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1.1 noro 1: /*
1.7 ! noro 2: * $OpenXM: OpenXM_contrib2/asir2000/engine/dalg.c,v 1.6 2004/12/07 15:15:52 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;
1.7 ! noro 508: Q dn,dnsol,mul,nmc,dn1;
1.3 noro 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;
1.7 ! noro 529: dp_ptozp(a->nm,&u); divq((Q)BDY(a->nm)->c,(Q)BDY(u)->c,&nmc);
! 530: MKDAlg(u,ONE,a0);
1.3 noro 531: simp = (DAlg *)ALLOCA(dim*sizeof(DAlg));
532: current_spec = dp_current_spec; initd(nf->spec);
533: for ( i = dim-1; i >= 0; i-- ) {
534: m = mb[i];
535: for ( j = i+1; j < dim; j++ )
536: if ( dp_redble(m,mb[j]) )
537: break;
538: if ( j < dim ) {
539: dp_subd(m,mb[j],&d);
540: muld(CO,d,simp[j]->nm,&u);
541: MKDAlg(u,simp[j]->dn,t);
542: simpdalg(t,&simp[i]);
543: } else {
544: MKDAlg(m,ONE,t);
545: muldalg(t,a0,&simp[i]);
546: }
547: gcdn(NM(simp[i]->dn),ln,&gn); divsn(ln,gn,&qn);
548: muln(NM(simp[i]->dn),qn,&ln);
549: }
550: initd(current_spec);
551: NTOQ(ln,1,dn);
552: MKMAT(mobj,dim,dim+1);
553: mat = (Q **)BDY(mobj);
554: mulq(dn,a->dn,&mat[dim-1][dim]);
555: for ( j = 0; j < dim; j++ ) {
556: divq(dn,simp[j]->dn,&mul);
557: for ( i = 0, mp = BDY(simp[j]->nm); mp && i < dim; i++ )
558: if ( dl_equal(n,BDY(mb[i])->dl,mp->dl) ) {
559: mulq(mul,(Q)mp->c,&mat[i][j]);
560: mp = NEXT(mp);
561: }
562: }
1.5 noro 563: get_eg(&eg0);
1.3 noro 564: generic_gauss_elim_hensel(mobj,&sol,&dnsol,&rinfo,&cinfo);
1.5 noro 565: get_eg(&eg1); add_eg(&eg_le,&eg0,&eg1);
1.3 noro 566: solmat = (Q **)BDY(sol);
567: for ( i = 0, mp0 = 0; i < dim; i++ )
568: if ( solmat[i][0] ) {
569: NEXTMP(mp0,mp);
570: mp->c = (P)solmat[i][0];
571: mp->dl = BDY(mb[i])->dl;
572: }
573: NEXT(mp) = 0; MKDP(n,mp0,u);
1.7 ! noro 574: mulq(dnsol,nmc,&dn1);
! 575: MKDAlg(u,dn1,r);
1.3 noro 576: rmcontdalg(r,c);
1.1 noro 577: }
578:
579: void chsgndalg(DAlg a,DAlg *c)
580: {
1.3 noro 581: DP nm;
1.4 noro 582: Q t;
1.3 noro 583:
584: if ( !a ) *c = 0;
1.4 noro 585: else if ( NID(a) == N_Q ) {
586: chsgnq((Q)a,&t); *c = (DAlg)t;
587: } else {
1.3 noro 588: chsgnd(a->nm,&nm);
589: MKDAlg(nm,a->dn,*c);
590: }
1.1 noro 591: }
592:
1.3 noro 593: void pwrdalg(DAlg a,Q e,DAlg *c)
1.1 noro 594: {
1.3 noro 595: NumberField nf;
596: DAlg t,z,y;
1.4 noro 597: Q q;
1.3 noro 598: N en,qn;
599: int r;
600:
601: if ( !(nf=current_numberfield) )
602: error("pwrdalg : current_numberfield is not set");
1.4 noro 603: if ( !a )
604: *c = !e ? (DAlg)ONE : 0;
605: else if ( NID(a) == N_Q ) {
606: pwrq((Q)a,e,&q); *c = (DAlg)q;
607: } else if ( !e )
1.3 noro 608: *c = nf->one;
609: else if ( UNIQ(e) )
610: *c = a;
611: else {
612: if ( SGN(e) < 0 ) {
613: invdalg(a,&t); a = t;
614: }
615: en = NM(e);
616: y = nf->one;
617: z = a;
618: while ( 1 ) {
619: r = divin(en,2,&qn); en = qn;
620: if ( r ) {
621: muldalg(z,y,&t); y = t;
622: if ( !en ) {
623: *c = y;
624: return;
625: }
626: }
627: muldalg(z,z,&t); z = t;
628: }
629: }
1.1 noro 630: }
631:
1.3 noro 632: int cmpdalg(DAlg a,DAlg b)
1.1 noro 633: {
1.3 noro 634: DAlg c;
635:
636: subdalg(a,b,&c);
637: if ( !c ) return 0;
638: else
639: return SGN((Q)BDY(c->nm)->c);
1.1 noro 640: }