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hdegree.cc
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1/****************************************
2* Computer Algebra System SINGULAR *
3****************************************/
4/*
5* ABSTRACT - dimension, multiplicity, HC, kbase
6*/
7
8#include "kernel/mod2.h"
9
10#include "misc/intvec.h"
11#include "coeffs/numbers.h"
12
13#include "kernel/structs.h"
14#include "kernel/ideals.h"
15#include "kernel/polys.h"
16
20#include "reporter/reporter.h"
21
22#ifdef HAVE_SHIFTBBA
23#include <vector>
24#include "misc/options.h"
25#endif
26
28VAR long hMu;
30
31/*0 implementation*/
32
33// dimension
34
36 varset var, int Nvar)
37{
38 int dn, iv, rad0, b, c, x;
39 scmon pn;
40 scfmon rn;
41 if (Nrad < 2)
42 {
43 dn = Npure + Nrad;
44 if (dn < hCo)
45 hCo = dn;
46 return;
47 }
48 if (Npure+1 >= hCo)
49 return;
50 iv = Nvar;
51 while(pure[var[iv]]) iv--;
52 hStepR(rad, Nrad, var, iv, &rad0);
53 if (rad0!=0)
54 {
55 iv--;
56 if (rad0 < Nrad)
57 {
58 pn = hGetpure(pure);
59 rn = hGetmem(Nrad, rad, radmem[iv]);
60 hDimSolve(pn, Npure + 1, rn, rad0, var, iv);
61 b = rad0;
62 c = Nrad;
63 hElimR(rn, &rad0, b, c, var, iv);
64 hPure(rn, b, &c, var, iv, pn, &x);
65 hLex2R(rn, rad0, b, c, var, iv, hwork);
66 rad0 += (c - b);
67 hDimSolve(pn, Npure + x, rn, rad0, var, iv);
68 }
69 else
70 {
71 hDimSolve(pure, Npure, rad, Nrad, var, iv);
72 }
73 }
74 else
75 hCo = Npure + 1;
76}
77
79{
80 id_Test(S, currRing);
81 if( Q!=NULL ) id_Test(Q, currRing);
82
83 int mc;
84 hexist = hInit(S, Q, &hNexist);
85 if (!hNexist)
86 return (currRing->N);
87 hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
88 hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
89 hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
90 mc = hisModule;
91 if (!mc)
92 {
93 hrad = hexist;
94 hNrad = hNexist;
95 }
96 else
97 hrad = (scfmon)omAlloc(hNexist * sizeof(scmon));
98 radmem = hCreate((currRing->N) - 1);
99 hCo = (currRing->N) + 1;
100 loop
101 {
102 if (mc)
103 hComp(hexist, hNexist, mc, hrad, &hNrad);
104 if (hNrad)
105 {
106 hNvar = (currRing->N);
109 if (hNvar)
110 {
111 memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
112 hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
115 }
116 }
117 else
118 {
119 hCo = 0;
120 break;
121 }
122 mc--;
123 if (mc <= 0)
124 break;
125 }
126 hKill(radmem, (currRing->N) - 1);
127 omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
128 omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
129 omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
131 if (hisModule)
132 omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon));
133 return (currRing->N) - hCo;
134}
135
137{
138#ifdef HAVE_RINGS
140 {
141 int i = idPosConstant(vid);
142 if ((i != -1) && (n_IsUnit(pGetCoeff(vid->m[i]),currRing->cf)))
143 { /* ideal v contains unit; dim = -1 */
144 return(-1);
145 }
149 int d;
150 if(i == -1)
151 {
152 d = scDimInt(vv, Q);
154 d++;
155 }
156 else
157 {
158 if(n_IsUnit(pGetCoeff(vv->m[i]),currRing->cf))
159 d = -1;
160 else
161 d = scDimInt(vv, Q);
162 }
163 //Anne's Idea for std(4,2x) = 0 bug
164 int dcurr = d;
165 for(unsigned ii=0;ii<(unsigned)IDELEMS(vv);ii++)
166 {
167 if(vv->m[ii] != NULL && !n_IsUnit(pGetCoeff(vv->m[ii]),currRing->cf))
168 {
169 ideal vc = idCopy(vv);
170 poly c = pInit();
171 pSetCoeff0(c,nCopy(pGetCoeff(vv->m[ii])));
172 idInsertPoly(vc,c);
174 for(unsigned jj = 0;jj<(unsigned)IDELEMS(vc)-1;jj++)
175 {
176 if((vc->m[jj]!=NULL)
177 && (n_DivBy(pGetCoeff(vc->m[jj]),pGetCoeff(c),currRing->cf)))
178 {
179 pDelete(&vc->m[jj]);
180 }
181 }
183 i = idPosConstant(vc);
184 if (i != -1) pDelete(&vc->m[i]);
185 dcurr = scDimInt(vc, Q);
186 // the following assumes the ground rings to be either zero- or one-dimensional
187 if((i==-1) && rField_is_Z(currRing))
188 {
189 // should also be activated for other euclidean domains as groundfield
190 dcurr++;
191 }
192 idDelete(&vc);
193 }
194 if(dcurr > d)
195 d = dcurr;
196 }
197 idDelete(&vv);
198 return d;
199 }
200#endif
201 return scDimInt(vid,Q);
202}
203
204// independent set
206
207static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad,
208 varset var, int Nvar)
209{
210 int dn, iv, rad0, b, c, x;
211 scmon pn;
212 scfmon rn;
213 if (Nrad < 2)
214 {
215 dn = Npure + Nrad;
216 if (dn < hCo)
217 {
218 hCo = dn;
219 for (iv=(currRing->N); iv; iv--)
220 {
221 if (pure[iv])
222 hInd[iv] = 0;
223 else
224 hInd[iv] = 1;
225 }
226 if (Nrad)
227 {
228 pn = *rad;
229 iv = Nvar;
230 loop
231 {
232 x = var[iv];
233 if (pn[x])
234 {
235 hInd[x] = 0;
236 break;
237 }
238 iv--;
239 }
240 }
241 }
242 return;
243 }
244 if (Npure+1 >= hCo)
245 return;
246 iv = Nvar;
247 while(pure[var[iv]]) iv--;
248 hStepR(rad, Nrad, var, iv, &rad0);
249 if (rad0)
250 {
251 iv--;
252 if (rad0 < Nrad)
253 {
254 pn = hGetpure(pure);
255 rn = hGetmem(Nrad, rad, radmem[iv]);
256 pn[var[iv + 1]] = 1;
257 hIndSolve(pn, Npure + 1, rn, rad0, var, iv);
258 pn[var[iv + 1]] = 0;
259 b = rad0;
260 c = Nrad;
261 hElimR(rn, &rad0, b, c, var, iv);
262 hPure(rn, b, &c, var, iv, pn, &x);
263 hLex2R(rn, rad0, b, c, var, iv, hwork);
264 rad0 += (c - b);
265 hIndSolve(pn, Npure + x, rn, rad0, var, iv);
266 }
267 else
268 {
269 hIndSolve(pure, Npure, rad, Nrad, var, iv);
270 }
271 }
272 else
273 {
274 hCo = Npure + 1;
275 for (x=(currRing->N); x; x--)
276 {
277 if (pure[x])
278 hInd[x] = 0;
279 else
280 hInd[x] = 1;
281 }
282 hInd[var[iv]] = 0;
283 }
284}
285
287{
288 id_Test(S, currRing);
289 if( Q!=NULL ) id_Test(Q, currRing);
290
291 intvec *Set=new intvec((currRing->N));
292 int mc,i;
293 hexist = hInit(S, Q, &hNexist);
294 if (hNexist==0)
295 {
296 for(i=0; i<(currRing->N); i++)
297 (*Set)[i]=1;
298 return Set;
299 }
300 hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
301 hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
302 hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
303 hInd = (scmon)omAlloc0((1 + (currRing->N)) * sizeof(int));
304 mc = hisModule;
305 if (mc==0)
306 {
307 hrad = hexist;
308 hNrad = hNexist;
309 }
310 else
311 hrad = (scfmon)omAlloc(hNexist * sizeof(scmon));
312 radmem = hCreate((currRing->N) - 1);
313 hCo = (currRing->N) + 1;
314 loop
315 {
316 if (mc!=0)
317 hComp(hexist, hNexist, mc, hrad, &hNrad);
318 if (hNrad!=0)
319 {
320 hNvar = (currRing->N);
323 if (hNvar!=0)
324 {
325 memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
326 hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
329 }
330 }
331 else
332 {
333 hCo = 0;
334 break;
335 }
336 mc--;
337 if (mc <= 0)
338 break;
339 }
340 for(i=0; i<(currRing->N); i++)
341 (*Set)[i] = hInd[i+1];
342 hKill(radmem, (currRing->N) - 1);
343 omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
344 omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int));
345 omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
346 omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
348 if (hisModule)
349 omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon));
350 return Set;
351}
352
354
355static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar)
356{
357 int k1, i;
358 k1 = var[Nvar];
359 i = 0;
360 loop
361 {
362 if (rad[i][k1]==0)
363 return FALSE;
364 i++;
365 if (i == Nrad)
366 return TRUE;
367 }
368}
369
370static void hIndep(scmon pure)
371{
372 int iv;
373 intvec *Set;
374
375 Set = ISet->set = new intvec((currRing->N));
376 for (iv=(currRing->N); iv!=0 ; iv--)
377 {
378 (*Set)[iv-1] = (pure[iv]==0);
379 }
381 hMu++;
382}
383
385 varset var, int Nvar)
386{
387 int dn, iv, rad0, b, c, x;
388 scmon pn;
389 scfmon rn;
390 if (Nrad < 2)
391 {
392 dn = Npure + Nrad;
393 if (dn == hCo)
394 {
395 if (Nrad==0)
396 hIndep(pure);
397 else
398 {
399 pn = *rad;
400 for (iv = Nvar; iv!=0; iv--)
401 {
402 x = var[iv];
403 if (pn[x])
404 {
405 pure[x] = 1;
406 hIndep(pure);
407 pure[x] = 0;
408 }
409 }
410 }
411 }
412 return;
413 }
414 iv = Nvar;
415 dn = Npure+1;
416 if (dn >= hCo)
417 {
418 if (dn > hCo)
419 return;
420 loop
421 {
422 if(!pure[var[iv]])
423 {
424 if(hNotZero(rad, Nrad, var, iv))
425 {
426 pure[var[iv]] = 1;
427 hIndep(pure);
428 pure[var[iv]] = 0;
429 }
430 }
431 iv--;
432 if (!iv)
433 return;
434 }
435 }
436 while(pure[var[iv]]) iv--;
437 hStepR(rad, Nrad, var, iv, &rad0);
438 iv--;
439 if (rad0 < Nrad)
440 {
441 pn = hGetpure(pure);
442 rn = hGetmem(Nrad, rad, radmem[iv]);
443 pn[var[iv + 1]] = 1;
444 hIndMult(pn, Npure + 1, rn, rad0, var, iv);
445 pn[var[iv + 1]] = 0;
446 b = rad0;
447 c = Nrad;
448 hElimR(rn, &rad0, b, c, var, iv);
449 hPure(rn, b, &c, var, iv, pn, &x);
450 hLex2R(rn, rad0, b, c, var, iv, hwork);
451 rad0 += (c - b);
452 hIndMult(pn, Npure + x, rn, rad0, var, iv);
453 }
454 else
455 {
456 hIndMult(pure, Npure, rad, Nrad, var, iv);
457 }
458}
459
460/*3
461* consider indset x := !pure
462* (for all i) (if(sm(i) > x) return FALSE)
463* else return TRUE
464*/
466{
467 int iv;
468 intvec *Set;
469 while (sm->nx != NULL)
470 {
471 Set = sm->set;
472 iv=(currRing->N);
473 loop
474 {
475 if (((*Set)[iv-1] == 0) && (pure[iv] == 0))
476 break;
477 iv--;
478 if (iv == 0)
479 return FALSE;
480 }
481 sm = sm->nx;
482 }
483 return TRUE;
484}
485
486/*3
487* consider indset x := !pure
488* (for all i) if(x > sm(i)) delete sm(i))
489* return (place for x)
490*/
492{
493 int iv;
494 intvec *Set;
495 indset be, a1 = NULL;
496 while (sm->nx != NULL)
497 {
498 Set = sm->set;
499 iv=(currRing->N);
500 loop
501 {
502 if ((pure[iv] == 1) && ((*Set)[iv-1] == 1))
503 break;
504 iv--;
505 if (iv == 0)
506 {
507 if (a1 == NULL)
508 {
509 a1 = sm;
510 }
511 else
512 {
513 hMu2--;
514 be->nx = sm->nx;
515 delete Set;
517 sm = be;
518 }
519 break;
520 }
521 }
522 be = sm;
523 sm = sm->nx;
524 }
525 if (a1 != NULL)
526 {
527 return a1;
528 }
529 else
530 {
531 hMu2++;
532 sm->set = new intvec((currRing->N));
534 return sm;
535 }
536}
537
538/*2
539* definition x >= y
540* x(i) == 0 => y(i) == 0
541* > ex. j with x(j) == 1 and y(j) == 0
542*/
544{
545 intvec *Set;
546 indset res;
547 int iv;
548 if (hCheck1(ISet, pure))
549 {
550 if (hCheck1(JSet, pure))
551 {
552 res = hCheck2(JSet,pure);
553 if (res == NULL)
554 return;
555 Set = res->set;
556 for (iv=(currRing->N); iv; iv--)
557 {
558 (*Set)[iv-1] = (pure[iv]==0);
559 }
560 }
561 }
562}
563
565 varset var, int Nvar)
566{
567 int dn, iv, rad0, b, c, x;
568 scmon pn;
569 scfmon rn;
570 if (Nrad < 2)
571 {
572 dn = Npure + Nrad;
573 if (dn > hCo)
574 {
575 if (!Nrad)
577 else
578 {
579 pn = *rad;
580 for (iv = Nvar; iv; iv--)
581 {
582 x = var[iv];
583 if (pn[x])
584 {
585 pure[x] = 1;
587 pure[x] = 0;
588 }
589 }
590 }
591 }
592 return;
593 }
594 iv = Nvar;
595 while(pure[var[iv]]) iv--;
596 hStepR(rad, Nrad, var, iv, &rad0);
597 iv--;
598 if (rad0 < Nrad)
599 {
600 pn = hGetpure(pure);
601 rn = hGetmem(Nrad, rad, radmem[iv]);
602 pn[var[iv + 1]] = 1;
603 hIndAllMult(pn, Npure + 1, rn, rad0, var, iv);
604 pn[var[iv + 1]] = 0;
605 b = rad0;
606 c = Nrad;
607 hElimR(rn, &rad0, b, c, var, iv);
608 hPure(rn, b, &c, var, iv, pn, &x);
609 hLex2R(rn, rad0, b, c, var, iv, hwork);
610 rad0 += (c - b);
611 hIndAllMult(pn, Npure + x, rn, rad0, var, iv);
612 }
613 else
614 {
615 hIndAllMult(pure, Npure, rad, Nrad, var, iv);
616 }
617}
618
619// multiplicity
620
621static long hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar)
622{
623 int iv = Nvar -1, a, a0, a1, b, i;
624 long sum;
625 int x, x0;
626 scmon pn;
627 scfmon sn;
628 if (!iv)
629 return pure[var[1]];
630 else if (!Nstc)
631 {
632 sum = 1;
633 for (i = Nvar; i; i--)
634 sum *= pure[var[i]];
635 return sum;
636 }
637 x = a = 0;
638 pn = hGetpure(pure);
639 sn = hGetmem(Nstc, stc, stcmem[iv]);
640 hStepS(sn, Nstc, var, Nvar, &a, &x);
641 if (a == Nstc)
642 {
643 #if SIZEOF_LONG==8
644 return (long)pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv);
645 #else
646 int64 t=hZeroMult(pn, sn, a, var, iv);
647 t *= pure[var[Nvar]];
648 if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t;
649 else if (!errorreported) WerrorS("int overflow in vdim 3");
650 return sum;
651 #endif
652 }
653 else
654 {
655 #if SIZEOF_LONG==8
656 sum = x * hZeroMult(pn, sn, a, var, iv);
657 #else
658 int64 t=hZeroMult(pn, sn, a, var, iv);
659 t *= x;
660 if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t;
661 else if (!errorreported) WerrorS("int overflow in vdim 4");
662 #endif
663 }
664 b = a;
665 loop
666 {
667 a0 = a;
668 x0 = x;
669 hStepS(sn, Nstc, var, Nvar, &a, &x);
670 hElimS(sn, &b, a0, a, var, iv);
671 a1 = a;
672 hPure(sn, a0, &a1, var, iv, pn, &i);
673 hLex2S(sn, b, a0, a1, var, iv, hwork);
674 b += (a1 - a0);
675 if (a < Nstc)
676 {
677 #if SIZEOF_LONG==8
678 sum += (long)(x - x0) * hZeroMult(pn, sn, b, var, iv);
679 #else
680 int64 t=hZeroMult(pn, sn, b, var, iv);
681 t *= (x-x0);
682 t += sum;
683 if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t;
684 else if (!errorreported) WerrorS("int overflow in vdim 1");
685 #endif
686 }
687 else
688 {
689 #if SIZEOF_LONG==8
690 sum += (long)(pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv);
691 #else
692 int64 t=hZeroMult(pn, sn, b, var, iv);
693 t *= (pure[var[Nvar]]-x0);
694 t += sum;
695 if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t;
696 else if (!errorreported) WerrorS("int overflow in vdim 2");
697 #endif
698 return sum;
699 }
700 }
701}
702
704{
705 int i, i0, k;
706 i0 = 0;
707 for (i = 1; i <= (currRing->N); i++)
708 {
709 if (pure[i])
710 {
711 i0++;
712 sel[i0] = i;
713 }
714 }
715 i = hNstc;
716 memcpy(hwork, hstc, i * sizeof(scmon));
717 hStaircase(hwork, &i, sel, i0);
718 if ((i0 > 2) && (i > 10))
719 hOrdSupp(hwork, i, sel, i0);
720 memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int));
721 hPure(hwork, 0, &i, sel, i0, hpur0, &k);
722 hLexS(hwork, i, sel, i0);
723 hMu += hZeroMult(hpur0, hwork, i, sel, i0);
724}
725
726static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad,
727 varset var, int Nvar)
728{
729 int dn, iv, rad0, b, c, x;
730 scmon pn;
731 scfmon rn;
732 if (Nrad < 2)
733 {
734 dn = Npure + Nrad;
735 if (dn == hCo)
736 {
737 if (!Nrad)
739 else
740 {
741 pn = *rad;
742 for (iv = Nvar; iv; iv--)
743 {
744 x = var[iv];
745 if (pn[x])
746 {
747 pure[x] = 1;
749 pure[x] = 0;
750 }
751 }
752 }
753 }
754 return;
755 }
756 iv = Nvar;
757 dn = Npure+1;
758 if (dn >= hCo)
759 {
760 if (dn > hCo)
761 return;
762 loop
763 {
764 if(!pure[var[iv]])
765 {
766 if(hNotZero(rad, Nrad, var, iv))
767 {
768 pure[var[iv]] = 1;
770 pure[var[iv]] = 0;
771 }
772 }
773 iv--;
774 if (!iv)
775 return;
776 }
777 }
778 while(pure[var[iv]]) iv--;
779 hStepR(rad, Nrad, var, iv, &rad0);
780 iv--;
781 if (rad0 < Nrad)
782 {
783 pn = hGetpure(pure);
784 rn = hGetmem(Nrad, rad, radmem[iv]);
785 pn[var[iv + 1]] = 1;
786 hDimMult(pn, Npure + 1, rn, rad0, var, iv);
787 pn[var[iv + 1]] = 0;
788 b = rad0;
789 c = Nrad;
790 hElimR(rn, &rad0, b, c, var, iv);
791 hPure(rn, b, &c, var, iv, pn, &x);
792 hLex2R(rn, rad0, b, c, var, iv, hwork);
793 rad0 += (c - b);
794 hDimMult(pn, Npure + x, rn, rad0, var, iv);
795 }
796 else
797 {
798 hDimMult(pure, Npure, rad, Nrad, var, iv);
799 }
800}
801
802static void hDegree(ideal S, ideal Q)
803{
804 id_Test(S, currRing);
805 if( Q!=NULL ) id_Test(Q, currRing);
806
807 int di;
808 int mc;
809 hexist = hInit(S, Q, &hNexist);
810 if (!hNexist)
811 {
812 hCo = 0;
813 hMu = 1;
814 return;
815 }
816 //hWeight();
817 hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
818 hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
819 hsel = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
820 hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
821 hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
822 mc = hisModule;
823 hrad = (scfmon)omAlloc(hNexist * sizeof(scmon));
824 if (!mc)
825 {
826 memcpy(hrad, hexist, hNexist * sizeof(scmon));
827 hstc = hexist;
828 hNrad = hNstc = hNexist;
829 }
830 else
831 hstc = (scfmon)omAlloc(hNexist * sizeof(scmon));
832 radmem = hCreate((currRing->N) - 1);
833 stcmem = hCreate((currRing->N) - 1);
834 hCo = (currRing->N) + 1;
835 di = hCo + 1;
836 loop
837 {
838 if (mc)
839 {
840 hComp(hexist, hNexist, mc, hrad, &hNrad);
841 hNstc = hNrad;
842 memcpy(hstc, hrad, hNrad * sizeof(scmon));
843 }
844 if (hNrad)
845 {
846 hNvar = (currRing->N);
849 if (hNvar)
850 {
851 hCo = hNvar;
852 memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
853 hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
856 }
857 }
858 else
859 {
860 hNvar = 1;
861 hCo = 0;
862 }
863 if (hCo < di)
864 {
865 di = hCo;
866 hMu = 0;
867 }
868 if (hNvar && (hCo == di))
869 {
870 if (di && (di < (currRing->N)))
872 else if (!di)
873 hMu++;
874 else
875 {
877 if ((hNvar > 2) && (hNstc > 10))
879 memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int));
880 hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure);
883 }
884 }
885 mc--;
886 if (mc <= 0)
887 break;
888 }
889 hCo = di;
890 hKill(stcmem, (currRing->N) - 1);
891 hKill(radmem, (currRing->N) - 1);
892 omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
893 omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
894 omFreeSize((ADDRESS)hsel, ((currRing->N) + 1) * sizeof(int));
895 omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
896 omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
897 omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon));
899 if (hisModule)
900 omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon));
901}
902
904{
905 id_Test(S, currRing);
906 if( Q!=NULL ) id_Test(Q, currRing);
907
908 hDegree(S, Q);
909 return hMu;
910}
911
912void scPrintDegree(int co, int mu)
913{
914 int di = (currRing->N)-co;
915 if (currRing->OrdSgn == 1)
916 {
917 if (di>0)
918 Print("// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1, mu);
919 else
920 Print("// dimension (affine) = 0\n// degree (affine) = %d\n", mu);
921 }
922 else
923 Print("// dimension (local) = %d\n// multiplicity = %d\n", di, mu);
924}
925
927{
928 id_Test(S, currRing);
929 if( Q!=NULL ) id_Test(Q, currRing);
930
931 int co, mu, l;
934 if (errorreported) return;
935 l = hseries1->length()-1;
936 if (l > 1)
938 else
941 if ((l == 1) &&(mu == 0))
942 scPrintDegree((currRing->N)+1, 0);
943 else
945 if (l>1)
946 delete hseries1;
947 delete hseries2;
948}
949
951{
953 if (Q!=NULL) id_LmTest(Q, currRing);
954
955 int mc;
956 hexist = hInit(S, Q, &hNexist);
957 if (!hNexist)
958 {
959 hMu = -1;
960 return -1;
961 }
962 else
963 hMu = 0;
964
965 const ring r = currRing;
966
967 hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
968 hvar = (varset)omAlloc(((r->N) + 1) * sizeof(int));
969 hpur0 = (scmon)omAlloc((1 + ((r->N) * (r->N))) * sizeof(int));
970 mc = hisModule;
971 if (!mc)
972 {
973 hstc = hexist;
974 hNstc = hNexist;
975 }
976 else
977 hstc = (scfmon)omAlloc(hNexist * sizeof(scmon));
978 stcmem = hCreate((r->N) - 1);
979 loop
980 {
981 if (mc)
982 {
983 hComp(hexist, hNexist, mc, hstc, &hNstc);
984 if (!hNstc)
985 {
986 hMu = -1;
987 break;
988 }
989 }
990 hNvar = (r->N);
991 for (int i = hNvar; i; i--)
992 hvar[i] = i;
995 if ((hNvar == (r->N)) && (hNstc >= (r->N)))
996 {
997 if ((hNvar > 2) && (hNstc > 10))
999 memset(hpur0, 0, ((r->N) + 1) * sizeof(int));
1000 hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure);
1001 if (hNpure == hNvar)
1002 {
1005 }
1006 else
1007 hMu = -1;
1008 }
1009 else if (hNvar)
1010 hMu = -1;
1011 mc--;
1012 if (mc <= 0 || hMu < 0)
1013 break;
1014 }
1015 hKill(stcmem, (r->N) - 1);
1016 omFreeSize((ADDRESS)hpur0, (1 + ((r->N) * (r->N))) * sizeof(int));
1017 omFreeSize((ADDRESS)hvar, ((r->N) + 1) * sizeof(int));
1018 omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1020 if (hisModule)
1021 omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon));
1022 return hMu;
1023}
1024
1025// HC
1026
1028
1029static void hHedge(poly hEdge)
1030{
1031 pSetm(pWork);
1032 if (pLmCmp(pWork, hEdge) == currRing->OrdSgn)
1033 {
1034 for (int i = hNvar; i>0; i--)
1036 pSetm(hEdge);
1037 }
1038}
1039
1041 int Nstc, varset var, int Nvar,poly hEdge)
1042{
1043 int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i;
1044 int x/*, x0*/;
1045 scmon pn;
1046 scfmon sn;
1047 if (iv==0)
1048 {
1049 pSetExp(pWork, k, pure[k]);
1050 hHedge(hEdge);
1051 return;
1052 }
1053 else if (Nstc==0)
1054 {
1055 for (i = Nvar; i>0; i--)
1056 pSetExp(pWork, var[i], pure[var[i]]);
1057 hHedge(hEdge);
1058 return;
1059 }
1060 x = a = 0;
1061 pn = hGetpure(pure);
1062 sn = hGetmem(Nstc, stc, stcmem[iv]);
1063 hStepS(sn, Nstc, var, Nvar, &a, &x);
1064 if (a == Nstc)
1065 {
1066 pSetExp(pWork, k, pure[k]);
1067 hHedgeStep(pn, sn, a, var, iv,hEdge);
1068 return;
1069 }
1070 else
1071 {
1072 pSetExp(pWork, k, x);
1073 hHedgeStep(pn, sn, a, var, iv,hEdge);
1074 }
1075 b = a;
1076 loop
1077 {
1078 a0 = a;
1079 // x0 = x;
1080 hStepS(sn, Nstc, var, Nvar, &a, &x);
1081 hElimS(sn, &b, a0, a, var, iv);
1082 a1 = a;
1083 hPure(sn, a0, &a1, var, iv, pn, &i);
1084 hLex2S(sn, b, a0, a1, var, iv, hwork);
1085 b += (a1 - a0);
1086 if (a < Nstc)
1087 {
1088 pSetExp(pWork, k, x);
1089 hHedgeStep(pn, sn, b, var, iv,hEdge);
1090 }
1091 else
1092 {
1093 pSetExp(pWork, k, pure[k]);
1094 hHedgeStep(pn, sn, b, var, iv,hEdge);
1095 return;
1096 }
1097 }
1098}
1099
1100void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge)
1101{
1102 id_LmTest(S, currRing);
1103 if (Q!=NULL) id_LmTest(Q, currRing);
1104
1105 int i;
1106 int k = ak;
1107 #ifdef HAVE_RINGS
1108 if (rField_is_Ring(currRing) && (currRing->OrdSgn == -1))
1109 {
1110 //consider just monic generators (over rings with zero-divisors)
1112 for(i=0;i<=idElem(S);i++)
1113 {
1114 if((SS->m[i]!=NULL)
1115 && ((p_IsPurePower(SS->m[i],currRing)==0)
1116 ||(!n_IsUnit(pGetCoeff(SS->m[i]), currRing->cf))))
1117 {
1118 p_Delete(&SS->m[i],currRing);
1119 }
1120 }
1121 S=id_Copy(SS,currRing);
1122 idSkipZeroes(S);
1123 }
1124 #if 0
1125 printf("\nThis is HC:\n");
1126 for(int ii=0;ii<=idElem(S);ii++)
1127 {
1128 pWrite(S->m[ii]);
1129 }
1130 //getchar();
1131 #endif
1132 #endif
1133 if(idElem(S) == 0)
1134 return;
1135 hNvar = (currRing->N);
1136 hexist = hInit(S, Q, &hNexist);
1137 if (k!=0)
1139 else
1140 hNstc = hNexist;
1141 assume(hNexist > 0);
1142 hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
1143 hvar = (varset)omAlloc((hNvar + 1) * sizeof(int));
1144 hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int));
1145 stcmem = hCreate(hNvar - 1);
1146 for (i = hNvar; i>0; i--)
1147 hvar[i] = i;
1149 if ((hNvar > 2) && (hNstc > 10))
1151 memset(hpure, 0, (hNvar + 1) * sizeof(int));
1152 hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure);
1154 if (hEdge!=NULL)
1155 pLmFree(hEdge);
1156 hEdge = pInit();
1157 pWork = pInit();
1159 pSetComp(hEdge,ak);
1160 hKill(stcmem, hNvar - 1);
1161 omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1162 omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int));
1163 omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int));
1165 pLmFree(pWork);
1166}
1167
1168
1169
1170// kbase
1171
1174
1175static void scElKbase()
1176{
1177 poly q = pInit();
1178 pSetCoeff0(q,nInit(1));
1179 pSetExpV(q,act);
1180 pNext(q) = NULL;
1181 last = pNext(last) = q;
1182}
1183
1184static int scMax( int i, scfmon stc, int Nvar)
1185{
1186 int x, y=stc[0][Nvar];
1187 for (; i;)
1188 {
1189 i--;
1190 x = stc[i][Nvar];
1191 if (x > y) y = x;
1192 }
1193 return y;
1194}
1195
1196static int scMin( int i, scfmon stc, int Nvar)
1197{
1198 int x, y=stc[0][Nvar];
1199 for (; i;)
1200 {
1201 i--;
1202 x = stc[i][Nvar];
1203 if (x < y) y = x;
1204 }
1205 return y;
1206}
1207
1208static int scRestrict( int &Nstc, scfmon stc, int Nvar)
1209{
1210 int x, y;
1211 int i, j, Istc = Nstc;
1212
1213 y = MAX_INT_VAL;
1214 for (i=Nstc-1; i>=0; i--)
1215 {
1216 j = Nvar-1;
1217 loop
1218 {
1219 if(stc[i][j] != 0) break;
1220 j--;
1221 if (j == 0)
1222 {
1223 Istc--;
1224 x = stc[i][Nvar];
1225 if (x < y) y = x;
1226 stc[i] = NULL;
1227 break;
1228 }
1229 }
1230 }
1231 if (Istc < Nstc)
1232 {
1233 for (i=Nstc-1; i>=0; i--)
1234 {
1235 if (stc[i] && (stc[i][Nvar] >= y))
1236 {
1237 Istc--;
1238 stc[i] = NULL;
1239 }
1240 }
1241 j = 0;
1242 while (stc[j]) j++;
1243 i = j+1;
1244 for(; i<Nstc; i++)
1245 {
1246 if (stc[i])
1247 {
1248 stc[j] = stc[i];
1249 j++;
1250 }
1251 }
1252 Nstc = Istc;
1253 return y;
1254 }
1255 else
1256 return -1;
1257}
1258
1259static void scAll( int Nvar, int deg)
1260{
1261 int i;
1262 int d = deg;
1263 if (d == 0)
1264 {
1265 for (i=Nvar; i; i--) act[i] = 0;
1266 scElKbase();
1267 return;
1268 }
1269 if (Nvar == 1)
1270 {
1271 act[1] = d;
1272 scElKbase();
1273 return;
1274 }
1275 do
1276 {
1277 act[Nvar] = d;
1278 scAll(Nvar-1, deg-d);
1279 d--;
1280 } while (d >= 0);
1281}
1282
1283static void scAllKbase( int Nvar, int ideg, int deg)
1284{
1285 do
1286 {
1287 act[Nvar] = ideg;
1288 scAll(Nvar-1, deg-ideg);
1289 ideg--;
1290 } while (ideg >= 0);
1291}
1292
1293static void scDegKbase( scfmon stc, int Nstc, int Nvar, int deg)
1294{
1295 int Ivar, Istc, i, j;
1296 scfmon sn;
1297 int x, ideg;
1298
1299 if (deg == 0)
1300 {
1301 for (i=Nstc-1; i>=0; i--)
1302 {
1303 for (j=Nvar;j;j--){ if(stc[i][j]) break; }
1304 if (j==0){return;}
1305 }
1306 for (i=Nvar; i; i--) act[i] = 0;
1307 scElKbase();
1308 return;
1309 }
1310 if (Nvar == 1)
1311 {
1312 for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return;
1313 act[1] = deg;
1314 scElKbase();
1315 return;
1316 }
1317 Ivar = Nvar-1;
1318 sn = hGetmem(Nstc, stc, stcmem[Ivar]);
1319 x = scRestrict(Nstc, sn, Nvar);
1320 if (x <= 0)
1321 {
1322 if (x == 0) return;
1323 ideg = deg;
1324 }
1325 else
1326 {
1327 if (deg < x) ideg = deg;
1328 else ideg = x-1;
1329 if (Nstc == 0)
1330 {
1331 scAllKbase(Nvar, ideg, deg);
1332 return;
1333 }
1334 }
1335 loop
1336 {
1337 x = scMax(Nstc, sn, Nvar);
1338 while (ideg >= x)
1339 {
1340 act[Nvar] = ideg;
1341 scDegKbase(sn, Nstc, Ivar, deg-ideg);
1342 ideg--;
1343 }
1344 if (ideg < 0) return;
1345 Istc = Nstc;
1346 for (i=Nstc-1; i>=0; i--)
1347 {
1348 if (ideg < sn[i][Nvar])
1349 {
1350 Istc--;
1351 sn[i] = NULL;
1352 }
1353 }
1354 if (Istc == 0)
1355 {
1356 scAllKbase(Nvar, ideg, deg);
1357 return;
1358 }
1359 j = 0;
1360 while (sn[j]) j++;
1361 i = j+1;
1362 for (; i<Nstc; i++)
1363 {
1364 if (sn[i])
1365 {
1366 sn[j] = sn[i];
1367 j++;
1368 }
1369 }
1370 Nstc = Istc;
1371 }
1372}
1373
1374static void scInKbase( scfmon stc, int Nstc, int Nvar)
1375{
1376 int Ivar, Istc, i, j;
1377 scfmon sn;
1378 int x, ideg;
1379
1380 if (Nvar == 1)
1381 {
1382 ideg = scMin(Nstc, stc, 1);
1383 while (ideg > 0)
1384 {
1385 ideg--;
1386 act[1] = ideg;
1387 scElKbase();
1388 }
1389 return;
1390 }
1391 Ivar = Nvar-1;
1392 sn = hGetmem(Nstc, stc, stcmem[Ivar]);
1393 x = scRestrict(Nstc, sn, Nvar);
1394 if (x == 0) return;
1395 ideg = x-1;
1396 loop
1397 {
1398 x = scMax(Nstc, sn, Nvar);
1399 while (ideg >= x)
1400 {
1401 act[Nvar] = ideg;
1402 scInKbase(sn, Nstc, Ivar);
1403 ideg--;
1404 }
1405 if (ideg < 0) return;
1406 Istc = Nstc;
1407 for (i=Nstc-1; i>=0; i--)
1408 {
1409 if (ideg < sn[i][Nvar])
1410 {
1411 Istc--;
1412 sn[i] = NULL;
1413 }
1414 }
1415 j = 0;
1416 while (sn[j]) j++;
1417 i = j+1;
1418 for (; i<Nstc; i++)
1419 {
1420 if (sn[i])
1421 {
1422 sn[j] = sn[i];
1423 j++;
1424 }
1425 }
1426 Nstc = Istc;
1427 }
1428}
1429
1430static ideal scIdKbase(poly q, const int rank)
1431{
1432 ideal res = idInit(pLength(q), rank);
1433 polyset mm = res->m;
1434 do
1435 {
1436 *mm = q; ++mm;
1437
1438 const poly p = pNext(q);
1439 pNext(q) = NULL;
1440 q = p;
1441
1442 } while (q!=NULL);
1443
1444 id_Test(res, currRing); // WRONG RANK!!!???
1445 return res;
1446}
1447
1449{
1450 if( Q!=NULL) id_Test(Q, currRing);
1451
1452 int i, di;
1453 poly p;
1454
1455 if (deg < 0)
1456 {
1457 di = scDimInt(s, Q);
1458 if (di != 0)
1459 {
1460 //Werror("KBase not finite");
1461 return idInit(1,s->rank);
1462 }
1463 }
1464 stcmem = hCreate((currRing->N) - 1);
1465 hexist = hInit(s, Q, &hNexist);
1466 p = last = pInit();
1467 /*pNext(p) = NULL;*/
1468 act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int));
1469 *act = 0;
1470 if (!hNexist)
1471 {
1472 scAll((currRing->N), deg);
1473 goto ende;
1474 }
1475 if (!hisModule)
1476 {
1477 if (deg < 0) scInKbase(hexist, hNexist, (currRing->N));
1478 else scDegKbase(hexist, hNexist, (currRing->N), deg);
1479 }
1480 else
1481 {
1482 hstc = (scfmon)omAlloc(hNexist * sizeof(scmon));
1483 for (i = 1; i <= hisModule; i++)
1484 {
1485 *act = i;
1487 int deg_ei=deg;
1488 if (mv!=NULL) deg_ei -= (*mv)[i-1];
1489 if ((deg < 0) || (deg_ei>=0))
1490 {
1491 if (hNstc)
1492 {
1493 if (deg < 0) scInKbase(hstc, hNstc, (currRing->N));
1494 else scDegKbase(hstc, hNstc, (currRing->N), deg_ei);
1495 }
1496 else
1497 scAll((currRing->N), deg_ei);
1498 }
1499 }
1500 omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon));
1501 }
1502ende:
1504 omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int));
1505 hKill(stcmem, (currRing->N) - 1);
1506 pLmFree(&p);
1507 if (p == NULL)
1508 return idInit(1,s->rank);
1509
1510 last = p;
1511 return scIdKbase(p, s->rank);
1512}
1513
1514#if 0 //-- alternative implementation of scComputeHC
1515/*
1516void scComputeHCw(ideal ss, ideal Q, int ak, poly &hEdge)
1517{
1518 id_LmTest(ss, currRing);
1519 if (Q!=NULL) id_LmTest(Q, currRing);
1520
1521 int i, di;
1522 poly p;
1523
1524 if (hEdge!=NULL)
1525 pLmFree(hEdge);
1526
1527 ideal s=idInit(IDELEMS(ss),ak);
1528 for(i=IDELEMS(ss)-1;i>=0;i--)
1529 {
1530 if (ss->m[i]!=NULL) s->m[i]=pHead(ss->m[i]);
1531 }
1532 di = scDimInt(s, Q);
1533 stcmem = hCreate((currRing->N) - 1);
1534 hexist = hInit(s, Q, &hNexist);
1535 p = last = pInit();
1536 // pNext(p) = NULL;
1537 act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int));
1538 *act = 0;
1539 if (!hNexist)
1540 {
1541 scAll((currRing->N), -1);
1542 goto ende;
1543 }
1544 if (!hisModule)
1545 {
1546 scInKbase(hexist, hNexist, (currRing->N));
1547 }
1548 else
1549 {
1550 hstc = (scfmon)omAlloc(hNexist * sizeof(scmon));
1551 for (i = 1; i <= hisModule; i++)
1552 {
1553 *act = i;
1554 hComp(hexist, hNexist, i, hstc, &hNstc);
1555 if (hNstc)
1556 {
1557 scInKbase(hstc, hNstc, (currRing->N));
1558 }
1559 else
1560 scAll((currRing->N), -1);
1561 }
1562 omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon));
1563 }
1564ende:
1565 hDelete(hexist, hNexist);
1566 omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int));
1567 hKill(stcmem, (currRing->N) - 1);
1568 pDeleteLm(&p);
1569 idDelete(&s);
1570 if (p == NULL)
1571 {
1572 return; // no HEdge
1573 }
1574 else
1575 {
1576 last = p;
1577 ideal res=scIdKbase(p, ss->rank);
1578 poly p_ind=res->m[0]; int ind=0;
1579 for(i=IDELEMS(res)-1;i>0;i--)
1580 {
1581 if (pCmp(res->m[i],p_ind)==-1) { p_ind=res->m[i]; ind=i; }
1582 }
1583 assume(p_ind!=NULL);
1584 assume(res->m[ind]==p_ind);
1585 hEdge=p_ind;
1586 res->m[ind]=NULL;
1587 nDelete(&pGetCoeff(hEdge));
1588 pGetCoeff(hEdge)=NULL;
1589 for(i=(currRing->N);i>0;i--)
1590 pIncrExp(hEdge,i);
1591 pSetm(hEdge);
1592
1593 idDelete(&res);
1594 return;
1595 }
1596}
1597 */
1598#endif
1599
1600#ifdef HAVE_SHIFTBBA
1601
1602/*
1603 * Computation of the Gel'fand-Kirillov Dimension
1604 */
1605
1606#include "polys/shiftop.h"
1607#include <vector>
1608
1609static std::vector<int> countCycles(const intvec* _G, int v, std::vector<int> path, std::vector<BOOLEAN> visited, std::vector<BOOLEAN> cyclic, std::vector<int> cache)
1610{
1611 intvec* G = ivCopy(_G); // modifications must be local
1612
1613 if (cache[v] != -2) return cache; // value is already cached
1614
1615 visited[v] = TRUE;
1616 path.push_back(v);
1617
1618 int cycles = 0;
1619 for (int w = 0; w < G->cols(); w++)
1620 {
1621 if (IMATELEM(*G, v + 1, w + 1)) // edge v -> w exists in G
1622 {
1623 if (!visited[w])
1624 { // continue with w
1626 if (cache[w] == -1)
1627 {
1628 cache[v] = -1;
1629 return cache;
1630 }
1631 cycles = si_max(cycles, cache[w]);
1632 }
1633 else
1634 { // found new cycle
1635 int pathIndexOfW = -1;
1636 for (int i = path.size() - 1; i >= 0; i--) {
1637 if (cyclic[path[i]] == 1) { // found an already cyclic vertex
1638 cache[v] = -1;
1639 return cache;
1640 }
1641 cyclic[path[i]] = TRUE;
1642
1643 if (path[i] == w) { // end of the cycle
1644 assume(IMATELEM(*G, v + 1, w + 1) != 0);
1645 IMATELEM(*G, v + 1, w + 1) = 0; // remove edge v -> w
1646 pathIndexOfW = i;
1647 break;
1648 } else {
1649 assume(IMATELEM(*G, path[i - 1] + 1, path[i] + 1) != 0);
1650 IMATELEM(*G, path[i - 1] + 1, path[i] + 1) = 0; // remove edge vi-1 -> vi
1651 }
1652 }
1653 assume(pathIndexOfW != -1); // should never happen
1654 for (int i = path.size() - 1; i >= pathIndexOfW; i--) {
1656 if (cache[path[i]] == -1)
1657 {
1658 cache[v] = -1;
1659 return cache;
1660 }
1661 cycles = si_max(cycles, cache[path[i]] + 1);
1662 }
1663 }
1664 }
1665 }
1666 cache[v] = cycles;
1667
1668 delete G;
1669 return cache;
1670}
1671
1672// -1 is infinity
1673static int graphGrowth(const intvec* G)
1674{
1675 // init
1676 int n = G->cols();
1677 std::vector<int> path;
1678 std::vector<BOOLEAN> visited;
1679 std::vector<BOOLEAN> cyclic;
1680 std::vector<int> cache;
1681 visited.resize(n, FALSE);
1682 cyclic.resize(n, FALSE);
1683 cache.resize(n, -2);
1684
1685 // get max number of cycles
1686 int cycles = 0;
1687 for (int v = 0; v < n; v++)
1688 {
1690 if (cache[v] == -1)
1691 return -1;
1692 cycles = si_max(cycles, cache[v]);
1693 }
1694 return cycles;
1695}
1696
1697// ATTENTION:
1698// - `words` contains the words normal modulo M of length n
1699// - `numberOfNormalWords` contains the number of words normal modulo M of length 0 ... n
1701{
1702 if (length <= 0){
1703 poly one = pOne();
1704 if (p_LPDivisibleBy(M, one, currRing)) // 1 \in M => no normal words at all
1705 {
1706 pDelete(&one);
1707 last = -1;
1709 }
1710 else
1711 {
1712 words->m[0] = one;
1713 last = 0;
1715 }
1716 return;
1717 }
1718
1720
1721 int nVars = currRing->isLPring - currRing->LPncGenCount;
1722 int numberOfNewNormalWords = 0;
1723
1724 for (int j = nVars - 1; j >= 0; j--)
1725 {
1726 for (int i = last; i >= 0; i--)
1727 {
1728 int index = (j * (last + 1)) + i;
1729
1730 if (words->m[i] != NULL)
1731 {
1732 if (j > 0) {
1733 words->m[index] = pCopy(words->m[i]);
1734 }
1735
1736 int varOffset = ((length - 1) * currRing->isLPring) + 1;
1737 pSetExp(words->m[index], varOffset + j, 1);
1738 pSetm(words->m[index]);
1739 pTest(words->m[index]);
1740
1742 {
1743 pDelete(&words->m[index]);
1744 words->m[index] = NULL;
1745 }
1746 else
1747 {
1749 }
1750 }
1751 }
1752 }
1753
1754 last = nVars * last + nVars - 1;
1755
1757}
1758
1760{
1761 long minDeg = IDELEMS(M) > 0 ? pTotaldegree(M->m[0]) : 0;
1762 for (int i = 1; i < IDELEMS(M); i++)
1763 {
1765 }
1766
1767 int nVars = currRing->isLPring - currRing->LPncGenCount;
1768
1769 int maxElems = 1;
1770 for (int i = 0; i < length; i++) // maxElems = nVars^n
1771 maxElems *= nVars;
1776 return words;
1777}
1778
1780{
1781 long minDeg = IDELEMS(M) > 0 ? pTotaldegree(M->m[0]) : 0;
1782 for (int i = 1; i < IDELEMS(M); i++)
1783 {
1785 }
1786
1787 int nVars = currRing->isLPring - currRing->LPncGenCount;
1788
1789 int maxElems = 1;
1790 for (int i = 0; i < upToLength; i++) // maxElems = nVars^n
1791 maxElems *= nVars;
1795 idDelete(&words);
1796 return numberOfNormalWords;
1797}
1798
1799// NULL if graph is undefined
1801{
1802 long l = 0;
1803 for (int i = 0; i < IDELEMS(G); i++)
1804 l = si_max(pTotaldegree(G->m[i]), l);
1805 l--;
1806 if (l <= 0)
1807 {
1808 WerrorS("Ufnarovski graph not implemented for l <= 0");
1809 return NULL;
1810 }
1811 int lV = currRing->isLPring;
1812
1814
1815 int n = IDELEMS(standardWords);
1816 intvec* UG = new intvec(n, n, 0);
1817 for (int i = 0; i < n; i++)
1818 {
1819 for (int j = 0; j < n; j++)
1820 {
1821 poly v = standardWords->m[i];
1822 poly w = standardWords->m[j];
1823
1824 // check whether v*x1 = x2*w (overlap)
1825 bool overlap = true;
1826 for (int k = 1; k <= (l - 1) * lV; k++)
1827 {
1828 if (pGetExp(v, k + lV) != pGetExp(w, k)) {
1829 overlap = false;
1830 break;
1831 }
1832 }
1833
1834 if (overlap)
1835 {
1836 // create the overlap
1837 poly p = pMult(pCopy(v), p_LPVarAt(w, l, currRing));
1838
1839 // check whether the overlap is normal
1840 bool normal = true;
1841 for (int k = 0; k < IDELEMS(G); k++)
1842 {
1843 if (p_LPDivisibleBy(G->m[k], p, currRing))
1844 {
1845 normal = false;
1846 break;
1847 }
1848 }
1849
1850 if (normal)
1851 {
1852 IMATELEM(*UG, i + 1, j + 1) = 1;
1853 }
1854 }
1855 }
1856 }
1857 return UG;
1858}
1859
1860// -1 is infinity, -2 is error
1862{
1864
1865 if (rField_is_Ring(currRing)) {
1866 WerrorS("GK-Dim not implemented for rings");
1867 return -2;
1868 }
1869
1870 for (int i=IDELEMS(_G)-1;i>=0; i--)
1871 {
1872 if (_G->m[i] != NULL)
1873 {
1874 if (pGetComp(_G->m[i]) != 0)
1875 {
1876 WerrorS("GK-Dim not implemented for modules");
1877 return -2;
1878 }
1879 if (pGetNCGen(_G->m[i]) != 0)
1880 {
1881 WerrorS("GK-Dim not implemented for bi-modules");
1882 return -2;
1883 }
1884 }
1885 }
1886
1887 ideal G = id_Head(_G, currRing); // G = LM(G) (and copy)
1888 idSkipZeroes(G); // remove zeros
1889 id_DelLmEquals(G, currRing); // remove duplicates
1890
1891 // check if G is the zero ideal
1892 if (IDELEMS(G) == 1 && G->m[0] == NULL)
1893 {
1894 // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1!
1895 int lV = currRing->isLPring;
1896 int ncGenCount = currRing->LPncGenCount;
1897 if (lV - ncGenCount == 0)
1898 {
1899 idDelete(&G);
1900 return 0;
1901 }
1902 if (lV - ncGenCount == 1)
1903 {
1904 idDelete(&G);
1905 return 1;
1906 }
1907 if (lV - ncGenCount >= 2)
1908 {
1909 idDelete(&G);
1910 return -1;
1911 }
1912 }
1913
1914 // get the max deg
1915 long maxDeg = 0;
1916 for (int i = 0; i < IDELEMS(G); i++)
1917 {
1919
1920 // also check whether G = <1>
1921 if (pIsConstantComp(G->m[i]))
1922 {
1923 WerrorS("GK-Dim not defined for 0-ring");
1924 idDelete(&G);
1925 return -2;
1926 }
1927 }
1928
1929 // early termination if G \subset X
1930 if (maxDeg <= 1)
1931 {
1932 int lV = currRing->isLPring;
1933 int ncGenCount = currRing->LPncGenCount;
1934 if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges
1935 {
1936 idDelete(&G);
1937 return 0;
1938 }
1939 if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop
1940 {
1941 idDelete(&G);
1942 return 1;
1943 }
1944 if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop
1945 {
1946 idDelete(&G);
1947 return -1;
1948 }
1949 }
1950
1953 if (UG == NULL)
1954 {
1955 idDelete(&G);
1956 return -2;
1957 }
1958 if (errorreported)
1959 {
1960 delete UG;
1961 idDelete(&G);
1962 return -2;
1963 }
1964 int gkDim = graphGrowth(UG);
1965 delete UG;
1966 idDelete(&G);
1967 return gkDim;
1968}
1969
1970// converts an intvec matrix to a vector<vector<int> >
1971static std::vector<std::vector<int> > iv2vv(intvec* M)
1972{
1973 int rows = M->rows();
1974 int cols = M->cols();
1975
1976 std::vector<std::vector<int> > mat(rows, std::vector<int>(cols));
1977
1978 for (int i = 0; i < rows; i++)
1979 {
1980 for (int j = 0; j < cols; j++)
1981 {
1982 mat[i][j] = IMATELEM(*M, i + 1, j + 1);
1983 }
1984 }
1985
1986 return mat;
1987}
1988
1989static void vvPrint(const std::vector<std::vector<int> >& mat)
1990{
1991 for (int i = 0; i < mat.size(); i++)
1992 {
1993 for (int j = 0; j < mat[i].size(); j++)
1994 {
1995 Print("%d ", mat[i][j]);
1996 }
1997 PrintLn();
1998 }
1999}
2000
2001static void vvTest(const std::vector<std::vector<int> >& mat)
2002{
2003 if (mat.size() > 0)
2004 {
2005 int cols = mat[0].size();
2006 for (int i = 1; i < mat.size(); i++)
2007 {
2008 if (cols != mat[i].size())
2009 WerrorS("number of cols in matrix inconsistent");
2010 }
2011 }
2012}
2013
2014static void vvDeleteRow(std::vector<std::vector<int> >& mat, int row)
2015{
2016 mat.erase(mat.begin() + row);
2017}
2018
2019static void vvDeleteColumn(std::vector<std::vector<int> >& mat, int col)
2020{
2021 for (int i = 0; i < mat.size(); i++)
2022 {
2023 mat[i].erase(mat[i].begin() + col);
2024 }
2025}
2026
2027static BOOLEAN vvIsRowZero(const std::vector<std::vector<int> >& mat, int row)
2028{
2029 for (int i = 0; i < mat[row].size(); i++)
2030 {
2031 if (mat[row][i] != 0)
2032 return FALSE;
2033 }
2034 return TRUE;
2035}
2036
2037static BOOLEAN vvIsColumnZero(const std::vector<std::vector<int> >& mat, int col)
2038{
2039 for (int i = 0; i < mat.size(); i++)
2040 {
2041 if (mat[i][col] != 0)
2042 return FALSE;
2043 }
2044 return TRUE;
2045}
2046
2047static BOOLEAN vvIsZero(const std::vector<std::vector<int> >& mat)
2048{
2049 for (int i = 0; i < mat.size(); i++)
2050 {
2051 if (!vvIsRowZero(mat, i))
2052 return FALSE;
2053 }
2054 return TRUE;
2055}
2056
2057static std::vector<std::vector<int> > vvMult(const std::vector<std::vector<int> >& a, const std::vector<std::vector<int> >& b)
2058{
2059 int ra = a.size();
2060 int rb = b.size();
2061 int ca = a.size() > 0 ? a[0].size() : 0;
2062 int cb = b.size() > 0 ? b[0].size() : 0;
2063
2064 if (ca != rb)
2065 {
2066 WerrorS("matrix dimensions do not match");
2067 return std::vector<std::vector<int> >();
2068 }
2069
2070 std::vector<std::vector<int> > res(ra, std::vector<int>(cb));
2071 for (int i = 0; i < ra; i++)
2072 {
2073 for (int j = 0; j < cb; j++)
2074 {
2075 int sum = 0;
2076 for (int k = 0; k < ca; k++)
2077 sum += a[i][k] * b[k][j];
2078 res[i][j] = sum;
2079 }
2080 }
2081 return res;
2082}
2083
2085{
2086 // init
2087 int n = G->cols();
2088 std::vector<int> path;
2089 std::vector<BOOLEAN> visited;
2090 std::vector<BOOLEAN> cyclic;
2091 std::vector<int> cache;
2092 visited.resize(n, FALSE);
2093 cyclic.resize(n, FALSE);
2094 cache.resize(n, -2);
2095
2096 for (int v = 0; v < n; v++)
2097 {
2099 // check that there are 0 cycles from v
2100 if (cache[v] != 0)
2101 return FALSE;
2102 }
2103 return TRUE;
2104}
2105
2106/*
2107 * Computation of the K-Dimension
2108 */
2109
2110// -1 is infinity, -2 is error
2111int lp_kDim(const ideal _G)
2112{
2113 if (rField_is_Ring(currRing)) {
2114 WerrorS("K-Dim not implemented for rings");
2115 return -2;
2116 }
2117
2118 for (int i=IDELEMS(_G)-1;i>=0; i--)
2119 {
2120 if (_G->m[i] != NULL)
2121 {
2122 if (pGetComp(_G->m[i]) != 0)
2123 {
2124 WerrorS("K-Dim not implemented for modules");
2125 return -2;
2126 }
2127 if (pGetNCGen(_G->m[i]) != 0)
2128 {
2129 WerrorS("K-Dim not implemented for bi-modules");
2130 return -2;
2131 }
2132 }
2133 }
2134
2135 ideal G = id_Head(_G, currRing); // G = LM(G) (and copy)
2136 if (TEST_OPT_PROT)
2137 Print("%d original generators\n", IDELEMS(G));
2138 idSkipZeroes(G); // remove zeros
2139 id_DelLmEquals(G, currRing); // remove duplicates
2140 if (TEST_OPT_PROT)
2141 Print("%d non-zero unique generators\n", IDELEMS(G));
2142
2143 // check if G is the zero ideal
2144 if (IDELEMS(G) == 1 && G->m[0] == NULL)
2145 {
2146 // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1!
2147 int lV = currRing->isLPring;
2148 int ncGenCount = currRing->LPncGenCount;
2149 if (lV - ncGenCount == 0)
2150 {
2151 idDelete(&G);
2152 return 1;
2153 }
2154 if (lV - ncGenCount == 1)
2155 {
2156 idDelete(&G);
2157 return -1;
2158 }
2159 if (lV - ncGenCount >= 2)
2160 {
2161 idDelete(&G);
2162 return -1;
2163 }
2164 }
2165
2166 // get the max deg
2167 long maxDeg = 0;
2168 for (int i = 0; i < IDELEMS(G); i++)
2169 {
2171
2172 // also check whether G = <1>
2173 if (pIsConstantComp(G->m[i]))
2174 {
2175 WerrorS("K-Dim not defined for 0-ring"); // TODO is it minus infinity ?
2176 idDelete(&G);
2177 return -2;
2178 }
2179 }
2180 if (TEST_OPT_PROT)
2181 Print("max deg: %ld\n", maxDeg);
2182
2183
2184 // for normal words of length minDeg ... maxDeg-1
2185 // brute-force the normal words
2186 if (TEST_OPT_PROT)
2187 PrintS("Computing normal words normally...\n");
2189
2190 if (TEST_OPT_PROT)
2191 Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1);
2192
2193 // early termination if G \subset X
2194 if (maxDeg <= 1)
2195 {
2196 int lV = currRing->isLPring;
2197 int ncGenCount = currRing->LPncGenCount;
2198 if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges
2199 {
2200 idDelete(&G);
2201 return numberOfNormalWords;
2202 }
2203 if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop
2204 {
2205 idDelete(&G);
2206 return -1;
2207 }
2208 if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop
2209 {
2210 idDelete(&G);
2211 return -1;
2212 }
2213 }
2214
2215 if (TEST_OPT_PROT)
2216 PrintS("Computing Ufnarovski graph...\n");
2217
2220 if (UG == NULL)
2221 {
2222 idDelete(&G);
2223 return -2;
2224 }
2225 if (errorreported)
2226 {
2227 delete UG;
2228 idDelete(&G);
2229 return -2;
2230 }
2231
2232 if (TEST_OPT_PROT)
2233 Print("Ufnarovski graph is %dx%d.\n", UG->rows(), UG->cols());
2234
2235 if (TEST_OPT_PROT)
2236 PrintS("Checking whether Ufnarovski graph is acyclic...\n");
2237
2238 if (!isAcyclic(UG))
2239 {
2240 // in this case we have infinitely many normal words
2241 return -1;
2242 }
2243
2244 std::vector<std::vector<int> > vvUG = iv2vv(UG);
2245 for (int i = 0; i < vvUG.size(); i++)
2246 {
2247 if (vvIsRowZero(vvUG, i) && vvIsColumnZero(vvUG, i)) // i is isolated vertex
2248 {
2249 vvDeleteRow(vvUG, i);
2251 i--;
2252 }
2253 }
2254 if (TEST_OPT_PROT)
2255 Print("Simplified Ufnarovski graph to %dx%d.\n", (int)vvUG.size(), (int)vvUG.size());
2256
2257 // for normal words of length >= maxDeg
2258 // use Ufnarovski graph
2259 if (TEST_OPT_PROT)
2260 PrintS("Computing normal words via Ufnarovski graph...\n");
2261 std::vector<std::vector<int> > UGpower = vvUG;
2262 long nUGpower = 1;
2263 while (!vvIsZero(UGpower))
2264 {
2265 if (TEST_OPT_PROT)
2266 PrintS("Start count graph entries.\n");
2267 for (int i = 0; i < UGpower.size(); i++)
2268 {
2269 for (int j = 0; j < UGpower[i].size(); j++)
2270 {
2272 }
2273 }
2274
2275 if (TEST_OPT_PROT)
2276 {
2277 PrintS("Done count graph entries.\n");
2278 Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1 + nUGpower);
2279 }
2280
2281 if (TEST_OPT_PROT)
2282 PrintS("Start mat mult.\n");
2283 UGpower = vvMult(UGpower, vvUG); // TODO: avoid creation of new intvec
2284 if (TEST_OPT_PROT)
2285 PrintS("Done mat mult.\n");
2286 nUGpower++;
2287 }
2288
2289 delete UG;
2290 idDelete(&G);
2291 return numberOfNormalWords;
2292}
2293#endif
long int64
Definition auxiliary.h:68
static int si_max(const int a, const int b)
Definition auxiliary.h:124
int BOOLEAN
Definition auxiliary.h:87
#define TRUE
Definition auxiliary.h:100
#define FALSE
Definition auxiliary.h:96
static int si_min(const int a, const int b)
Definition auxiliary.h:125
int size(const CanonicalForm &f, const Variable &v)
int size ( const CanonicalForm & f, const Variable & v )
Definition cf_ops.cc:600
int l
Definition cfEzgcd.cc:100
int i
Definition cfEzgcd.cc:132
int k
Definition cfEzgcd.cc:99
Variable x
Definition cfModGcd.cc:4090
int p
Definition cfModGcd.cc:4086
CanonicalForm b
Definition cfModGcd.cc:4111
int length() const
static FORCE_INLINE BOOLEAN n_IsUnit(number n, const coeffs r)
TRUE iff n has a multiplicative inverse in the given coeff field/ring r.
Definition coeffs.h:519
static FORCE_INLINE BOOLEAN n_DivBy(number a, number b, const coeffs r)
test whether 'a' is divisible 'b'; for r encoding a field: TRUE iff 'b' does not represent zero in Z:...
Definition coeffs.h:757
#define Print
Definition emacs.cc:80
const CanonicalForm int s
Definition facAbsFact.cc:51
const CanonicalForm int const CFList const Variable & y
Definition facAbsFact.cc:53
CanonicalForm res
Definition facAbsFact.cc:60
const CanonicalForm & w
Definition facAbsFact.cc:51
const Variable & v
< [in] a sqrfree bivariate poly
Definition facBivar.h:39
int j
Definition facHensel.cc:110
VAR short errorreported
Definition feFopen.cc:23
void WerrorS(const char *s)
Definition feFopen.cc:24
#define STATIC_VAR
Definition globaldefs.h:7
#define VAR
Definition globaldefs.h:5
static long hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar)
Definition hdegree.cc:621
static ideal lp_computeNormalWords(int length, ideal M)
Definition hdegree.cc:1759
void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge)
Definition hdegree.cc:1100
STATIC_VAR scmon hInd
Definition hdegree.cc:205
static void hHedgeStep(scmon pure, scfmon stc, int Nstc, varset var, int Nvar, poly hEdge)
Definition hdegree.cc:1040
static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
Definition hdegree.cc:726
ideal scKBase(int deg, ideal s, ideal Q, intvec *mv)
Definition hdegree.cc:1448
int scDimIntRing(ideal vid, ideal Q)
scDimInt for ring-coefficients
Definition hdegree.cc:136
static std::vector< int > countCycles(const intvec *_G, int v, std::vector< int > path, std::vector< BOOLEAN > visited, std::vector< BOOLEAN > cyclic, std::vector< int > cache)
Definition hdegree.cc:1609
long scMult0Int(ideal S, ideal Q)
Definition hdegree.cc:950
void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
Definition hdegree.cc:384
static std::vector< std::vector< int > > vvMult(const std::vector< std::vector< int > > &a, const std::vector< std::vector< int > > &b)
Definition hdegree.cc:2057
static int scMin(int i, scfmon stc, int Nvar)
Definition hdegree.cc:1196
intvec * scIndIntvec(ideal S, ideal Q)
Definition hdegree.cc:286
static void vvDeleteRow(std::vector< std::vector< int > > &mat, int row)
Definition hdegree.cc:2014
static indset hCheck2(indset sm, scmon pure)
Definition hdegree.cc:491
STATIC_VAR poly last
Definition hdegree.cc:1172
static BOOLEAN hCheck1(indset sm, scmon pure)
Definition hdegree.cc:465
static int graphGrowth(const intvec *G)
Definition hdegree.cc:1673
static BOOLEAN vvIsColumnZero(const std::vector< std::vector< int > > &mat, int col)
Definition hdegree.cc:2037
VAR omBin indlist_bin
Definition hdegree.cc:29
STATIC_VAR poly pWork
Definition hdegree.cc:1027
VAR int hMu2
Definition hdegree.cc:27
static void hDegree(ideal S, ideal Q)
Definition hdegree.cc:802
static void vvDeleteColumn(std::vector< std::vector< int > > &mat, int col)
Definition hdegree.cc:2019
static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar)
Definition hdegree.cc:355
int lp_kDim(const ideal _G)
Definition hdegree.cc:2111
static void scElKbase()
Definition hdegree.cc:1175
static void hHedge(poly hEdge)
Definition hdegree.cc:1029
static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
Definition hdegree.cc:207
VAR int hCo
Definition hdegree.cc:27
intvec * lp_ufnarovskiGraph(ideal G, ideal &standardWords)
Definition hdegree.cc:1800
static int scRestrict(int &Nstc, scfmon stc, int Nvar)
Definition hdegree.cc:1208
int lp_gkDim(const ideal _G)
Definition hdegree.cc:1861
VAR indset ISet
Definition hdegree.cc:353
static std::vector< std::vector< int > > iv2vv(intvec *M)
Definition hdegree.cc:1971
static void vvPrint(const std::vector< std::vector< int > > &mat)
Definition hdegree.cc:1989
static void vvTest(const std::vector< std::vector< int > > &mat)
Definition hdegree.cc:2001
static void scAllKbase(int Nvar, int ideg, int deg)
Definition hdegree.cc:1283
VAR long hMu
Definition hdegree.cc:28
static void scAll(int Nvar, int deg)
Definition hdegree.cc:1259
int scMultInt(ideal S, ideal Q)
Definition hdegree.cc:903
static void scDegKbase(scfmon stc, int Nstc, int Nvar, int deg)
Definition hdegree.cc:1293
STATIC_VAR scmon act
Definition hdegree.cc:1173
static void hCheckIndep(scmon pure)
Definition hdegree.cc:543
void scPrintDegree(int co, int mu)
Definition hdegree.cc:912
VAR indset JSet
Definition hdegree.cc:353
static int lp_countNormalWords(int upToLength, ideal M)
Definition hdegree.cc:1779
static BOOLEAN isAcyclic(const intvec *G)
Definition hdegree.cc:2084
static int scMax(int i, scfmon stc, int Nvar)
Definition hdegree.cc:1184
static ideal scIdKbase(poly q, const int rank)
Definition hdegree.cc:1430
static void hIndep(scmon pure)
Definition hdegree.cc:370
static void scInKbase(scfmon stc, int Nstc, int Nvar)
Definition hdegree.cc:1374
static void hProject(scmon pure, varset sel)
Definition hdegree.cc:703
void scDegree(ideal S, intvec *modulweight, ideal Q)
Definition hdegree.cc:926
static BOOLEAN vvIsZero(const std::vector< std::vector< int > > &mat)
Definition hdegree.cc:2047
int scDimInt(ideal S, ideal Q)
ideal dimension
Definition hdegree.cc:78
static BOOLEAN vvIsRowZero(const std::vector< std::vector< int > > &mat, int row)
Definition hdegree.cc:2027
static void _lp_computeNormalWords(ideal words, int &numberOfNormalWords, int length, ideal M, int minDeg, int &last)
Definition hdegree.cc:1700
void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
Definition hdegree.cc:35
void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
Definition hdegree.cc:564
intvec * hSecondSeries(intvec *hseries1)
Definition hilb.cc:706
intvec * hFirstSeries(ideal A, intvec *module_w, ideal Q, intvec *wdegree)
Definition hilb.cc:2167
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
Definition hilb.cc:741
monf hCreate(int Nvar)
Definition hutil.cc:996
void hComp(scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
Definition hutil.cc:154
void hLex2S(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
Definition hutil.cc:812
VAR scfmon hstc
Definition hutil.cc:16
VAR varset hvar
Definition hutil.cc:18
void hKill(monf xmem, int Nvar)
Definition hutil.cc:1010
VAR int hNexist
Definition hutil.cc:19
void hElimS(scfmon stc, int *e1, int a2, int e2, varset var, int Nvar)
Definition hutil.cc:672
void hLexS(scfmon stc, int Nstc, varset var, int Nvar)
Definition hutil.cc:506
void hDelete(scfmon ev, int ev_length)
Definition hutil.cc:140
VAR scmon hpur0
Definition hutil.cc:17
VAR monf stcmem
Definition hutil.cc:21
scfmon hGetmem(int lm, scfmon old, monp monmem)
Definition hutil.cc:1023
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
Definition hutil.cc:621
VAR scfmon hwork
Definition hutil.cc:16
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
Definition hutil.cc:174
void hLexR(scfmon rad, int Nrad, varset var, int Nvar)
Definition hutil.cc:565
VAR scmon hpure
Definition hutil.cc:17
void hStepR(scfmon rad, int Nrad, varset var, int Nvar, int *a)
Definition hutil.cc:974
void hLex2R(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
Definition hutil.cc:880
VAR scfmon hrad
Definition hutil.cc:16
VAR int hisModule
Definition hutil.cc:20
void hStepS(scfmon stc, int Nstc, varset var, int Nvar, int *a, int *x)
Definition hutil.cc:949
void hStaircase(scfmon stc, int *Nstc, varset var, int Nvar)
Definition hutil.cc:313
void hElimR(scfmon rad, int *e1, int a2, int e2, varset var, int Nvar)
Definition hutil.cc:742
VAR monf radmem
Definition hutil.cc:21
void hOrdSupp(scfmon stc, int Nstc, varset var, int Nvar)
Definition hutil.cc:202
VAR varset hsel
Definition hutil.cc:18
VAR int hNpure
Definition hutil.cc:19
VAR int hNrad
Definition hutil.cc:19
scfmon hInit(ideal S, ideal Q, int *Nexist)
Definition hutil.cc:31
VAR scfmon hexist
Definition hutil.cc:16
void hRadical(scfmon rad, int *Nrad, int Nvar)
Definition hutil.cc:411
scmon hGetpure(scmon p)
Definition hutil.cc:1052
VAR int hNstc
Definition hutil.cc:19
VAR int hNvar
Definition hutil.cc:19
scmon * scfmon
Definition hutil.h:15
indlist * indset
Definition hutil.h:28
int * varset
Definition hutil.h:16
int * scmon
Definition hutil.h:14
#define idDelete(H)
delete an ideal
Definition ideals.h:29
BOOLEAN idInsertPoly(ideal h1, poly h2)
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted
ideal id_Copy(ideal h1, const ring r)
copy an ideal
ideal idCopy(ideal A)
Definition ideals.h:60
#define idPosConstant(I)
index of generator with leading term in ground ring (if any); otherwise -1
Definition ideals.h:37
static BOOLEAN length(leftv result, leftv arg)
Definition interval.cc:257
intvec * ivCopy(const intvec *o)
Definition intvec.h:145
#define IMATELEM(M, I, J)
Definition intvec.h:85
STATIC_VAR TreeM * G
Definition janet.cc:31
static matrix mu(matrix A, const ring R)
Definition matpol.cc:2025
#define assume(x)
Definition mod2.h:387
#define pNext(p)
Definition monomials.h:36
#define pSetCoeff0(p, n)
Definition monomials.h:59
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition monomials.h:44
const int MAX_INT_VAL
Definition mylimits.h:12
#define nCopy(n)
Definition numbers.h:15
#define nInit(i)
Definition numbers.h:24
#define omFreeSize(addr, size)
#define omAlloc(size)
#define omAlloc0Bin(bin)
#define omAlloc0(size)
#define omFreeBin(addr, bin)
#define omGetSpecBin(size)
Definition omBin.h:11
#define NULL
Definition omList.c:12
omBin_t * omBin
Definition omStructs.h:12
#define TEST_OPT_PROT
Definition options.h:103
static int index(p_Length length, p_Ord ord)
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
Definition p_polys.cc:1229
static int pLength(poly a)
Definition p_polys.h:190
static void p_Delete(poly *p, const ring r)
Definition p_polys.h:901
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition polys.cc:13
Compatibility layer for legacy polynomial operations (over currRing)
static long pTotaldegree(poly p)
Definition polys.h:282
#define pTest(p)
Definition polys.h:414
#define pDelete(p_ptr)
Definition polys.h:186
#define pSetm(p)
Definition polys.h:271
#define pGetComp(p)
Component.
Definition polys.h:37
#define pIsConstantComp(p)
return true if p is either NULL, or if all exponents of p are 0, Comp of p might be !...
Definition polys.h:236
#define pSetExpV(p, e)
Definition polys.h:97
#define pSetComp(p, v)
Definition polys.h:38
#define pMult(p, q)
Definition polys.h:207
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced
Definition polys.h:70
void pWrite(poly p)
Definition polys.h:308
#define pGetExp(p, i)
Exponent.
Definition polys.h:41
#define pInit()
allocates a new monomial and initializes everything to 0
Definition polys.h:61
#define pSetExp(p, i, v)
Definition polys.h:42
#define pLmCmp(p, q)
returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering
Definition polys.h:105
#define pCopy(p)
return a copy of the poly
Definition polys.h:185
#define pOne()
Definition polys.h:315
poly * polyset
Definition polys.h:259
void PrintS(const char *s)
Definition reporter.cc:284
void PrintLn()
Definition reporter.cc:310
static BOOLEAN rField_is_Z(const ring r)
Definition ring.h:514
#define rField_is_Ring(R)
Definition ring.h:490
BOOLEAN p_LPDivisibleBy(poly a, poly b, const ring r)
Definition shiftop.cc:776
poly p_LPVarAt(poly p, int pos, const ring r)
Definition shiftop.cc:845
#define pGetNCGen(p)
Definition shiftop.h:65
ideal idInit(int idsize, int rank)
initialise an ideal / module
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
void id_DelLmEquals(ideal id, const ring r)
Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i.
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
#define IDELEMS(i)
#define id_Test(A, lR)
static int idElem(const ideal F)
number of non-zero polys in F
#define id_LmTest(A, lR)
#define M
Definition sirandom.c:25
#define Q
Definition sirandom.c:26
#define loop
Definition structs.h:75