57 WarnS(
"minbase applies only to the local or homogeneous case over coefficient fields");
66 WarnS(
"minbase applies only to the local or homogeneous case over coefficient fields");
90 while ((
k > 0) && (h3->m[
k-1] ==
NULL))
k--;
93 while ((
l > 0) && (h2->m[
l-1] ==
NULL))
l--;
94 for (
i=
l-1;
i>=0;
i--)
99 while ((ll <
k) && ((h3->m[ll] ==
NULL)
155 for (
j=0;
j<
r->N-1;
j++) names[
j]=
r->names[
j];
209 int rank=
si_max(h1->rank,h2->rank);
212 ideal first,second,temp,temp1,
result;
224 int t=flength; flength=slength; slength=t;
226 length =
si_max(flength,slength);
244 while ((
j>0) && (first->m[
j-1]==
NULL))
j--;
249 if (first->m[
i]!=
NULL)
251 if (syz_ring==orig_ring)
252 temp->m[
k] =
pCopy(first->m[
i]);
254 temp->m[
k] =
prCopyR(first->m[
i], orig_ring, syz_ring);
267 if (second->m[
i]!=
NULL)
269 if (syz_ring==orig_ring)
270 temp->m[
k] =
pCopy(second->m[
i]);
281 if(syz_ring!=orig_ring)
288 if ((temp1->m[
i]!=
NULL)
291 if(syz_ring==orig_ring)
297 p =
prMoveR(temp1->m[
i], syz_ring,orig_ring);
314 if(syz_ring!=orig_ring)
347 ideal bigmat,tempstd,
result;
353 for (
i=0;
i<length;
i++)
360 if (realrki>maxrk) maxrk = realrki;
386 for (
i=0;
i<maxrk;
i++)
393 bigmat->m[
i] =
pAdd(bigmat->m[
i],
p);
399 for (
j=0;
j<length;
j++)
407 if (syz_ring==orig_ring)
423 if(syz_ring!=orig_ring)
433 if (syz_ring==orig_ring)
443 if(syz_ring!=orig_ring)
446 if(syz_ring!=orig_ring)
477 Warn(
"syzcomp too low, should be %d instead of %d",
k,syzcomp);
481 h2->rank = syzcomp+
i;
526 Werror(
"error %d in >>groebner<<",err);
549 Werror(
"wrong algorith %d for SB",(
int)alg);
566 int j,
k, length=0,reg;
568 int ii, idElemens_h1;
574 for(ii=0;ii<idElemens_h1 ;ii++)
pTest(h1->m[ii]);
590 if (orig_ring != syz_ring)
608 if (orig_ring != syz_ring)
613 if (s_h3->m[
j] !=
NULL)
641 if (s_h3->m[
j] !=
NULL)
645 e->m[
j] = s_h3->m[
j];
646 isMonomial=isMonomial && (
pNext(s_h3->m[
j])==
NULL);
666 if (dp_C_ring != syz_ring)
675 for (
j=0;
j<length;
j++)
681 if (dp_C_ring != syz_ring)
714 if (orig_ring != syz_ring)
730 if (orig_ring != syz_ring)
767 return idInit(1,h1->rank);
784 if (orig_ring != syz_ring)
803 if (s_h3->m[
j] !=
NULL)
830 (*syz)->m[
j]=s_h3->m[
j];
852 if (syz_ring!=orig_ring)
863 if (s_h2->m[
j] !=
NULL)
865 q =
prMoveR( s_h2->m[
j], syz_ring,orig_ring);
899 if (syz_ring!=orig_ring)
rDelete(syz_ring);
919 if (s_temp->m[
j]!=
NULL)
960 WerrorS(
"2nd module does not lie in the first");
965 comps_to_add =
IDELEMS(submod);
966 while ((comps_to_add>0) && (submod->m[comps_to_add-1]==
NULL))
970 if ((
k!=0) && (lsmod==0)) lsmod=1;
972 if (k<submod->rank) {
WarnS(
"rk(submod) > rk(mod) ?");
k=submod->rank; }
980 if (orig_ring != syz_ring)
1015 for(
j = 0;
j<comps_to_add;
j++)
1028 s_temp->rank += (
k+comps_to_add);
1031 s_result->rank = s_h3->rank;
1038 if (s_result->m[
j]!=
NULL)
1046 WarnS(
"first module not a standardbasis\n" 1047 "// ** or second not a proper submodule");
1050 WerrorS(
"2nd module does not lie in the first");
1058 p = s_rest->m[
j] = s_result->m[
j];
1065 pNeg(s_result->m[
j]);
1068 if ((lsmod==0) && (s_rest!=
NULL))
1072 if (s_rest->m[
j-1]!=
NULL)
1075 s_rest->m[
j-1] = s_rest->m[
j-1];
1079 if(syz_ring!=orig_ring)
1094 *unit=
mpNew(comps_to_add,comps_to_add);
1116 else p=s_result->m[
i];
1206 int i,
l,ll,
k,kkk,kmax;
1214 if ((k2==0) && (
k>1)) *addOnlyOne =
FALSE;
1221 if (weights!=
NULL)
delete weights;
1226 if (h2->m[
i] !=
NULL)
1237 *kkmax = kmax =
j*
k+1;
1246 ideal h4 =
idInit(16,kmax+
k-1);
1257 if (h4->m[
i-1]!=
NULL)
1270 if(temph1->m[
l]!=
NULL)
1272 for (ll=0; ll<
j; ll++)
1296 h4->m[
i] = h4->m[
i+1];
1338 if (orig_ring!=syz_ring)
1340 s_h4 =
idrMoveR(s_h4,orig_ring, syz_ring);
1363 m=idModule2Matrix(
idCopy(s_h3));
1364 Print(
"result, kmax=%d:\n",kmax);
1369 if (weights1!=
NULL)
delete weights1;
1387 s_h3->rank = h1->rank;
1388 if(syz_ring!=orig_ring)
1407 int *block0,*block1;
1421 WerrorS(
"cannot eliminate in a qring");
1434 WerrorS(
"no elimination is possible: subalgebra is not admissible");
1444 if (origR->order[
k]!=0) ordersize++;
1451 for (
k=0;
k<ordersize-1;
k++)
1453 block0[
k+1] = origR->block0[
k];
1454 block1[
k+1] = origR->block1[
k];
1455 ord[
k+1] = origR->order[
k];
1456 if (origR->wvhdl[
k]!=
NULL) wv[
k+1] = (
int*)
omMemDup(origR->wvhdl[
k]);
1466 double wNsqr = (double)2.0 / (
double)(
currRing->N);
1470 wCall(h1->m, sl,
x, wNsqr);
1471 for (sl = (
currRing->N); sl!=0; sl--)
1472 wv[1][sl-1] =
x[sl + (
currRing->N) + 1];
1488 block0=(
int*)
omAlloc0(4*
sizeof(
int));
1489 block1=(
int*)
omAlloc0(4*
sizeof(
int));
1490 wv=(
int**)
omAlloc0(4*
sizeof(
int**));
1491 block0[0] = block0[1] = 1;
1492 block1[0] = block1[1] =
rVar(origR);
1515 block0=(
int*)
omAlloc0(4*
sizeof(
int));
1516 block1=(
int*)
omAlloc0(4*
sizeof(
int));
1517 wv=(
int**)
omAlloc0(4*
sizeof(
int**));
1518 block0[0] = block0[1] = 1;
1519 block1[0] = block1[1] =
rVar(origR);
1537 block0=(
int*)
omAlloc0(ordersize*
sizeof(
int));
1538 block1=(
int*)
omAlloc0(ordersize*
sizeof(
int));
1539 wv=(
int**)
omAlloc0(ordersize*
sizeof(
int**));
1540 for (
k=0;
k<ordersize-1;
k++)
1542 block0[
k+1] = origR->block0[
k];
1543 block1[
k+1] = origR->block1[
k];
1544 ord[
k+1] = origR->order[
k];
1545 if (origR->wvhdl[
k]!=
NULL) wv[
k+1] = (
int*)
omMemDup(origR->wvhdl[
k]);
1548 block1[0] =
rVar(origR);
1561 tmpR->block0 = block0;
1562 tmpR->block1 = block1;
1572 WerrorS(
"no elimination is possible: ordering condition is violated");
1589 if (origR->qideal!=
NULL)
1591 WarnS(
"eliminate in q-ring: experimental");
1617 while ((
i >= 0) && (hh->m[
i] ==
NULL))
i--;
1620 for (
k=0;
k<=
i;
k++)
1632 h3->m[
j] =
prMoveR( hh->m[
k], tmpR,origR);
1644 #ifdef WITH_OLD_MINOR 1648 poly idMinor(
matrix a,
int ar,
unsigned long which, ideal
R)
1652 int *rowchoise,*colchoise;
1661 rowchoise=(
int *)
omAlloc(ar*
sizeof(
int));
1662 colchoise=(
int *)
omAlloc(ar*
sizeof(
int));
1677 for (
i=1;
i<=ar;
i++)
1679 for (
j=1;
j<=ar;
j++)
1694 for (
i=1;
i<=ar;
i++)
1718 int *rowchoise,*colchoise;
1727 rowchoise=(
int *)
omAlloc(ar*
sizeof(
int));
1728 colchoise=(
int *)
omAlloc(ar*
sizeof(
int));
1729 if ((
i>512) || (
j>512) || (
i*
j >512))
size=512;
1740 for (
i=1;
i<=ar;
i++)
1742 for (
j=1;
j<=ar;
j++)
1772 for (
i=1;
i<=ar;
i++)
1800 const int r =
a->nrows;
1801 const int c =
a->ncols;
1803 if((ar<=0) || (ar>
r) || (ar>c))
1805 Werror(
"%d-th minor, matrix is %dx%d",ar,
r,c);
1817 for (
int i=
r*c-1;
i>=0;
i--)
1871 if (id1->m[
i] !=
NULL)
1894 for (
i=length-1;
i>=0;
i--)
1900 if (
w->length()+1 < cmax)
1909 for (
i=length-1;
i>=0;
i--)
2042 int i,
k,rk,flength=0,slength,length;
2050 length =
si_max(flength,slength);
2062 for (
i=0;
i<length;
i++)
2063 ((*wtmp)[
i])=(**w)[
i];
2073 ((*wtmp)[
i+length]) = d;
2084 if(temp->m[
i]!=
NULL)
2123 if (syz_ring != orig_ring)
2141 ((**
w)[
i])=(*wtmp)[
i+length];
2143 if (wtmp!=
NULL)
delete wtmp;
2147 if ((s_temp1->m[
i]!=
NULL)
2148 && (((int)
pGetComp(s_temp1->m[
i]))<=length))
2160 if (syz_ring!=orig_ring)
2205 for (
i=0;
i<(*convert)->length();
i++)
2219 while ((
j>0) && (kbase->m[
j-1]==
NULL))
j--;
2220 if (
j==0)
return -1;
2229 if (
j==0)
return -1;
2291 while ((
i>0) && (kbase->m[
i-1]==
NULL))
i--;
2294 while ((
j>0) && (arg->m[
j-1]==
NULL))
j--;
2298 while ((
j>0) && (arg->m[
j-1]==
NULL))
j--;
2352 int i,next_gen,next_comp;
2356 int *red_comp=(
int*)
omAlloc((
res->rank+1)*
sizeof(int));
2357 for (
i=
res->rank;
i>=0;
i--) red_comp[
i]=
i;
2363 if (next_gen<0)
break;
2366 for(
i=next_comp+1;
i<=arg->rank;
i++) red_comp[
i]--;
2369 for(
i=next_comp;
i<(*w)->length();
i++) (**
w)[
i-1]=(**w)[
i];
2379 int nl=
si_max((*w)->length()-del,1);
2381 for(
i=0;
i<
res->rank;
i++) (*wtmp)[
i]=(**w)[
i];
2395 ideal I=
idInit(2,1); I->m[0]=
f; I->m[1]=
g;
2409 ideal I=
idInit(2,1); I->m[0]=
f; I->m[1]=
g;
2437 int cnt=
IDELEMS(xx[0])*xx[0]->nrows;
2439 result->nrows=xx[0]->nrows;
2440 result->ncols=xx[0]->ncols;
2443 number *
x=(number *)
omAlloc(rl*
sizeof(number));
2444 for(
i=cnt-1;
i>=0;
i--)
2450 for(
j=rl-1;
j>=0;
j--)
2459 for(
j=rl-1;
j>=0;
j--)
2472 number n=n_ChineseRemainder(
x,q,rl,
R->cf);
2474 for(
j=rl-1;
j>=0;
j--)
2518 for(
i=cnt-1;
i>=0;
i--)
2622 for (
int i = 0;
i < idsize;
i++)
2624 id_sort[
i].
p =
id->m[
i];
2628 int index, index_i, index_j;
2630 for (
int j = 1;
j < idsize;
j++)
2634 index_i = id_sort[
i].
index;
2635 index_j = id_sort[
j].
index;
2636 if (index_j > index_i)
2658 if (strcmp(n,
"slimgb")==0) alg=
GbSlimgb;
2659 else if (strcmp(n,
"std")==0) alg=
GbStd;
2660 else if (strcmp(n,
"sba")==0) alg=
GbSba;
2661 else if (strcmp(n,
"singmatic")==0) alg=
GbSingmatic;
2662 else if (strcmp(n,
"groebner")==0) alg=
GbGroebner;
2663 else if (strcmp(n,
"modstd")==0) alg=
GbModstd;
2664 else if (strcmp(n,
"ffmod")==0) alg=
GbFfmod;
2665 else if (strcmp(n,
"nfmod")==0) alg=
GbNfmod;
2666 else Warn(
">>%s<< is an unknown algorithm",n);
2679 else if (alg==
GbSba)
#define TEST_OPT_NOTREGULARITY
matrix idDiff(matrix i, int k)
#define pSetmComp(p)
TODO:
void p_SetModDeg(intvec *w, ring r)
for idElimination, like a, except pFDeg, pWeigths ignore it
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
const CanonicalForm int s
ring sm_RingChange(const ring origR, long bound)
void idDelEquals(ideal id)
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
void idKeepFirstK(ideal id, const int k)
keeps the first k (>= 1) entries of the given ideal (Note that the kept polynomials may be zero...
static ideal idPrepare(ideal h1, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
static void idPrepareStd(ideal s_temp, int k)
static CanonicalForm bound(const CFMatrix &M)
poly idDecompose(poly monom, poly how, ideal kbase, int *pos)
static BOOLEAN idHomIdeal(ideal id, ideal Q=NULL)
poly prCopyR(poly p, ring src_r, ring dest_r)
#define idDelete(H)
delete an ideal
void idLiftW(ideal P, ideal Q, int n, matrix &T, ideal &R, short *w)
Compatiblity layer for legacy polynomial operations (over currRing)
int idIndexOfKBase(poly monom, ideal kbase)
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
BOOLEAN nc_rComplete(const ring src, ring dest, bool bSetupQuotient)
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
poly prMoveR(poly &p, ring src_r, ring dest_r)
void mp_RecMin(int ar, ideal result, int &elems, matrix a, int lr, int lc, poly barDiv, ideal R, const ring r)
produces recursively the ideal of all arxar-minors of a
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
#define omFreeSize(addr, size)
#define idSimpleAdd(A, B)
matrix idDiffOp(ideal I, ideal J, BOOLEAN multiply)
static short rVar(const ring r)
#define rVar(r) (r->N)
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
int pCompare_qsort(const void *a, const void *b)
CanonicalForm divide(const CanonicalForm &ff, const CanonicalForm &f, const CFList &as)
ring rAssure_SyzOrder(const ring r, BOOLEAN complete)
ideal kStd(ideal F, ideal Q, tHomog h, intvec **w, intvec *hilb, int syzComp, int newIdeal, intvec *vw, s_poly_proc_t sp)
ideal idMultSect(resolvente arg, int length)
static BOOLEAN rField_is_Domain(const ring r)
static void ipPrint_MA0(matrix m, const char *name)
void WerrorS(const char *s)
ideal idModulo(ideal h2, ideal h1, tHomog hom, intvec **w)
static intvec * idSort(ideal id, BOOLEAN nolex=TRUE)
#define TEST_V_INTERSECT_ELIM
void mp_MinorToResult(ideal result, int &elems, matrix a, int r, int c, ideal R, const ring)
entries of a are minors and go to result (only if not in R)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
#define pEqualPolys(p1, p2)
ideal idMinEmbedding(ideal arg, BOOLEAN inPlace, intvec **w)
poly singclap_pdivide(poly f, poly g, const ring r)
long sm_ExpBound(ideal m, int di, int ra, int t, const ring currRing)
ideal idQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
static number p_SetCoeff(poly p, number n, ring r)
#define pGetComp(p)
Component.
static poly p_Copy(poly p, const ring r)
returns a copy of p
void * iiCallLibProc1(const char *n, void *arg, int arg_type, BOOLEAN &err)
ideal idMinBase(ideal h1)
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
static BOOLEAN idHomModule(ideal m, ideal Q, intvec **w)
int p_Weight(int i, const ring r)
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
#define pGetExp(p, i)
Exponent.
void id_Shift(ideal M, int s, const ring r)
static poly p_Head(poly p, const ring r)
long p_DegW(poly p, const short *w, const ring R)
static ideal idInitializeQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
ideal idSect(ideal h1, ideal h2)
long p_Deg(poly a, const ring r)
Coefficient rings, fields and other domains suitable for Singular polynomials.
ideal idSeries(int n, ideal M, matrix U, intvec *w)
ideal idElimination(ideal h1, poly delVar, intvec *hilb)
poly p_Farey(poly p, number N, const ring r)
void id_DelMultiples(ideal id, const ring r)
ideal id = (id[i]), c any unit if id[i] = c*id[j] then id[j] is deleted for j > i ...
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
intvec * idMWLift(ideal mod, intvec *weights)
const CanonicalForm CFMap CFMap & N
BOOLEAN rComplete(ring r, int force)
this needs to be called whenever a new ring is created: new fields in ring are created (like VarOffse...
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent : the integer VarOffset encodes:
END_NAMESPACE BEGIN_NAMESPACE_SINGULARXX ideal poly int syzComp
ideal idMinors(matrix a, int ar, ideal R)
compute all ar-minors of the matrix a the caller of mpRecMin the elements of the result are not in R ...
ideal idFreeModule(int i)
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
ideal idSectWithElim(ideal h1, ideal h2)
ring rAssure_SyzComp(const ring r, BOOLEAN complete)
ring rAssure_dp_C(const ring r)
void idSort_qsort(poly_sort *id_sort, int idsize)
ideal t_rep_gb(const ring r, ideal arg_I, int syz_comp, BOOLEAN F4_mode)
ideal idrMoveR(ideal &id, ring src_r, ring dest_r)
static int p_LmCmp(poly p, poly q, const ring r)
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
static int si_max(const int a, const int b)
int p_Compare(const poly a, const poly b, const ring R)
void PrintS(const char *s)
static long p_MinComp(poly p, ring lmRing, ring tailRing)
char name(const Variable &v)
ideal idCreateSpecialKbase(ideal kBase, intvec **convert)
static poly p_LmFreeAndNext(poly p, ring)
BOOLEAN idIsSubModule(ideal id1, ideal id2)
resolvente sySchreyerResolvente(ideal arg, int maxlength, int *length, BOOLEAN isMonomial=FALSE, BOOLEAN notReplace=FALSE)
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL ...
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
static poly pReverse(poly p)
ideal idLiftStd(ideal h1, matrix *ma, tHomog hi, ideal *syz, GbVariant alg)
static int index(p_Length length, p_Ord ord)
void rSetSyzComp(int k, const ring r)
void rChangeCurrRing(ring r)
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp, BOOLEAN setRegularity, int *deg, GbVariant alg)
poly id_GCD(poly f, poly g, const ring r)
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
matrix mpNew(int r, int c)
create a r x c zero-matrix
#define TEST_OPT_RETURN_SB
static void p_Delete(poly *p, const ring r)
matrix mp_MultP(matrix a, poly p, const ring R)
multiply a matrix 'a' by a poly 'p', destroy the args
#define SI_RESTORE_OPT2(A)
ideal idInit(int idsize, int rank)
initialise an ideal / module
#define pSeries(n, p, u, w)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent : VarOffset encodes the position in p->exp
poly p_DivideM(poly a, poly b, const ring r)
static BOOLEAN rField_is_Ring(const ring r)
#define pDivisibleBy(a, b)
returns TRUE, if leading monom of a divides leading monom of b i.e., if there exists a expvector c > ...
ideal id_Farey(ideal x, number N, const ring r)
void pEnlargeSet(poly **p, int l, int increment)
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
BOOLEAN rHasGlobalOrdering(const ring r)
void rDelete(ring r)
unconditionally deletes fields in r
GbVariant syGetAlgorithm(char *n, const ring r, const ideal)
void pTakeOutComp(poly *p, long comp, poly *q, int *lq, const ring R=currRing)
Splits *p into two polys: *q which consists of all monoms with component == comp and *p of all other ...
void sm_KillModifiedRing(ring r)
static void idDeleteComps(ideal arg, int *red_comp, int del)
ideal kMin_std(ideal F, ideal Q, tHomog h, intvec **w, ideal &M, intvec *hilb, int syzComp, int reduced)
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
poly mp_DetBareiss(matrix a, const ring r)
returns the determinant of the matrix m; uses Bareiss algorithm
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
static void p_Setm(poly p, const ring r)
void syGaussForOne(ideal syz, int elnum, int ModComp, int from, int till)
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
static nc_type & ncRingType(nc_struct *p)
ideal idXXX(ideal h1, int k)
#define TEST_V_INTERSECT_SYZ
poly prMoveR_NoSort(poly &p, ring src_r, ring dest_r)
static poly p_Neg(poly p, const ring r)
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
int id_ReadOutPivot(ideal arg, int *comp, const ring r)
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
static poly p_Add_q(poly p, poly q, const ring r)
BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r)
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
#define SI_RESTORE_OPT1(A)
ideal idrCopyR_NoSort(ideal id, ring src_r, ring dest_r)
ideal id_Matrix2Module(matrix mat, const ring R)
static ideal idMult(ideal h1, ideal h2)
hh := h1 * h2
void Werror(const char *fmt,...)
ideal kGroebner(ideal F, ideal Q)
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
ideal idrMoveR_NoSort(ideal &id, ring src_r, ring dest_r)
#define pCopy(p)
return a copy of the poly
#define MATELEM(mat, i, j)