Annotation of OpenXM/src/kan96xx/Kan/gb.c, Revision 1.8
1.8 ! takayama 1: /* $OpenXM: OpenXM/src/kan96xx/Kan/gb.c,v 1.7 2003/07/30 09:00:52 takayama Exp $ */
1.5 takayama 2: /* untabify on May 4, 2001 */
1.1 maekawa 3: #include <stdio.h>
4: #include "datatype.h"
5: #include "extern2.h"
6: #include "matrix.h"
7: #include "gradedset.h"
8:
9: #define INITGRADE 4
10: #define INITSIZE 2
1.6 takayama 11: #define DMAX 100
1.1 maekawa 12:
13: int KanGBmessage = 1;
14:
15: static int Debug = 0;
16: static int sugarGrade(struct pair *inode,struct gradedPolySet *grG,
1.5 takayama 17: POLY gt,int gtSugarGrade);
1.1 maekawa 18: extern int Sugar;
19: extern int Statistics;
20: extern int Criterion1;
21: extern int UseCriterion1;
22: extern int UseCriterion2B;
23: extern int Spairs;
24: extern int Criterion2B, Criterion2F, Criterion2M;
1.3 takayama 25: extern int AutoReduce;
1.8 ! takayama 26: extern int TraceLift;
! 27: extern struct ring *TraceLift_ringmod;
1.6 takayama 28: static int MaxLength[DMAX];
29: static int SpNumber[DMAX];
1.1 maekawa 30:
31: struct gradedPairs *updatePairs(grD,gt,gtGrade,t,grG)
1.5 takayama 32: struct gradedPairs *grD; /* set of pairs */
33: POLY gt; /* new polynomial */
34: int gtGrade;
35: int t;
36: struct gradedPolySet *grG; /* (f,gt), f \in grG, should be added to grD. */
1.1 maekawa 37: {
38: int gmax,newGrade;
39: struct pair *node,*new,*inode,*jnode;
40: int i,k;
41: struct polySet *g;
42: POLY lcmp;
43: POLY it,jt;
44: extern int Verbose;
45:
46:
47: if (Verbose) {
48: printf("\nupdatePairs(): ");
49: }
50:
51: gmax = grG->maxGrade;
52: node = new = newPair((struct pair *)NULL);
53: /* (f,gt) are stored in new as a list. */
54: for (k=0; k<gmax; k++) {
55: g = grG->polys[k];
56: for (i=0; i<g->size; i++) {
57: if (g->del[i] == 0 && (gtGrade != k || t != i)) {
1.5 takayama 58: lcmp = (*lcm)(g->g[i],gt);
59: if (lcmp == ZERO) {
1.1 maekawa 60:
1.5 takayama 61: }else {
62: new->del = 0;
63: new->next = newPair(new);
64: new = new->next;
65: new->lcm = lcmp;
66: new->ig = k; new->ii = i; /* g->g[i] */
67: new->jg = gtGrade; new->ji = t; /* gt */
68: new->grade = -1; /* one do not need to set grade here. */
69: }
1.1 maekawa 70: }
71: }
72: }
73:
74:
75: /* Check the criterion */
76: /* See Gebauer and Mora, 1988, Journal of Symbolic Computation
77: 279. We must not use the test T(i)T(j) = T(i,j) because it
78: does not hold in the ring of diff op.
1.5 takayama 79: */
1.1 maekawa 80:
81: inode = node->next;
82: while (inode != (struct pair *)NULL) {
83: jnode = inode->next;
84: while (jnode != (struct pair *)NULL) {
85: it = inode->lcm;
86: jt = jnode->lcm;
87: if ((*mmLarger)(it,jt) == 2) {
1.5 takayama 88: /* F(j,t), i<j */
89: jnode->del = 1;
90: if (Verbose) printf("F[%d,%d]([%d,%d],[%d,%d]) ",
91: inode->ig,inode->ii,
92: jnode->ig,jnode->ii,
93: gtGrade,t);
94: Criterion2F++;
1.1 maekawa 95: }else {
1.5 takayama 96: /* g[i] > g[j] ?, M(i,t) */
97: if ((*isReducible)(it,jt)) {
98: inode->del = 1;
99: if (Verbose) printf("M[%d,%d]([%d,%d],[%d,%d]) ",
100: jnode->ig,jnode->ii,
101: inode->ig,inode->ii,
102: gtGrade,t);
103: Criterion2M++;
104: }
1.1 maekawa 105: /* M(j,t) */
1.5 takayama 106: if ((*isReducible)(jt,it)) {
107: jnode->del = 1;
108: if (Verbose) printf("M[%d,%d]([%d,%d],[%d,%d]) ",
109: inode->ig,inode->ii,
110: jnode->ig,jnode->ii,
111: gtGrade,t);
112: Criterion2M++;
113: }
1.1 maekawa 114: }
115: jnode = jnode->next;
116: }
117: inode = inode->next;
118: }
1.5 takayama 119:
1.1 maekawa 120: if (UseCriterion1) {
121: inode = node->next;
122: while (inode != NULL) {
123: if (inode->del == 0) {
1.5 takayama 124: if (criterion1(gt,grG->polys[inode->ig]->g[inode->ii],inode->lcm)) {
125: inode->del = 1;
126: if (Verbose) printf("Criterion1([%d,%d],[%d,%d]) ",
127: inode->ig,inode->ii,
128: gtGrade,t);
129: Criterion1++;
130: }
1.1 maekawa 131: }
132: inode = inode->next;
133: }
134: }
135:
136: if (UseCriterion2B) {
137: Criterion2B += deletePairByCriterion2B(grD,gt,grG);
138: }
139:
140: /* Merge to grD */
141: inode = node->next;
142: if (Debug) outputNode(inode);
143: while (inode != (struct pair *)NULL) {
144: if (inode->del == 0) {
145: if (Sugar) {
1.5 takayama 146: inode->grade = sugarGrade(inode,grG,gt,gtGrade);
1.1 maekawa 147: }else{
1.5 takayama 148: inode->grade = (*grade)(inode->lcm);
1.1 maekawa 149: }
150: if (grD->lim <= inode->grade) {
1.5 takayama 151: grD = enlargeGradedPairs(2*(inode->grade)+1,grD);
1.1 maekawa 152: }
153: insertPair(inode,grD->pairs[inode->grade]);
154: grD->maxGrade = max(grD->maxGrade,inode->grade+1); /* don't forget */
155: }
156: inode = inode->next;
157: }
158: if (Debug) printf("OK.\n");
159: if (Verbose) {
160: printf(" Remaining pairs are %d. maxGrade=%d\n",countPairs(grD),grD->maxGrade);
161: }
162: return(grD);
163: }
164:
165: struct gradedPolySet *groebner_gen(f,needBack,needSyz,grP,countDown,forceReduction)
1.5 takayama 166: struct arrayOfPOLY *f;
167: int needBack;
168: int needSyz;
169: struct pair **grP; /* if (needSyz), it is set. */
170: int countDown;
171: int forceReduction;
1.1 maekawa 172: {
173: int r;
174: struct gradedPolySet *g;
175: struct gradedPairs *d;
176: int i;
177: int grade,indx;
178: POLY gt;
179: struct pair *top;
180: int ig,ii,jg,ji;
181: POLY gi,gj;
182: struct spValue h;
183: struct syz0 syz;
184: int pgrade = 0;
185: POLY rd;
186: POLY syzPoly;
187: POLY syzCf;
188: struct syz0 *syzp;
189: int serial;
190: struct pair *listP;
191: extern int Verbose;
192: extern int ReduceLowerTerms;
193: extern int StopDegree;
194: extern struct ring *CurrentRingp;
195: extern char *F_mpMult;
196: struct ring *rp;
1.8 ! takayama 197: int first;
1.6 takayama 198: int statisticsPL, statisticsCount;
1.1 maekawa 199:
1.6 takayama 200: if (Statistics) {
201: for (i=0; i<DMAX; i++) MaxLength[i] = SpNumber[i] = 0;
202: }
1.1 maekawa 203: r = f->n;
204: if (r<=0) return((struct gradedPolySet *)NULL);
205: if (UseCriterion1) {
206: if (needSyz) {
207: warningGradedSet("You cannot use both the options needSyz and UseCriterion1.\nInput [(UseCriterion1) 0] system_variable to turn off the use of the Criterion 1.");
208: }
209: if (strcmp(F_mpMult,"poly")!=0) {
210: warningGradedSet("You can use the option UseCriterion1 only for the computation in the ring of polynomials.\nInput [(UseCriterion1) 0] system_variable to turn off the use of the Criterion 1.");
211: }
212: }
213:
214: Spairs = Criterion1 = Criterion2B = Criterion2F = Criterion2M = 0;
215:
216: g = newGradedPolySet(INITGRADE);
217: d = newGradedPairs(INITGRADE*2);
218: for (i=0; i<g->lim; i++) {
219: g->polys[i] = newPolySet(INITSIZE);
220: }
221:
1.8 ! takayama 222: first = 1;
1.1 maekawa 223: for (i=0; i<r; i++) {
224: gt = getArrayOfPOLY(f,i);
225: if (gt ISZERO) { rp = CurrentRingp; } else { rp = gt->m->ringp; }
1.8 ! takayama 226: if (TraceLift && (!(gt ISZERO)) && first) {
! 227: TraceLift_ringmod = newRingOverFp(rp,getPrime(TraceLift)); first = 0;
! 228: if (KanGBmessage) printf("Prime number for the trace lift is %d.\n",
! 229: TraceLift_ringmod->p);
! 230: }
1.1 maekawa 231: grade = -1; whereInG(g,gt,&grade,&indx,Sugar);
232: if (KanGBmessage == 2) {
233: printf("init=%s, ",POLYToString(head(gt),'*',1));
234: printf("(gr,indx)=(%d,%d).\n",grade,indx);
235: }
236: d = updatePairs(d,gt,grade,indx,g);
237: serial = i;
238: if (!needBack) {
239: g = putPolyInG(g,gt,grade,indx,
1.5 takayama 240: (struct syz0 *)NULL,1,serial);
1.1 maekawa 241: }else {
242: syzp = newSyz0();
243: syzp->cf = cxx(1,0,0,rp);
244: syzp->syz = toSyzPoly(cxx(1,0,0,rp),grade,indx);
245: g = putPolyInG(g,gt,grade,indx,syzp,1,serial);
246: }
247:
1.7 takayama 248: /* markRedundant0(g,grade,indx); ?*/
249: markGeneratorInG(g,grade,indx); /*?*/
1.1 maekawa 250: if (Debug) {
251: outputGradedPairs(d); outputGradedPolySet(g,needSyz);
252: }
253: }
254: if (needSyz) {
255: *grP = newPair((struct pair *)NULL);
256: listP = *grP;
257: }
258:
259: while ((top = getPair(d)) != (struct pair *)NULL) {
260: ig = top->ig; ii = top->ii; /* [ig,ii] */
261: jg = top->jg; ji = top->ji; /* [jg,ji] */
1.7 takayama 262: /*
263: if (g->polys[ig]->del[ii] || g->polys[jg]->del[ji]) {
264: if (KanGBmessage) printf("p");
265: continue;
266: } Don't do this.
267: */
1.1 maekawa 268: gi = g->polys[ig]->g[ii];
269: gj = g->polys[jg]->g[ji];
270:
271: Spairs++;
272: h = (*sp)(gi,gj);
273: rd = ppAddv(ppMult(h.a,gi),ppMult(h.b,gj));
1.6 takayama 274:
275: if (Statistics) {
276: if (top->grade >=0 && top->grade < DMAX) {
277: statisticsPL = pLength(rd);
278: SpNumber[top->grade]++;
279: if (MaxLength[top->grade] < statisticsPL) {
280: MaxLength[top->grade] = statisticsPL;
281: }
282: }
283: }
284:
1.1 maekawa 285: if (!Sugar || forceReduction) {
286: rd = (*reduction)(rd,g,needBack,&syz);
287: }else{
288: rd = reduction_sugar(rd,g,needBack,&syz,top->grade);
289: }
290: syzPoly = syz.syz;
291: syzCf = syz.cf;
292:
293: if (KanGBmessage) {
294: if (KanGBmessage == 2) {
1.5 takayama 295: printf("sp([%d,%d],[%d,%d]), ",ig,ii,jg,ji);
296: if (rd ISZERO) {
297: printf(" 0 \n");
298: } else{
299: printf(" terms=%d, grade=%d, ",pLength(rd),top->grade);
300: printf(" init=%s, ",POLYToString(head(rd),'*',1));
301: }
1.1 maekawa 302: }else{
1.5 takayama 303: if (pgrade != top->grade) {
304: pgrade = top->grade;
305: printf(" %d",pgrade);
306: fflush(stdout);
307: }
308: if (rd ISZERO) {
309: printf("o"); fflush(stdout);
310: }else{
311: printf("."); fflush(stdout);
312: }
1.1 maekawa 313: }
314: }
315:
316: if (!(rd ISZERO)) {
317: if (needBack || needSyz) {
1.5 takayama 318: syzp = newSyz0();
319: syzp->cf = syzCf; /* no meaning */
320: syzp->syz = ppAdd(toSyzPoly(h.a,ig,ii),toSyzPoly(h.b,jg,ji));
321: syzp->syz = cpMult(toSyzCoeff(syzCf),syzp->syz);
322: syzp->syz = ppAdd(syzp->syz,syzPoly);
1.1 maekawa 323: }
324:
325: if (ReduceLowerTerms && !(Sugar)) {
1.5 takayama 326: rd = (*reductionCdr)(rd,g,needBack,&syz);
327: if (needBack || needSyz) {
328: /* syzp->cf = ppMult(syz.cf,syzp->cf); no meaning */
329: syzp->syz = ppAdd(syz.syz,
330: cpMult(toSyzCoeff(syz.cf),syzp->syz));
331: }
1.1 maekawa 332: }
333:
334: if(Sugar && (!forceReduction)){grade=top->grade;}else{grade=-1;}whereInG(g,rd,&grade,&indx,Sugar);
335: if (KanGBmessage == 2) {
1.5 takayama 336: printf("(gr,indx)=(%d,%d).\n",grade,indx);
337: /*
338: printf("sp(%s,%s)-->%s\n",POLYToString(gi,' ',1),
339: POLYToString(gj,' ',1),
340: POLYToString(rd,' ',1));
341: */
1.1 maekawa 342: }
1.5 takayama 343:
1.1 maekawa 344: d = updatePairs(d,rd,grade,indx,g);
345: g = putPolyInG(g,rd,grade,indx,syzp,0,-1);
346: if (Sugar) { markRedundant0(g,grade,indx);}
347: else {markRedundant(g,rd,grade,indx,Sugar);}
348:
349: if (countDown) {
1.5 takayama 350: if (eliminated(rd) == 1) {
351: --countDown;
352: printf("x"); fflush(stdout);
353: if (countDown == 0) {
354: printf("\nThe computation of the Groebner basis is suspended because of countDown==0.\n");
355: printf("Note that the result is NOT groebner basis.\n");
356: break;
357: }
358: }
1.1 maekawa 359: }
360: if (Debug) {
1.5 takayama 361: outputGradedPairs(d); outputGradedPolySet(g,needSyz);
1.1 maekawa 362: }
363: }else{
364: if (needSyz) {
1.5 takayama 365: top->syz = ppAdd(toSyzPoly(h.a,ig,ii),toSyzPoly(h.b,jg,ji));
366: top->syz = cpMult(toSyzCoeff(syzCf),top->syz);
367: top->syz = ppAdd(top->syz,syzPoly);
368: listP->next = top; top->prev = listP; listP = listP->next;
369: }
370: }
371: if (StopDegree < pgrade) {
372: fprintf(stderr,"Obtained a partial GB (StopDegree=%d)\n",StopDegree);
373: if (KanGBmessage) {
374: printf("Computation of the Groebner basis is suspended bacause of StopDegree < computing grade.\n");
375: printf("Note that the result is NOT groebner basis.\n");
1.1 maekawa 376: }
1.5 takayama 377: break;
1.1 maekawa 378: }
379: }
380:
381: if (KanGBmessage == 2) {
382: outputGradedPolySet(g,needSyz);
383: }
384: if (KanGBmessage) {
385: if (Sugar) {
386: printf("\nCompleted (GB with sugar).\n");
387: }else{
388: printf("\nCompleted.\n");
389: }
390: }
391:
392: if (Statistics) {
393: printf("\nThe number of s-pairs is %d.\n",Spairs);
394: printf("Criterion1 is applied %d times.\n",Criterion1);
395: printf("Criterions M,F and B are applied M=%d, F=%d, B=%d times.\n",Criterion2M,Criterion2F,Criterion2B);
396: Spairs = Criterion1 = Criterion2M = Criterion2F = Criterion2B = 0;
1.6 takayama 397:
398: printf("degree(number of spolys): maximal polynomial size\n");
399: statisticsCount = 0;
400: for (i=0; i<DMAX; i++) {
401: if (SpNumber[i] > 0) {
402: printf("%3d(%3d): %5d, ",i,SpNumber[i],MaxLength[i]);
403: if (statisticsCount % 4 == 3) {
404: printf("\n");
405: statisticsCount = 0;
406: }else{ statisticsCount++; }
407: }
408: }
409: printf("\n");
1.1 maekawa 410: }
411:
1.3 takayama 412: if (AutoReduce) {
413: toReducedBasis(g,needBack,needSyz);
414: }
1.1 maekawa 415:
416: return(g);
417: }
418:
419:
420: static int sugarGrade(struct pair *inode,struct gradedPolySet *grG,
1.5 takayama 421: POLY gt,int gtSugarGrade)
1.1 maekawa 422: {
423: int a,b,ans;
424: int debug = 0;
425: a = grade_gen(inode->lcm)-grade_gen(grG->polys[inode->ig]->g[inode->ii]);
426: b = grade_gen(inode->lcm)-grade_gen(gt);
427: /* inode = lcm(f_i, gt) = p f_i = q gt modulo lower order terms.
428: a = tdeg(p), b = tdeg(gt);
1.5 takayama 429: */
1.1 maekawa 430: if (debug) {
431: printf("Sugar grade of sp([%d,%d],[%d,%d]) ",inode->ig,inode->ii,
1.5 takayama 432: inode->jg,inode->ji);
1.1 maekawa 433: printf("is max(%d+%d,%d+%d)\n",a,inode->ig,b,gtSugarGrade);
434: }
435: a = a+(inode->ig); /* new sugar degree of p f_i. */
436: b = b + gtSugarGrade; /* new sugar degree of q gt */
437: return( a > b ? a : b);
438: }
439:
1.3 takayama 440: void toReducedBasis(struct gradedPolySet *grP,int needBack, int needSyz)
441: {
442: int changed, grd, i, reduced, grade,indx;
443: struct syz0 syz;
444: struct syz0 *syzp;
445: POLY f;
446: POLY rd;
447: struct polySet *set;
448:
449: /* KanGBmessage=1; */
450: do {
451: if (KanGBmessage) {
452: printf("s"); fflush(stdout);
453: }
454: changed = 0;
455: grd = 0;
456: while (grd < grP->maxGrade) {
457: set = grP->polys[grd];
458: for (i=0; i<set->size; i++) {
1.5 takayama 459: if (set->del[i] == 0) {
460: f = set->g[i];
461: if (KanGBmessage) {
462: /* printf("(%d,%d)",grd,i); */
463: fflush(stdout);
464: }
465: rd = reductionCdr_except_grd_i(f,grP,needBack,&syz,grd,i,&reduced);
466: if (KanGBmessage) {
467: if (reduced) {
468: printf(".");
469: }else{
470: printf("o");
471: }
472: fflush(stdout);
473: }
474: if (reduced) {
475: changed = 1;
476: set->del[i] = 1;
477: if (rd != ZERO) {
478: if (needSyz) {
479: syzp = newSyz0();
480: syzp->cf = syz.cf; /* no meaning */
481: syzp->syz = toSyzPoly(cxx(1,0,0,rd->m->ringp),grd,i);
482: syzp->syz = cpMult(toSyzCoeff(syz.cf),syzp->syz);
483: syzp->syz = ppAdd(syzp->syz,syz.syz);
484: /* rd = c*f + \sum c_{d,i} g_{d,i}
485: c : syz.cf, \sum c_{d,j} g_{d,j} : syz.syz.
486: c*grade^grd*index^i + \sum c_{d,j} grade^d*index^j
487: grP is a set of polynomials. Polynomials are indexed by
488: grade and index.
489: */
490: /* printf("%s, ",POLYToString(syzp->cf,' ',1));
491: printf("%s\n",POLYToString(syzp->syz,' ',1)); */
492: }else{
493: syzp = NULL;
494: }
495: grade = -1; whereInG(grP,rd,&grade,&indx,Sugar);
496: /* Do not forget to set grade to -1 */
497: /* printf("grade=%d, indx=%d, ",grade,indx); */
498: putPolyInG(grP,rd,grade,indx,syzp,0,-1);
499: }
500: }
501: }
1.3 takayama 502: }
503: grd++;
504: }
505: } while(changed);
506: if (KanGBmessage) {
507: printf("Done(reduced basis)\n");
508: }
509: }
1.1 maekawa 510:
511:
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