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1.1 noro 1: /*
1.6 ! noro 2: * $OpenXM: OpenXM_contrib2/asir2000/engine/dalg.c,v 1.5 2004/12/04 09:39:27 noro Exp $
1.1 noro 3: */
4:
5: #include "ca.h"
6: #include "base.h"
7:
8: static NumberField current_numberfield;
9: extern struct order_spec *dp_current_spec;
1.2 noro 10: void simpdalg(DAlg da,DAlg *r);
1.3 noro 11: void invdalg(DAlg a,DAlg *c);
12: void rmcontdalg(DAlg a, DAlg *c);
1.6 ! noro 13: void algtodalg(Alg a,DAlg *r);
! 14: void dalgtoalg(DAlg da,Alg *r);
1.1 noro 15:
1.5 noro 16: NumberField get_numberfield()
17: {
18: return current_numberfield;
19: }
20:
1.1 noro 21: void setfield_dalg(NODE alist)
22: {
23: NumberField nf;
24: VL vl,vl1,vl2;
25: int n,i,dim;
26: Alg *gen;
27: P *defpoly;
28: P p;
29: Q c,iq,two;
30: DP *ps,*mb;
1.3 noro 31: DP one;
1.1 noro 32: NODE t,b,b1,b2,hlist,mblist;
33: struct order_spec *current_spec;
34:
35: nf = (NumberField)MALLOC(sizeof(struct oNumberField));
36: current_numberfield = nf;
37: vl = 0;
38: for ( t = alist; t; t = NEXT(t) ) {
39: clctalg(BDY((Alg)BDY(t)),&vl1);
40: mergev(ALG,vl,vl1,&vl2); vl = vl2;
41: }
42: for ( n = 0, vl1 = vl; vl1; vl1 = NEXT(vl1), n++ );
43: nf->n = n;
44: nf->vl = vl;
45: nf->defpoly = defpoly = (P *)MALLOC(n*sizeof(P));
46: nf->ps = ps = (DP *)MALLOC(n*sizeof(DP));
47: current_spec = dp_current_spec;
48: STOQ(2,two);
49: create_order_spec(0,(Obj)two,&nf->spec);
50: initd(nf->spec);
51: for ( b = hlist = 0, i = 0, vl1 = vl; i < n; vl1 = NEXT(vl1), i++ ) {
52: ptozp(vl1->v->attr,1,&c,&defpoly[i]);
53: ptod(ALG,vl,defpoly[i],&ps[i]);
54: STOQ(i,iq); MKNODE(b1,(pointer)iq,b); b = b1;
1.3 noro 55: MKNODE(b2,(pointer)ps[i],hlist); hlist = b2;
1.1 noro 56: }
1.3 noro 57: ptod(ALG,vl,(P)ONE,&one);
58: MKDAlg(one,ONE,nf->one);
59: nf->ind = b;
60: dp_mbase(hlist,&mblist);
1.1 noro 61: initd(current_spec);
62: nf->dim = dim = length(mblist);
63: nf->mb = mb = (DP *)MALLOC(dim*sizeof(DP));
64: for ( i = 0, t = mblist; t; t = NEXT(t), i++ )
1.3 noro 65: mb[i] = (DP)BDY(t);
1.1 noro 66: }
67:
1.4 noro 68: void qtodalg(Q q,DAlg *r)
69: {
70: NumberField nf;
71: Q t;
72: DP nm;
73:
74: if ( !(nf=current_numberfield) )
75: error("qtodalg : current_numberfield is not set");
76: if ( !q )
77: *r = 0;
78: else if ( NID(q) == N_DA )
79: *r = (DAlg)q;
80: else if ( NID(q) == N_Q ) {
81: if ( INT(q) ) {
82: muldc(CO,nf->one->nm,(P)q,&nm);
83: MKDAlg(nm,ONE,*r);
84: } else {
85: NTOQ(NM(q),SGN(q),t);
86: muldc(CO,nf->one->nm,(P)t,&nm);
87: NTOQ(DN(q),1,t);
88: MKDAlg(nm,t,*r);
89: }
90: } else
91: error("qtodalg : invalid argument");
1.6 ! noro 92: }
! 93:
! 94: void obj_algtodalg(Obj obj,Obj *r)
! 95: {
! 96: DAlg d;
! 97: DCP dc,dcr0,dcr;
! 98: P c,p;
! 99: Obj t;
! 100: Obj nm,dn;
! 101: NODE b,s,s0;
! 102: R rat;
! 103: VECT v;
! 104: MAT mat;
! 105: LIST list;
! 106: pointer *a;
! 107: pointer **m;
! 108: int len,row,col,i,j,l;
! 109:
! 110: if ( !obj ) {
! 111: *r = 0;
! 112: return;
! 113: }
! 114: switch ( OID(obj) ) {
! 115: case O_N:
! 116: algtodalg((Alg)obj,&d); *r = (Obj)d;
! 117: break;
! 118: case O_P:
! 119: for ( dcr0 = 0, dc = DC((P)obj); dc; dc = NEXT(dc) ) {
! 120: obj_algtodalg((Obj)COEF(dc),&t);
! 121: if ( t ) {
! 122: NEXTDC(dcr0,dcr);
! 123: COEF(dcr) = (P)t;
! 124: DEG(dcr) = DEG(dc);
! 125: }
! 126: }
! 127: if ( dcr0 ) {
! 128: MKP(VR((P)obj),dcr0,p);
! 129: *r = (Obj)p;
! 130: } else
! 131: *r = 0;
! 132: break;
! 133: case O_R:
! 134: obj_algtodalg((Obj)NM((R)obj),&nm);
! 135: obj_algtodalg((Obj)DN((R)obj),&dn);
! 136: if ( !dn )
! 137: error("obj_algtodalg : division by 0");
! 138: if ( !nm )
! 139: *r = 0;
! 140: else {
! 141: MKRAT((P)nm,(P)dn,0,rat); *r = (Obj)rat;
! 142: }
! 143: break;
! 144: case O_LIST:
! 145: s0 = 0;
! 146: for ( b = BDY((LIST)obj); b; b = NEXT(b) ) {
! 147: NEXTNODE(s0,s);
! 148: obj_algtodalg((Obj)BDY(b),&t);
! 149: BDY(s) = (pointer)t;
! 150: }
! 151: NEXT(s) = 0;
! 152: MKLIST(list,s0);
! 153: *r = (Obj)list;
! 154: break;
! 155: case O_VECT:
! 156: l = ((VECT)obj)->len;
! 157: a = BDY((VECT)obj);
! 158: MKVECT(v,l);
! 159: for ( i = 0; i < l; i++ ) {
! 160: obj_algtodalg((Obj)a[i],&t);
! 161: BDY(v)[i] = (pointer)t;
! 162: }
! 163: *r = (Obj)v;
! 164: break;
! 165: case O_MAT:
! 166: row = ((MAT)obj)->row; col = ((MAT)obj)->col;
! 167: m = BDY((MAT)obj);
! 168: MKMAT(mat,row,col);
! 169: for ( i = 0; i < row; i++ )
! 170: for ( j = 0; j < col; j++ ) {
! 171: obj_algtodalg((Obj)m[i][j],&t);
! 172: BDY(mat)[i][j] = (pointer)t;
! 173: }
! 174: *r = (Obj)mat;
! 175: break;
! 176: default:
! 177: *r = obj;
! 178: break;
! 179: }
! 180: }
! 181:
! 182: void obj_dalgtoalg(Obj obj,Obj *r)
! 183: {
! 184: Alg d;
! 185: DCP dc,dcr0,dcr;
! 186: P c,p;
! 187: Obj t;
! 188: Obj nm,dn;
! 189: NODE b,s,s0;
! 190: R rat;
! 191: VECT v;
! 192: MAT mat;
! 193: LIST list;
! 194: pointer *a;
! 195: pointer **m;
! 196: int len,row,col,i,j,l;
! 197:
! 198: if ( !obj ) {
! 199: *r = 0;
! 200: return;
! 201: }
! 202: switch ( OID(obj) ) {
! 203: case O_N:
! 204: dalgtoalg((DAlg)obj,&d); *r = (Obj)d;
! 205: break;
! 206: case O_P:
! 207: for ( dcr0 = 0, dc = DC((P)obj); dc; dc = NEXT(dc) ) {
! 208: obj_dalgtoalg((Obj)COEF(dc),&t);
! 209: if ( t ) {
! 210: NEXTDC(dcr0,dcr);
! 211: COEF(dcr) = (P)t;
! 212: DEG(dcr) = DEG(dc);
! 213: }
! 214: }
! 215: if ( dcr0 ) {
! 216: MKP(VR((P)obj),dcr0,p);
! 217: *r = (Obj)p;
! 218: } else
! 219: *r = 0;
! 220: break;
! 221: case O_R:
! 222: obj_dalgtoalg((Obj)NM((R)obj),&nm);
! 223: obj_dalgtoalg((Obj)DN((R)obj),&dn);
! 224: if ( !dn )
! 225: error("obj_dalgtoalg : division by 0");
! 226: if ( !nm )
! 227: *r = 0;
! 228: else {
! 229: MKRAT((P)nm,(P)dn,0,rat); *r = (Obj)rat;
! 230: }
! 231: break;
! 232: case O_LIST:
! 233: s0 = 0;
! 234: for ( b = BDY((LIST)obj); b; b = NEXT(b) ) {
! 235: NEXTNODE(s0,s);
! 236: obj_dalgtoalg((Obj)BDY(b),&t);
! 237: BDY(s) = (pointer)t;
! 238: }
! 239: NEXT(s) = 0;
! 240: MKLIST(list,s0);
! 241: *r = (Obj)list;
! 242: break;
! 243: case O_VECT:
! 244: l = ((VECT)obj)->len;
! 245: a = BDY((VECT)obj);
! 246: MKVECT(v,l);
! 247: for ( i = 0; i < l; i++ ) {
! 248: obj_dalgtoalg((Obj)a[i],&t);
! 249: BDY(v)[i] = (pointer)t;
! 250: }
! 251: *r = (Obj)v;
! 252: break;
! 253: case O_MAT:
! 254: row = ((MAT)obj)->row; col = ((MAT)obj)->col;
! 255: m = BDY((MAT)obj);
! 256: MKMAT(mat,row,col);
! 257: for ( i = 0; i < row; i++ )
! 258: for ( j = 0; j < col; j++ ) {
! 259: obj_dalgtoalg((Obj)m[i][j],&t);
! 260: BDY(mat)[i][j] = (pointer)t;
! 261: }
! 262: *r = (Obj)mat;
! 263: break;
! 264: default:
! 265: *r = obj;
! 266: break;
! 267: }
1.4 noro 268: }
269:
1.1 noro 270: void algtodalg(Alg a,DAlg *r)
271: {
272: P ap,p,p1;
1.3 noro 273: Q c,c1,d1,dn,nm;
1.1 noro 274: DP dp;
275: DAlg da;
276: NumberField nf;
277: struct order_spec *current_spec;
1.3 noro 278: VL vl,tvl,svl;
279: V v;
1.1 noro 280:
281: if ( !(nf=current_numberfield) )
282: error("algtodalg : current_numberfield is not set");
1.3 noro 283: if ( !a ) {
284: *r = 0;
285: return;
286: }
287: switch (NID((Num)a) ) {
288: case N_Q:
289: c = (Q)a;
290: if ( INT(c) ) {
291: muldc(CO,nf->one->nm,(P)c,&dp);
292: MKDAlg(dp,ONE,*r);
293: } else {
294: NTOQ(NM(c),SGN(c),c1);
295: NTOQ(DN(c),1,d1);
296: muldc(CO,nf->one->nm,(P)c1,&dp);
297: MKDAlg(dp,c1,*r);
298: }
299: break;
300: case N_A:
301: ap = (P)BDY(a);
302: ptozp(ap,1,&c,&p);
303: if ( INT(c) ) {
304: p = ap;
305: dn = ONE;
306: } else {
307: NTOQ(NM(c),SGN(c),nm);
308: NTOQ(DN(c),1,dn);
309: mulpq(p,(P)nm,&p1); p = p1;
310: }
311: current_spec = dp_current_spec; initd(nf->spec);
312: get_vars(p,&vl);
313: for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
314: v = tvl->v;
315: for ( svl = nf->vl; svl; svl = NEXT(svl) )
316: if ( v == svl->v )
317: break;
318: if ( !svl )
319: error("algtodalg : incompatible numberfield");
320: }
321: ptod(ALG,nf->vl,p,&dp);
322: MKDAlg(dp,dn,da);
323: simpdalg(da,r);
324: break;
325: default:
326: error("algtodalg : invalid argument");
327: break;
1.1 noro 328: }
329: }
330:
1.2 noro 331: void dalgtoalg(DAlg da,Alg *r)
1.1 noro 332: {
1.2 noro 333: NumberField nf;
334: P p,p1;
335: Q inv;
336:
337: if ( !(nf=current_numberfield) )
1.3 noro 338: error("dalgtoalg : current_numberfield is not set");
1.2 noro 339: dtop(ALG,nf->vl,da->nm,&p);
340: invq(da->dn,&inv);
341: mulpq(p,(P)inv,&p1);
342: MKAlg(p1,*r);
1.1 noro 343: }
344:
345: void simpdalg(DAlg da,DAlg *r)
346: {
1.2 noro 347: NumberField nf;
348: DP nm;
1.3 noro 349: DAlg d;
1.2 noro 350: Q dn,dn1;
1.5 noro 351: struct order_spec *current_spec;
1.2 noro 352:
353: if ( !(nf=current_numberfield) )
1.3 noro 354: error("simpdalg : current_numberfield is not set");
355: if ( !da ) {
356: *r = 0;
357: return;
358: }
1.5 noro 359: current_spec = dp_current_spec; initd(nf->spec);
1.2 noro 360: dp_true_nf(nf->ind,da->nm,nf->ps,1,&nm,&dn);
1.5 noro 361: initd(current_spec);
1.2 noro 362: mulq(da->dn,dn,&dn1);
1.3 noro 363: MKDAlg(nm,dn1,d);
364: rmcontdalg(d,r);
1.1 noro 365: }
366:
367: void adddalg(DAlg a,DAlg b,DAlg *c)
368: {
1.3 noro 369: NumberField nf;
370: Q dna,dnb,a1,b1,dn,g;
371: N an,bn,gn;
1.4 noro 372: DAlg t;
1.3 noro 373: DP ta,tb,nm;
374: struct order_spec *current_spec;
375:
376: if ( !(nf=current_numberfield) )
377: error("adddalg : current_numberfield is not set");
378: if ( !a )
379: *c = b;
380: else if ( !b )
381: *c = a;
382: else {
1.4 noro 383: qtodalg((Q)a,&t); a = t; qtodalg((Q)b,&t); b = t;
1.3 noro 384: dna = a->dn;
385: dnb = b->dn;
386: gcdn(NM(dna),NM(dnb),&gn);
387: divsn(NM(dna),gn,&an); divsn(NM(dnb),gn,&bn);
388: NTOQ(an,SGN(dna),a1); NTOQ(bn,SGN(dnb),b1);
389: /* nma/dna+nmb/dnb = (nma*b1+nmb*a1)/(dna*b1) */
390: muldc(CO,a->nm,(P)b1,&ta); muldc(CO,b->nm,(P)a1,&tb);
391: current_spec = dp_current_spec; initd(nf->spec);
392: addd(CO,ta,tb,&nm);
393: initd(current_spec);
394: if ( !nm )
395: *c = 0;
396: else {
397: mulq(dna,b1,&dn);
398: MKDAlg(nm,dn,*c);
399: }
400: }
1.1 noro 401: }
402:
403: void subdalg(DAlg a,DAlg b,DAlg *c)
404: {
1.3 noro 405: NumberField nf;
406: Q dna,dnb,a1,b1,dn,g;
407: N an,bn,gn;
408: DP ta,tb,nm;
1.4 noro 409: DAlg t;
1.3 noro 410: struct order_spec *current_spec;
411:
412: if ( !(nf=current_numberfield) )
413: error("subdalg : current_numberfield is not set");
414: if ( !a )
415: *c = b;
416: else if ( !b )
417: *c = a;
418: else {
1.4 noro 419: qtodalg((Q)a,&t); a = t; qtodalg((Q)b,&t); b = t;
1.3 noro 420: dna = a->dn;
421: dnb = b->dn;
422: gcdn(NM(dna),NM(dnb),&gn);
423: divsn(NM(dna),gn,&an); divsn(NM(dnb),gn,&bn);
424: NTOQ(an,SGN(dna),a1); NTOQ(bn,SGN(dnb),b1);
425: /* nma/dna-nmb/dnb = (nma*b1-nmb*a1)/(dna*b1) */
426: muldc(CO,a->nm,(P)b1,&ta); muldc(CO,b->nm,(P)a1,&tb);
427: current_spec = dp_current_spec; initd(nf->spec);
428: subd(CO,ta,tb,&nm);
429: initd(current_spec);
430: if ( !nm )
431: *c = 0;
432: else {
433: mulq(dna,b1,&dn);
434: MKDAlg(nm,dn,*c);
435: }
436: }
1.1 noro 437: }
438:
1.2 noro 439: void muldalg(DAlg a,DAlg b,DAlg *c)
440: {
1.3 noro 441: NumberField nf;
442: DP nm;
443: Q dn;
444: DAlg t;
445: struct order_spec *current_spec;
446:
447: if ( !(nf=current_numberfield) )
448: error("muldalg : current_numberfield is not set");
449: if ( !a || !b )
450: *c = 0;
451: else {
1.4 noro 452: qtodalg((Q)a,&t); a = t; qtodalg((Q)b,&t); b = t;
1.3 noro 453: current_spec = dp_current_spec; initd(nf->spec);
454: muld(CO,a->nm,b->nm,&nm);
455: initd(current_spec);
456: mulq(a->dn,b->dn,&dn);
457: MKDAlg(nm,dn,t);
458: simpdalg(t,c);
459: }
1.2 noro 460: }
461:
462:
1.1 noro 463: void divdalg(DAlg a,DAlg b,DAlg *c)
464: {
1.4 noro 465: DAlg inv,t;
1.3 noro 466:
1.1 noro 467: if ( !current_numberfield )
1.3 noro 468: error("divdalg : current_numberfield is not set");
469: if ( !b )
470: error("divdalg : division by 0");
471: if ( !a )
472: c = 0;
473: else {
1.4 noro 474: qtodalg((Q)a,&t); a = t; qtodalg((Q)b,&t); b = t;
1.3 noro 475: invdalg(b,&inv);
476: muldalg(a,inv,c);
477: }
478: }
479:
480: void rmcontdalg(DAlg a, DAlg *r)
481: {
482: DP u,u1;
483: Q cont,c,d;
484: N gn,cn,dn;
485:
486: if ( !a )
487: *r = a;
488: else {
489: dp_ptozp(a->nm,&u);
490: divq((Q)BDY(a->nm)->c,(Q)BDY(u)->c,&cont);
491: gcdn(NM(cont),NM(a->dn),&gn);
492: divsn(NM(cont),gn,&cn); NTOQ(cn,SGN(cont),c);
493: divsn(NM(a->dn),gn,&dn); NTOQ(dn,SGN(a->dn),d);
494: muldc(CO,u,(P)c,&u1);
495: MKDAlg(u1,d,*r);
496: }
1.1 noro 497: }
498:
499: void invdalg(DAlg a,DAlg *c)
500: {
1.3 noro 501: NumberField nf;
502: int dim,n,i,j;
503: DP *mb;
504: DP m,d,u;
505: N ln,gn,qn;
506: DAlg *simp;
507: DAlg t,a0,r;
508: Q dn,dnsol,mul;
509: MAT mobj,sol;
510: Q **mat,**solmat;
511: MP mp0,mp;
512: int *rinfo,*cinfo;
513: struct order_spec *current_spec;
1.5 noro 514: struct oEGT eg0,eg1;
515: extern struct oEGT eg_le;
1.3 noro 516:
517: if ( !(nf=current_numberfield) )
518: error("invdalg : current_numberfield is not set");
519: if ( !a )
520: error("invdalg : division by 0");
1.4 noro 521: else if ( NID(a) == N_Q ) {
522: invq((Q)a,&dn); *c = (DAlg)dn;
523: return;
524: }
1.3 noro 525: dim = nf->dim;
526: mb = nf->mb;
527: n = nf->n;
528: ln = ONEN;
529: MKDAlg(a->nm,ONE,a0);
530: simp = (DAlg *)ALLOCA(dim*sizeof(DAlg));
531: current_spec = dp_current_spec; initd(nf->spec);
532: for ( i = dim-1; i >= 0; i-- ) {
533: m = mb[i];
534: for ( j = i+1; j < dim; j++ )
535: if ( dp_redble(m,mb[j]) )
536: break;
537: if ( j < dim ) {
538: dp_subd(m,mb[j],&d);
539: muld(CO,d,simp[j]->nm,&u);
540: MKDAlg(u,simp[j]->dn,t);
541: simpdalg(t,&simp[i]);
542: } else {
543: MKDAlg(m,ONE,t);
544: muldalg(t,a0,&simp[i]);
545: }
546: gcdn(NM(simp[i]->dn),ln,&gn); divsn(ln,gn,&qn);
547: muln(NM(simp[i]->dn),qn,&ln);
548: }
549: initd(current_spec);
550: NTOQ(ln,1,dn);
551: MKMAT(mobj,dim,dim+1);
552: mat = (Q **)BDY(mobj);
553: mulq(dn,a->dn,&mat[dim-1][dim]);
554: for ( j = 0; j < dim; j++ ) {
555: divq(dn,simp[j]->dn,&mul);
556: for ( i = 0, mp = BDY(simp[j]->nm); mp && i < dim; i++ )
557: if ( dl_equal(n,BDY(mb[i])->dl,mp->dl) ) {
558: mulq(mul,(Q)mp->c,&mat[i][j]);
559: mp = NEXT(mp);
560: }
561: }
1.5 noro 562: get_eg(&eg0);
1.3 noro 563: generic_gauss_elim_hensel(mobj,&sol,&dnsol,&rinfo,&cinfo);
1.5 noro 564: get_eg(&eg1); add_eg(&eg_le,&eg0,&eg1);
1.3 noro 565: solmat = (Q **)BDY(sol);
566: for ( i = 0, mp0 = 0; i < dim; i++ )
567: if ( solmat[i][0] ) {
568: NEXTMP(mp0,mp);
569: mp->c = (P)solmat[i][0];
570: mp->dl = BDY(mb[i])->dl;
571: }
572: NEXT(mp) = 0; MKDP(n,mp0,u);
573: MKDAlg(u,dnsol,r);
574: rmcontdalg(r,c);
1.1 noro 575: }
576:
577: void chsgndalg(DAlg a,DAlg *c)
578: {
1.3 noro 579: DP nm;
1.4 noro 580: Q t;
1.3 noro 581:
582: if ( !a ) *c = 0;
1.4 noro 583: else if ( NID(a) == N_Q ) {
584: chsgnq((Q)a,&t); *c = (DAlg)t;
585: } else {
1.3 noro 586: chsgnd(a->nm,&nm);
587: MKDAlg(nm,a->dn,*c);
588: }
1.1 noro 589: }
590:
1.3 noro 591: void pwrdalg(DAlg a,Q e,DAlg *c)
1.1 noro 592: {
1.3 noro 593: NumberField nf;
594: DAlg t,z,y;
1.4 noro 595: Q q;
1.3 noro 596: N en,qn;
597: int r;
598:
599: if ( !(nf=current_numberfield) )
600: error("pwrdalg : current_numberfield is not set");
1.4 noro 601: if ( !a )
602: *c = !e ? (DAlg)ONE : 0;
603: else if ( NID(a) == N_Q ) {
604: pwrq((Q)a,e,&q); *c = (DAlg)q;
605: } else if ( !e )
1.3 noro 606: *c = nf->one;
607: else if ( UNIQ(e) )
608: *c = a;
609: else {
610: if ( SGN(e) < 0 ) {
611: invdalg(a,&t); a = t;
612: }
613: en = NM(e);
614: y = nf->one;
615: z = a;
616: while ( 1 ) {
617: r = divin(en,2,&qn); en = qn;
618: if ( r ) {
619: muldalg(z,y,&t); y = t;
620: if ( !en ) {
621: *c = y;
622: return;
623: }
624: }
625: muldalg(z,z,&t); z = t;
626: }
627: }
1.1 noro 628: }
629:
1.3 noro 630: int cmpdalg(DAlg a,DAlg b)
1.1 noro 631: {
1.3 noro 632: DAlg c;
633:
634: subdalg(a,b,&c);
635: if ( !c ) return 0;
636: else
637: return SGN((Q)BDY(c->nm)->c);
1.1 noro 638: }