Annotation of OpenXM/src/kan96xx/Kan/gb.c, Revision 1.9
1.9 ! takayama 1: /* $OpenXM: OpenXM/src/kan96xx/Kan/gb.c,v 1.8 2003/08/19 08:02:09 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:
1.9 ! takayama 165: struct gradedPolySet *groebner_gen(f,needBack,needSyz,grP,countDown,forceReduction,reduceOnly)
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;
1.9 ! takayama 172: int reduceOnly;
1.1 maekawa 173: {
174: int r;
175: struct gradedPolySet *g;
176: struct gradedPairs *d;
177: int i;
178: int grade,indx;
179: POLY gt;
180: struct pair *top;
181: int ig,ii,jg,ji;
182: POLY gi,gj;
183: struct spValue h;
184: struct syz0 syz;
185: int pgrade = 0;
186: POLY rd;
187: POLY syzPoly;
188: POLY syzCf;
189: struct syz0 *syzp;
190: int serial;
191: struct pair *listP;
192: extern int Verbose;
193: extern int ReduceLowerTerms;
194: extern int StopDegree;
195: extern struct ring *CurrentRingp;
196: extern char *F_mpMult;
197: struct ring *rp;
1.8 takayama 198: int first;
1.6 takayama 199: int statisticsPL, statisticsCount;
1.1 maekawa 200:
1.9 ! takayama 201:
1.6 takayama 202: if (Statistics) {
203: for (i=0; i<DMAX; i++) MaxLength[i] = SpNumber[i] = 0;
204: }
1.1 maekawa 205: r = f->n;
206: if (r<=0) return((struct gradedPolySet *)NULL);
207: if (UseCriterion1) {
208: if (needSyz) {
209: warningGradedSet("You cannot use both the options needSyz and UseCriterion1.\nInput [(UseCriterion1) 0] system_variable to turn off the use of the Criterion 1.");
210: }
211: if (strcmp(F_mpMult,"poly")!=0) {
212: 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.");
213: }
214: }
215:
216: Spairs = Criterion1 = Criterion2B = Criterion2F = Criterion2M = 0;
217:
218: g = newGradedPolySet(INITGRADE);
219: d = newGradedPairs(INITGRADE*2);
220: for (i=0; i<g->lim; i++) {
221: g->polys[i] = newPolySet(INITSIZE);
222: }
223:
1.8 takayama 224: first = 1;
1.1 maekawa 225: for (i=0; i<r; i++) {
226: gt = getArrayOfPOLY(f,i);
227: if (gt ISZERO) { rp = CurrentRingp; } else { rp = gt->m->ringp; }
1.8 takayama 228: if (TraceLift && (!(gt ISZERO)) && first) {
229: TraceLift_ringmod = newRingOverFp(rp,getPrime(TraceLift)); first = 0;
230: if (KanGBmessage) printf("Prime number for the trace lift is %d.\n",
231: TraceLift_ringmod->p);
232: }
1.1 maekawa 233: grade = -1; whereInG(g,gt,&grade,&indx,Sugar);
234: if (KanGBmessage == 2) {
235: printf("init=%s, ",POLYToString(head(gt),'*',1));
236: printf("(gr,indx)=(%d,%d).\n",grade,indx);
237: }
238: d = updatePairs(d,gt,grade,indx,g);
239: serial = i;
240: if (!needBack) {
241: g = putPolyInG(g,gt,grade,indx,
1.5 takayama 242: (struct syz0 *)NULL,1,serial);
1.1 maekawa 243: }else {
244: syzp = newSyz0();
245: syzp->cf = cxx(1,0,0,rp);
246: syzp->syz = toSyzPoly(cxx(1,0,0,rp),grade,indx);
247: g = putPolyInG(g,gt,grade,indx,syzp,1,serial);
248: }
249:
1.7 takayama 250: /* markRedundant0(g,grade,indx); ?*/
251: markGeneratorInG(g,grade,indx); /*?*/
1.1 maekawa 252: if (Debug) {
253: outputGradedPairs(d); outputGradedPolySet(g,needSyz);
254: }
255: }
256: if (needSyz) {
257: *grP = newPair((struct pair *)NULL);
258: listP = *grP;
259: }
260:
261: while ((top = getPair(d)) != (struct pair *)NULL) {
262: ig = top->ig; ii = top->ii; /* [ig,ii] */
263: jg = top->jg; ji = top->ji; /* [jg,ji] */
1.7 takayama 264: /*
265: if (g->polys[ig]->del[ii] || g->polys[jg]->del[ji]) {
266: if (KanGBmessage) printf("p");
267: continue;
268: } Don't do this.
269: */
1.1 maekawa 270: gi = g->polys[ig]->g[ii];
271: gj = g->polys[jg]->g[ji];
272:
273: Spairs++;
1.9 ! takayama 274: if (reduceOnly && (!needSyz) && (!needBack)) h = spZero(); /* rd = 0 */
! 275: else h = (*sp)(gi,gj);
1.1 maekawa 276: rd = ppAddv(ppMult(h.a,gi),ppMult(h.b,gj));
1.6 takayama 277:
278: if (Statistics) {
279: if (top->grade >=0 && top->grade < DMAX) {
280: statisticsPL = pLength(rd);
281: SpNumber[top->grade]++;
282: if (MaxLength[top->grade] < statisticsPL) {
283: MaxLength[top->grade] = statisticsPL;
284: }
285: }
286: }
287:
1.1 maekawa 288: if (!Sugar || forceReduction) {
289: rd = (*reduction)(rd,g,needBack,&syz);
290: }else{
291: rd = reduction_sugar(rd,g,needBack,&syz,top->grade);
292: }
293: syzPoly = syz.syz;
294: syzCf = syz.cf;
295:
296: if (KanGBmessage) {
297: if (KanGBmessage == 2) {
1.5 takayama 298: printf("sp([%d,%d],[%d,%d]), ",ig,ii,jg,ji);
299: if (rd ISZERO) {
300: printf(" 0 \n");
301: } else{
302: printf(" terms=%d, grade=%d, ",pLength(rd),top->grade);
303: printf(" init=%s, ",POLYToString(head(rd),'*',1));
304: }
1.1 maekawa 305: }else{
1.5 takayama 306: if (pgrade != top->grade) {
307: pgrade = top->grade;
308: printf(" %d",pgrade);
309: fflush(stdout);
310: }
311: if (rd ISZERO) {
312: printf("o"); fflush(stdout);
313: }else{
314: printf("."); fflush(stdout);
315: }
1.1 maekawa 316: }
317: }
318:
319: if (!(rd ISZERO)) {
320: if (needBack || needSyz) {
1.5 takayama 321: syzp = newSyz0();
322: syzp->cf = syzCf; /* no meaning */
323: syzp->syz = ppAdd(toSyzPoly(h.a,ig,ii),toSyzPoly(h.b,jg,ji));
324: syzp->syz = cpMult(toSyzCoeff(syzCf),syzp->syz);
325: syzp->syz = ppAdd(syzp->syz,syzPoly);
1.1 maekawa 326: }
327:
328: if (ReduceLowerTerms && !(Sugar)) {
1.5 takayama 329: rd = (*reductionCdr)(rd,g,needBack,&syz);
330: if (needBack || needSyz) {
331: /* syzp->cf = ppMult(syz.cf,syzp->cf); no meaning */
332: syzp->syz = ppAdd(syz.syz,
333: cpMult(toSyzCoeff(syz.cf),syzp->syz));
334: }
1.1 maekawa 335: }
336:
337: if(Sugar && (!forceReduction)){grade=top->grade;}else{grade=-1;}whereInG(g,rd,&grade,&indx,Sugar);
338: if (KanGBmessage == 2) {
1.5 takayama 339: printf("(gr,indx)=(%d,%d).\n",grade,indx);
340: /*
341: printf("sp(%s,%s)-->%s\n",POLYToString(gi,' ',1),
342: POLYToString(gj,' ',1),
343: POLYToString(rd,' ',1));
344: */
1.1 maekawa 345: }
1.5 takayama 346:
1.1 maekawa 347: d = updatePairs(d,rd,grade,indx,g);
348: g = putPolyInG(g,rd,grade,indx,syzp,0,-1);
349: if (Sugar) { markRedundant0(g,grade,indx);}
350: else {markRedundant(g,rd,grade,indx,Sugar);}
351:
352: if (countDown) {
1.5 takayama 353: if (eliminated(rd) == 1) {
354: --countDown;
355: printf("x"); fflush(stdout);
356: if (countDown == 0) {
357: printf("\nThe computation of the Groebner basis is suspended because of countDown==0.\n");
358: printf("Note that the result is NOT groebner basis.\n");
359: break;
360: }
361: }
1.1 maekawa 362: }
363: if (Debug) {
1.5 takayama 364: outputGradedPairs(d); outputGradedPolySet(g,needSyz);
1.1 maekawa 365: }
366: }else{
367: if (needSyz) {
1.5 takayama 368: top->syz = ppAdd(toSyzPoly(h.a,ig,ii),toSyzPoly(h.b,jg,ji));
369: top->syz = cpMult(toSyzCoeff(syzCf),top->syz);
370: top->syz = ppAdd(top->syz,syzPoly);
371: listP->next = top; top->prev = listP; listP = listP->next;
372: }
373: }
374: if (StopDegree < pgrade) {
375: fprintf(stderr,"Obtained a partial GB (StopDegree=%d)\n",StopDegree);
376: if (KanGBmessage) {
377: printf("Computation of the Groebner basis is suspended bacause of StopDegree < computing grade.\n");
378: printf("Note that the result is NOT groebner basis.\n");
1.1 maekawa 379: }
1.5 takayama 380: break;
1.1 maekawa 381: }
382: }
383:
384: if (KanGBmessage == 2) {
385: outputGradedPolySet(g,needSyz);
386: }
387: if (KanGBmessage) {
388: if (Sugar) {
389: printf("\nCompleted (GB with sugar).\n");
390: }else{
391: printf("\nCompleted.\n");
392: }
393: }
394:
395: if (Statistics) {
396: printf("\nThe number of s-pairs is %d.\n",Spairs);
397: printf("Criterion1 is applied %d times.\n",Criterion1);
398: printf("Criterions M,F and B are applied M=%d, F=%d, B=%d times.\n",Criterion2M,Criterion2F,Criterion2B);
399: Spairs = Criterion1 = Criterion2M = Criterion2F = Criterion2B = 0;
1.6 takayama 400:
401: printf("degree(number of spolys): maximal polynomial size\n");
402: statisticsCount = 0;
403: for (i=0; i<DMAX; i++) {
404: if (SpNumber[i] > 0) {
405: printf("%3d(%3d): %5d, ",i,SpNumber[i],MaxLength[i]);
406: if (statisticsCount % 4 == 3) {
407: printf("\n");
408: statisticsCount = 0;
409: }else{ statisticsCount++; }
410: }
411: }
412: printf("\n");
1.1 maekawa 413: }
414:
1.9 ! takayama 415: if (AutoReduce || reduceOnly) {
1.3 takayama 416: toReducedBasis(g,needBack,needSyz);
417: }
1.1 maekawa 418:
419: return(g);
420: }
421:
422:
423: static int sugarGrade(struct pair *inode,struct gradedPolySet *grG,
1.5 takayama 424: POLY gt,int gtSugarGrade)
1.1 maekawa 425: {
426: int a,b,ans;
427: int debug = 0;
428: a = grade_gen(inode->lcm)-grade_gen(grG->polys[inode->ig]->g[inode->ii]);
429: b = grade_gen(inode->lcm)-grade_gen(gt);
430: /* inode = lcm(f_i, gt) = p f_i = q gt modulo lower order terms.
431: a = tdeg(p), b = tdeg(gt);
1.5 takayama 432: */
1.1 maekawa 433: if (debug) {
434: printf("Sugar grade of sp([%d,%d],[%d,%d]) ",inode->ig,inode->ii,
1.5 takayama 435: inode->jg,inode->ji);
1.1 maekawa 436: printf("is max(%d+%d,%d+%d)\n",a,inode->ig,b,gtSugarGrade);
437: }
438: a = a+(inode->ig); /* new sugar degree of p f_i. */
439: b = b + gtSugarGrade; /* new sugar degree of q gt */
440: return( a > b ? a : b);
441: }
442:
1.3 takayama 443: void toReducedBasis(struct gradedPolySet *grP,int needBack, int needSyz)
444: {
445: int changed, grd, i, reduced, grade,indx;
446: struct syz0 syz;
447: struct syz0 *syzp;
448: POLY f;
449: POLY rd;
450: struct polySet *set;
451:
452: /* KanGBmessage=1; */
453: do {
454: if (KanGBmessage) {
455: printf("s"); fflush(stdout);
456: }
457: changed = 0;
458: grd = 0;
459: while (grd < grP->maxGrade) {
460: set = grP->polys[grd];
461: for (i=0; i<set->size; i++) {
1.5 takayama 462: if (set->del[i] == 0) {
463: f = set->g[i];
464: if (KanGBmessage) {
465: /* printf("(%d,%d)",grd,i); */
466: fflush(stdout);
467: }
468: rd = reductionCdr_except_grd_i(f,grP,needBack,&syz,grd,i,&reduced);
469: if (KanGBmessage) {
470: if (reduced) {
471: printf(".");
472: }else{
473: printf("o");
474: }
475: fflush(stdout);
476: }
477: if (reduced) {
478: changed = 1;
479: set->del[i] = 1;
480: if (rd != ZERO) {
481: if (needSyz) {
482: syzp = newSyz0();
483: syzp->cf = syz.cf; /* no meaning */
484: syzp->syz = toSyzPoly(cxx(1,0,0,rd->m->ringp),grd,i);
485: syzp->syz = cpMult(toSyzCoeff(syz.cf),syzp->syz);
486: syzp->syz = ppAdd(syzp->syz,syz.syz);
487: /* rd = c*f + \sum c_{d,i} g_{d,i}
488: c : syz.cf, \sum c_{d,j} g_{d,j} : syz.syz.
489: c*grade^grd*index^i + \sum c_{d,j} grade^d*index^j
490: grP is a set of polynomials. Polynomials are indexed by
491: grade and index.
492: */
493: /* printf("%s, ",POLYToString(syzp->cf,' ',1));
494: printf("%s\n",POLYToString(syzp->syz,' ',1)); */
495: }else{
496: syzp = NULL;
497: }
498: grade = -1; whereInG(grP,rd,&grade,&indx,Sugar);
499: /* Do not forget to set grade to -1 */
500: /* printf("grade=%d, indx=%d, ",grade,indx); */
501: putPolyInG(grP,rd,grade,indx,syzp,0,-1);
502: }
503: }
504: }
1.3 takayama 505: }
506: grd++;
507: }
508: } while(changed);
509: if (KanGBmessage) {
510: printf("Done(reduced basis)\n");
511: }
512: }
1.1 maekawa 513:
514:
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