! 436: if ( !divtp(nvl,lps[i],q,&t) )
! 437: break;
! 438: if ( i == m ) {
! 439: cont_pp_mv_sf(nvl,rvl,q,&t,&u);
! 440: mulp(nvl,cont,u,&t);
! 441: reorderp(vl,nvl,t,r);
! 442: return;
! 443: }
! 444: }
! 445: }
! 446: addp(nvl,g,adj,&t); g = t;
! 447: addp(nvl,cof1,coadj,&t); cof1 = t;
! 448: subp(nvl,x,s,&t); mulp(nvl,mod,t,&u); mod = u;
! 449: hm = he;
! 450: } else {
! 451: d1 = homdeg(hm); d2 = homdeg(he);
! 452: if ( d1 < d2 ) /* we use current hm */
! 453: continue;
! 454: else if ( d1 > d2 ) {
! 455: /* use he */
! 456: g = ge;
! 457: cof1 = cof1e;
! 458: hm = he;
! 459: subp(nvl,x,s,&mod);
! 460: } else {
! 461: /* d1==d2, but hm!=he => both are unlucky */
! 462: g = 0;
! 463: cof1 = 0;
! 464: itogfs(1,(GFS *)&mod);
! 465: }
! 466: }
! 467: }
! 468: }
! 469: }
! 470:
! 471: void head_monomial(VL vl,V v,P p,P *coef,P *term)
! 472: {
! 473: P t,s,u;
! 474: DCP dc;
! 475: GFS one;
! 476:
! 477: itogfs(1,&one);
! 478: t = (P)one;
! 479: while ( 1 ) {
! 480: if ( NUM(p) || VR(p) == v ) {
! 481: *coef = p;
! 482: *term = t;
! 483: return;
! 484: } else {
! 485: NEWDC(dc);
! 486: COEF(dc) = (P)one; DEG(dc) = DEG(DC(p));
! 487: MKP(VR(p),dc,s);
! 488: mulp(vl,t,s,&u); t = u;
! 489: p = COEF(DC(p));
! 490: }
! 491: }
! 492: }
! 493:
! 494: void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)
! 495: {
! 496: DP dp;
! 497: MP t;
! 498: int i,m;
! 499: P *ps;
! 500: struct order_spec *spec, *currentspec;
! 501: extern struct order_spec *dp_current_spec;
! 502:
! 503: currentspec = dp_current_spec;
! 504: create_order_spec(0,0,&spec);
! 505: initd(spec);
! 506: ptod(vl,rvl,p,&dp);
! 507: for ( t = BDY(dp), m = 0; t; t = NEXT(t), m++ );
! 508: ps = (P *)ALLOCA(m*sizeof(P));
! 509: for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ )
! 510: ps[i] = (P)C(t);
! 511: gcdsf(vl,ps,m,c);
! 512: divsp(vl,p,*c,pp);
! 513: initd(currentspec);
! 514: }
! 515:
! 516: void mfctrsf(VL vl, P f, DCP *dcp)
! 517: {
! 518: DCP dc0,dc,dct,dcs,dcr;
! 519: Obj obj;
! 520:
! 521: simp_ff((Obj)f,&obj); f = (P)obj;
! 522: sqfrsf(vl,f,&dct);
! 523: dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0;
! 524: for ( ; dct; dct = NEXT(dct) ) {
! 525: mfctrsfmain(vl,COEF(dct),&dcs);
! 526: for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
! 527: DEG(dcr) = DEG(dct);
! 528: for ( ; NEXT(dc); dc = NEXT(dc) );
! 529: NEXT(dc) = dcs;
! 530: }
! 531: *dcp = dc0;
! 532: }
! 533:
! 534: /* f : sqfr, non const */
! 535:
! 536: void mfctrsfmain(VL vl, P f, DCP *dcp)
! 537: {
! 538: VL tvl,nvl,rvl;
! 539: DCP dc,dc0,dc1,dc2,dct,lcfdc,dcs;
! 540: int imin,inext,i,j,n,k,np;
! 541: int *da;
! 542: V vx,vy;
! 543: V *va;
! 544: P *l,*tl;
! 545: P gcd,g,df,dfmin;
! 546: P pa[2];
! 547: P f0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s;
! 548: P ype,yme,fin;
! 549: GFS ev,evy;
! 550: P *fp0;
! 551: int *mev,*win;
! 552:
! 553: clctv(vl,f,&tvl); vl = tvl;
! 554: if ( !vl )
! 555: error("mfctrsfmain : cannot happen");
! 556: if ( !NEXT(vl) ) {
! 557: /* univariate */
! 558: ufctrsf(f,&dc);
! 559: /* remove lc */
! 560: *dcp = NEXT(dc);
! 561: return;
! 562: }
! 563: for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ );
! 564: va = (V *)ALLOCA(n*sizeof(V));
! 565: da = (int *)ALLOCA(n*sizeof(int));
! 566: /* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */
! 567: imin = -1;
! 568: for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) {
! 569: va[i] = tvl->v;
! 570: da[i] = getdeg(va[i],f);
! 571: diffp(vl,f,va[i],&df);
! 572: if ( !df )
! 573: continue;
! 574: if ( imin < 0 || da[i] < da[imin] ) {
! 575: dfmin = df;
! 576: imin = i;
! 577: }
! 578: }
! 579: /* find v1 neq v s.t. deg(f,v) is minimal */
! 580: inext = -1;
! 581: for ( i = 0; i < n; i++ ) {
! 582: if ( i == imin )
! 583: continue;
! 584: if ( inext < 0 || da[i] < da[inext] )
! 585: inext = i;
! 586: }
! 587: pa[0] = f;
! 588: pa[1] = dfmin;
! 589: gcdsf(vl,pa,2,&gcd);
! 590: if ( !NUM(gcd) ) {
! 591: /* f = gcd * f/gcd */
! 592: mfctrsfmain(vl,gcd,&dc1);
! 593: divsp(vl,f,gcd,&g);
! 594: mfctrsfmain(vl,g,&dc2);
! 595: for ( dct = dc1; NEXT(dct); dct = NEXT(dct) );
! 596: NEXT(dct) = dc2;
! 597: *dcp = dc1;
! 598: return;
! 599: }
! 600: /* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */
! 601: nvl = 0;
! 602: NEXTVL(nvl,tvl); tvl->v = va[imin];
! 603: NEXTVL(nvl,tvl); tvl->v = va[inext];
! 604: for ( i = 0; i < n; i++ ) {
! 605: if ( i == imin || i == inext )
! 606: continue;
! 607: NEXTVL(nvl,tvl); tvl->v = va[i];
! 608: }
! 609: NEXT(tvl) = 0;
! 610:
! 611: fin = f;
! 612: reorderp(nvl,vl,f,&g); f = g;
! 613: vx = nvl->v;
! 614: vy = NEXT(nvl)->v;
! 615: MKV(vx,x);
! 616: MKV(vy,y);
! 617: /* remaining variables */
! 618: rvl = NEXT(NEXT(nvl));
! 619: if ( !rvl ) {
! 620: /* bivariate */
! 621: sfbfctr(f,vx,vy,getdeg(vx,f),&dc1);
! 622: for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) {
! 623: NEXTDC(dc0,dc);
! 624: DEG(dc) = ONE;
! 625: reorderp(vl,nvl,COEF(dc1),&COEF(dc));
! 626: }
! 627: NEXT(dc) = 0;
! 628: *dcp = dc0;
! 629: return;
! 630: }
! 631: /* n >= 3; nvl = (vx,vy,X) */
! 632: /* find good evaluation pt for X */
! 633: mev = (int *)CALLOC(n-2,sizeof(int));
! 634: while ( 1 ) {
! 635: /* lcf(mev)=0 => invalid */
! 636: substvp_sf(nvl,rvl,COEF(DC(f)),mev,&t);
! 637: if ( t ) {
! 638: substvp_sf(nvl,rvl,f,mev,&f0);
! 639: pa[0] = f0;
! 640: diffp(nvl,f0,vx,&pa[1]);
! 641: if ( pa[1] ) {
! 642: gcdsf(nvl,pa,2,&gcd);
! 643: /* XXX maybe we have to accept the case where gcd is a poly of y */
! 644: if ( NUM(gcd) )
! 645: break;
! 646: }
! 647: }
! 648: /* XXX if generated indices exceed q of GF(q) => error in indextogfs */
! 649: next_evaluation_point(mev,n-2);
! 650: }
! 651: /* f0 = f(x,y,mev) */
! 652: /* separate content; f0 may have the content wrt x */
! 653: cont_pp_sfp(nvl,f0,&c0,&pp0);
! 654:
! 655: /* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */
! 656: sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0;
! 657:
! 658: if ( !NEXT(dc) ) {
! 659: /* f is irreducible */
! 660: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = fin; NEXT(dc) = 0;
! 661: *dcp = dc;
! 662: return;
! 663: }
! 664: /* ype = y+evy, yme = y-evy */
! 665: addp(nvl,y,(P)evy,&ype); subp(nvl,y,(P)evy,&yme);
! 666:
! 667: /* shift c0; c0 <- c0(y+evy) */
! 668: substp(nvl,c0,vy,ype,&s); c0 = s;
! 669:
! 670: /* shift f; f <- f(y+evy) */
! 671: substp(nvl,f,vy,ype,&s); f = s;
! 672:
! 673: /* now f(x,0,mev) = c0 * prod dc */
! 674:
! 675: /* factorize lc_x(f) */
! 676: lcf = COEF(DC(f));
! 677: mfctrsf(nvl,lcf,&dct);
! 678: /* skip the first element (= a number) */
! 679: lcfdc = NEXT(dct);
! 680:
! 681: /* np = number of bivariate factors */
! 682: for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ );
! 683: fp0 = (P *)ALLOCA((np+1)*sizeof(P));
! 684: for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ )
! 685: fp0[i] = COEF(dct);
! 686: fp0[np] = 0;
! 687: l = tl = (P *)ALLOCA((np+1)*sizeof(P));
! 688: win = W_ALLOC(np+1);
! 689:
! 690: for ( k = 1, win[0] = 1, --np; ; ) {
! 691: itogfs(1,(GFS *)&u0);
! 692: /* u0 = product of selected factors */
! 693: for ( i = 0; i < k; i++ ) {
! 694: mulp(nvl,u0,fp0[win[i]],&t); u0 = t;
! 695: }
! 696: /* we have to consider the content */
! 697: /* f0 = c0*u0*v0 */
! 698: mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcu);
! 699: divsp(nvl,pp0,u0,&v0);
! 700: mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcv);
! 701: mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,mev,&u);
! 702: if ( u ) {
! 703: /* save the factor */
! 704: reorderp(vl,nvl,u,&t);
! 705: /* y -> y-evy */
! 706: substp(vl,t,vy,yme,tl++);
! 707:
! 708: /* update f,pp0 */
! 709: divsp(nvl,f,u,&t); f = t;
! 710: divsp(nvl,pp0,u0,&t); pp0 = t;
! 711: /* update win, fp0 */
! 712: for ( i = 0; i < k-1; i++ )
! 713: for ( j = win[i]+1; j < win[i+1]; j++ )
! 714: fp0[j-i-1] = fp0[j];
! 715: for ( j = win[k-1]+1; j <= np; j++ )
! 716: fp0[j-k] = fp0[j];
! 717: if ( ( np -= k ) < k ) break;
! 718: if ( np-win[0]+1 < k )
! 719: if ( ++k <= np ) {
! 720: for ( i = 0; i < k; i++ )
! 721: win[i] = i + 1;
! 722: continue;
! 723: } else
! 724: break;
! 725: else
! 726: for ( i = 1; i < k; i++ )
! 727: win[i] = win[0] + i;
! 728: } else {
! 729: if ( ncombi(1,np,k,win) == 0 ) {
! 730: if ( k == np ) break;
! 731: else
! 732: for ( i = 0, ++k; i < k; i++ )
! 733: win[i] = i + 1;
! 734: }
! 735: }
! 736: }
! 737: reorderp(vl,nvl,f,&t);
! 738: /* y -> y-evy */
! 739: substp(vl,t,vy,yme,tl++);
! 740: *tl = 0;
! 741: for ( dc0 = 0, i = 0; l[i]; i++ ) {
! 742: NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = l[i];
! 743: }
! 744: NEXT(dc) = 0; *dcp = dc0;
! 745: }
! 746:
! 747: void next_evaluation_point(int *e,int n)
! 748: {
! 749: int i,t,j;
! 750:
! 751: for ( i = n-1; i >= 0; i-- )
! 752: if ( e[i] ) break;
! 753: if ( i < 0 ) e[n-1] = 1;
! 754: else if ( i == 0 ) {
! 755: t = e[0]; e[0] = 0; e[n-1] = t+1;
! 756: } else {
! 757: e[i-1]++; t = e[i];
! 758: for ( j = i; j < n-1; j++ )
! 759: e[j] = 0;
! 760: e[n-1] = t-1;
! 761: }
! 762: }
! 763:
! 764: /*
! 765: * dc : f1^E1*...*fk^Ek
! 766: * find e1,...,ek s.t. fi(mev)^ei | c
! 767: * and return f1^e1*...*fk^ek
! 768: * vl = (vx,vy,rvl)
! 769: */
! 770:
! 771: void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp)
! 772: {
! 773: DCP dct;
! 774: P r,c1,c2,t,s,f;
! 775: int i,d;
! 776: Z q;
! 777:
! 778: for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) {
! 779: if ( NUM(COEF(dct)) )
! 780: continue;
! 781: /* constant part */
! 782: substvp_sf(vl,rvl,COEF(dct),mev,&f);
! 783: d = QTOS(DEG(dct));
! 784: for ( i = 0, c1 = c; i < d; i++ )
! 785: if ( !divtp(vl,c1,f,&c2) )
! 786: break;
! 787: else
! 788: c1 = c2;
! 789: if ( i ) {
! 790: STOQ(i,q);
! 791: pwrp(vl,COEF(dct),q,&s); mulp(vl,r,s,&t); r = t;
! 792: }
! 793: }
! 794: *lcp = r;
! 795: }
! 796:
! 797: void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r)
! 798: {
! 799: int i;
! 800: VL tvl;
! 801: P g,t;
! 802: GFS ev;
! 803:
! 804: for ( g = f, i = 0, tvl = rvl; tvl; tvl = NEXT(tvl), i++ ) {
! 805: if ( !mev )
! 806: ev = 0;
! 807: else
! 808: indextogfs(mev[i],&ev);
! 809: substp(vl,g,tvl->v,(P)ev,&t); g = t;
! 810: }
! 811: *r = g;
! 812: }
! 813:
! 814: /*
! 815: * f <- f(X+sgn*mev)
! 816: */
! 817:
! 818: void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r)
! 819: {
! 820: VL tvl;
! 821: int i;
! 822: P x,g,t,s;
! 823: GFS ev;
! 824:
! 825: for ( g = f, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) {
! 826: if ( !mev[i] )
! 827: continue;
! 828: indextogfs(mev[i],&ev);
! 829: MKV(tvl->v,x);
! 830: if ( sgn > 0 )
! 831: addp(vl,x,(P)ev,&t);
! 832: else
! 833: subp(vl,x,(P)ev,&t);
! 834: substp(vl,g,tvl->v,t,&s); g = s;
! 835: }
! 836: *r = g;
! 837: }
! 838:
! 839: /*
! 840: * pp(f(0)) = u0*v0
! 841: */
! 842:
! 843: void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,int *mev,P *up)
! 844: {
! 845: VL tvl,onevl;
! 846: P t,s,w,u,v,ff,si,wu,wv,fj,cont;
! 847: UM ydy;
! 848: V vx,vy;
! 849: int dy,n,i,dbd,nv,j;
! 850: int *md;
! 851: P *uh,*vh;
! 852: P x,du0,dv0,m,q,r,fin;
! 853: P *cu,*cv;
! 854: GFSN inv;
! 855:
! 856: /* check the validity of lc's and adjust coeffs */
! 857: /* f -> lcu*lcv*x^(m+l)+... */
! 858: mulp(vl,lcu,lcv,&t);
! 859: if ( !divtp(vl,t,LC(f),&m) ) {
! 860: *up = 0; return;
! 861: }
! 862: mulp(vl,m,f,&t); f = t;
! 863: /* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(mev)/am)*x^(m-1)+... */
! 864: /* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(mev)/bl)*x^(l-1)+... */
! 865: adjust_coef_sf(vl,rvl,lcu,u0,mev,&u);
! 866: adjust_coef_sf(vl,rvl,lcv,v0,mev,&v);
! 867:
! 868: /* f <- f(X+mev), u <- u(X+mev), v <- v(X+mev) */
! 869: fin = f;
! 870: shift_sf(vl,rvl,f,mev,1,&s); f = s;
! 871: shift_sf(vl,rvl,u,mev,1,&s); u = s;
! 872: shift_sf(vl,rvl,v,mev,1,&s); v = s;
! 873:
! 874: vx = vl->v; vy = NEXT(vl)->v;
! 875: n = getdeg(vx,f);
! 876: dy = getdeg(vy,f)+1;
! 877: MKV(vx,x);
! 878: cu = (P *)ALLOCA((n+1)*sizeof(P));
! 879: cv = (P *)ALLOCA((n+1)*sizeof(P));
! 880:
! 881: /* ydy = y^dy */
! 882: ydy = C_UMALLOC(dy); DEG(ydy) = dy; COEF(ydy)[dy] = _onesf();
! 883: setmod_gfsn(ydy);
! 884:
! 885: /* (R[y]/(y^dy))[x,X] */
! 886: poly_to_gfsn_poly(vl,f,vy,&ff);
! 887: poly_to_gfsn_poly(vl,u,vy,&t); u = t;
! 888: poly_to_gfsn_poly(vl,v,vy,&t); v = t;
! 889: substvp_sf(vl,rvl,u,0,&u0);
! 890: substvp_sf(vl,rvl,v,0,&v0);
! 891:
! 892: /* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */
! 893: extended_gcd_modyk(u0,v0,vx,vy,dy,&cu[0],&cv[0]);
! 894:
! 895: /* dv0 = LC(v0)^(-1)*v0 mod y^dy */
! 896: invgfsn((GFSN)LC(v0),&inv); mulp(vl,v0,(P)inv,&dv0);
! 897:
! 898: /* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */
! 899: /* (x*cu[i])*u0+(x*cv[i])*v0 = x^(i+1) */
! 900: /* x*cu[i] = q*dv0+r => cu[i+1] = r */
! 901: /* cv[i+1]*v0 = x*cv[i]*v0+q*u0*dv0 = (x*cv[i]+q*u0*inv)*v0 */
! 902: for ( i = 1; i <= n; i++ ) {
! 903: mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]);
! 904: mulp(vl,x,cv[i-1],&m); mulp(vl,q,(P)inv,&t);
! 905: mulp(vl,t,u0,&s);
! 906: addp(vl,m,s,&cv[i]);
! 907: }
! 908:
! 909: #if 0
! 910: /* XXX : check */
! 911: for ( i = 0; i <= n; i++ ) {
! 912: mulp(vl,cu[i],u0,&m); mulp(vl,cv[i],v0,&s);
! 913: addp(vl,m,s,&w);
! 914: printexpr(vl,w);
! 915: fprintf(asir_out,"\n");
! 916: }
! 917: #endif
! 918:
! 919: dbd = dbound(vx,f)+1;
! 920:
! 921: /* extract homogeneous parts */
! 922: W_CALLOC(dbd,P,uh); W_CALLOC(dbd,P,vh);
! 923: for ( i = 0; i <= dbd; i++ ) {
! 924: exthpc(vl,vx,u,i,&uh[i]); exthpc(vl,vx,v,i,&vh[i]);
! 925: }
! 926:
! 927: /* register degrees in each variables */
! 928: for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ );
! 929: md = (int *)ALLOCA(nv*sizeof(int));
! 930: for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
! 931: md[i] = getdeg(tvl->v,f);
! 932:
! 933: /* XXX for removing content of factor wrt vx */
! 934: NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0;
! 935:
! 936: for ( j = 1; j <= dbd; j++ ) {
! 937: for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
! 938: if ( getdeg(tvl->v,u)+getdeg(tvl->v,v) > md[i] ) {
! 939: *up = 0;
! 940: return;
! 941: }
! 942: for ( i = 0, t = 0; i <= j; i++ ) {
! 943: mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w;
! 944: }
! 945:
! 946: /* s = degree j part of (f-uv) */
! 947: exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s);
! 948: for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) {
! 949: if ( !s )
! 950: si = 0;
! 951: else if ( VR(s) == vx )
! 952: coefp(s,i,&si);
! 953: else if ( i == 0 )
! 954: si = s;
! 955: else
! 956: si = 0;
! 957: if ( si ) {
! 958: mulp(vl,si,cv[i],&m); addp(vl,wu,m,&t); wu = t;
! 959: mulp(vl,si,cu[i],&m); addp(vl,wv,m,&t); wv = t;
! 960: }
! 961: }
! 962: if ( !wu ) {
! 963: gfsn_poly_to_poly(vl,u,vy,&t);
! 964: shift_sf(vl,rvl,t,mev,-1,&s);
! 965: if ( divtp(vl,fin,s,&q) ) {
! 966: cont_pp_mv_sf(vl,onevl,s,&cont,up);
! 967: return;
! 968: }
! 969: }
! 970: if ( !wv ) {
! 971: gfsn_poly_to_poly(vl,v,vy,&t);
! 972: shift_sf(vl,rvl,t,mev,-1,&s);
! 973: if ( divtp(vl,fin,s,&q) ) {
! 974: cont_pp_mv_sf(vl,onevl,q,&cont,up);
! 975: return;
! 976: }
! 977: }
! 978: addp(vl,u,wu,&t); u = t;
! 979: addp(vl,uh[j],wu,&t); uh[j] = t;
! 980: addp(vl,v,wv,&t); v = t;
! 981: addp(vl,vh[j],wv,&t); vh[j] = t;
! 982: }
! 983: gfsn_poly_to_poly(vl,u,vy,&t);
! 984: shift_sf(vl,rvl,t,mev,-1,&s);
! 985: if ( divtp(vl,fin,s,&q) )
! 986: cont_pp_mv_sf(vl,onevl,s,&cont,up);
! 987: else
! 988: *up = 0;
! 989: }
! 990:
! 991: void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,int *mev,P *r)
! 992: {
! 993: P lcu0,cu;
! 994: DCP dc0,dcu,dc;
! 995:
! 996: substvp_sf(vl,rvl,lcu,mev,&lcu0);
! 997: divsp(vl,lcu0,LC(u0),&cu);
! 998: for ( dc0 = 0, dcu = DC(u0); dcu; dcu = NEXT(dcu) ) {
! 999: if ( !dc0 ) {
! 1000: NEXTDC(dc0,dc);
! 1001: COEF(dc) = lcu;
! 1002: } else {
! 1003: NEXTDC(dc0,dc);
! 1004: mulp(vl,cu,COEF(dcu),&COEF(dc));
! 1005: }
! 1006: DEG(dc) = DEG(dcu);
! 1007: }
! 1008: NEXT(dc) = 0;
! 1009: MKP(VR(u0),dc0,*r);
! 1010: }
! 1011:
! 1012: void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv)
! 1013: {
! 1014: BM g,h,a,b;
! 1015:
! 1016: gfsn_univariate_to_sfbm(u0,dy,&g);
! 1017: gfsn_univariate_to_sfbm(v0,dy,&h);
! 1018: sfexgcd_by_hensel(g,h,dy,&a,&b);
! 1019: sfbm_to_gfsn_univariate(a,x,y,cu);
! 1020: sfbm_to_gfsn_univariate(b,x,y,cv);
! 1021: }
! 1022:
! 1023: /* (F[y])[x] -> F[x][y] */
! 1024:
! 1025: void gfsn_univariate_to_sfbm(P f,int dy,BM *r)
! 1026: {
! 1027: int dx,d,i;
! 1028: BM b;
! 1029: UM cy;
! 1030: DCP dc;
! 1031:
! 1032: dx = getdeg(VR(f),f);
! 1033: b = BMALLOC(dx,dy);
! 1034: DEG(b) = dy;
! 1035: for ( dc = DC(f); dc; dc = NEXT(dc) ) {
! 1036: /* d : degree in x, cy : poly in y */
! 1037: d = QTOS(DEG(dc));
! 1038: cy = BDY((GFSN)COEF(dc));
! 1039: for ( i = DEG(cy); i >= 0; i-- )
! 1040: COEF(COEF(b)[i])[d] = COEF(cy)[i];
! 1041: }
! 1042: for ( i = 0; i <= dy; i++ )
! 1043: degum(COEF(b)[i],dx);
! 1044: *r = b;
! 1045: }
! 1046:
! 1047: void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r)
! 1048: {
! 1049: P g;
! 1050: VL vl;
! 1051:
! 1052: sfbmtop(f,x,y,&g);
! 1053: NEWVL(vl); vl->v = x;
! 1054: NEWVL(NEXT(vl)); NEXT(vl)->v = y;
! 1055: NEXT(NEXT(vl)) = 0;
! 1056: poly_to_gfsn_poly(vl,g,y,r);
! 1057: }
! 1058:
! 1059: void poly_to_gfsn_poly(VL vl,P f,V v,P *r)
! 1060: {
! 1061: VL tvl,nvl0,nvl;
! 1062: P g;
! 1063:
! 1064: /* (x,y,...,v,...) -> (x,y,...,v) */
! 1065: for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
! 1066: if ( tvl->v != v ) {
! 1067: NEXTVL(nvl0,nvl);
! 1068: nvl->v = tvl->v;
! 1069: }
! 1070: }
! 1071: NEXTVL(nvl0,nvl);
! 1072: nvl->v = v;
! 1073: NEXT(nvl) = 0;
! 1074: reorderp(nvl0,vl,f,&g);
! 1075: poly_to_gfsn_poly_main(g,v,r);
! 1076: }
! 1077:
! 1078: void poly_to_gfsn_poly_main(P f,V v,P *r)
! 1079: {
! 1080: int d;
! 1081: UM u;
! 1082: GFSN g;
! 1083: DCP dc,dct,dc0;
! 1084:
! 1085: if ( !f )
! 1086: *r = f;
! 1087: else if ( NUM(f) || VR(f) == v ) {
! 1088: d = getdeg(v,f);
! 1089: u = UMALLOC(d);
! 1090: ptosfum(f,u);
! 1091: MKGFSN(u,g);
! 1092: *r = (P)g;
! 1093: } else {
! 1094: for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
! 1095: NEXTDC(dc0,dc);
! 1096: DEG(dc) = DEG(dct);
! 1097: poly_to_gfsn_poly_main(COEF(dct),v,&COEF(dc));
! 1098: }
! 1099: NEXT(dc) = 0;
! 1100: MKP(VR(f),dc0,*r);
! 1101: }
! 1102: }
! 1103:
! 1104: void gfsn_poly_to_poly(VL vl,P f,V v,P *r)
! 1105: {
! 1106: VL tvl,nvl0,nvl;
! 1107: P g;
! 1108:
! 1109: gfsn_poly_to_poly_main(f,v,&g);
! 1110: /* (x,y,...,v,...) -> (x,y,...,v) */
! 1111: for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
! 1112: if ( tvl->v != v ) {
! 1113: NEXTVL(nvl0,nvl);
! 1114: nvl->v = tvl->v;
! 1115: }
! 1116: }
! 1117: NEXTVL(nvl0,nvl);
! 1118: nvl->v = v;
! 1119: NEXT(nvl) = 0;
! 1120: reorderp(vl,nvl0,g,r);
! 1121: }
! 1122:
! 1123: void gfsn_poly_to_poly_main(P f,V v,P *r)
! 1124: {
! 1125: DCP dc,dc0,dct;
! 1126:
! 1127: if ( !f )
! 1128: *r = f;
! 1129: else if ( NUM(f) ) {
! 1130: if ( NID((Num)f) == N_GFSN )
! 1131: sfumtop(v,BDY((GFSN)f),r);
! 1132: else
! 1133: *r = f;
! 1134: } else {
! 1135: for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
! 1136: NEXTDC(dc0,dc);
! 1137: DEG(dc) = DEG(dct);
! 1138: gfsn_poly_to_poly_main(COEF(dct),v,&COEF(dc));
! 1139: }
! 1140: NEXT(dc) = 0;
! 1141: MKP(VR(f),dc0,*r);
! 1142: }
! 1143: }
! 1144:
! 1145: void printsfum(UM f)
! 1146: {
! 1147: int i;
! 1148:
! 1149: for ( i = DEG(f); i >= 0; i-- ) {
! 1150: printf("+(");
! 1151: printf("%d",IFTOF(COEF(f)[i]));
! 1152: printf(")*y^%d",i);
! 1153: }
! 1154: }
! 1155:
! 1156: void printsfbm(BM f)
! 1157: {
! 1158: int i;
! 1159:
! 1160: for ( i = DEG(f); i >= 0; i-- ) {
! 1161: printf("+(");
! 1162: printsfum(COEF(f)[i]);
! 1163: printf(")*y^%d",i);
! 1164: }
! 1165: }
! 1166:
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