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ideals.cc
Go to the documentation of this file.
/****************************************
* Computer Algebra System SINGULAR *
****************************************/
/*
* ABSTRACT - all basic methods to manipulate ideals
*/
/* includes */
#include "kernel/mod2.h"
#include "misc/options.h"
#include "misc/intvec.h"
#include "coeffs/coeffs.h"
#include "coeffs/numbers.h"
// #include "coeffs/longrat.h"
#include "polys/monomials/ring.h"
#include "polys/matpol.h"
#include "polys/weight.h"
#include "polys/sparsmat.h"
#include "polys/prCopy.h"
#include "polys/nc/nc.h"
#include "kernel/ideals.h"
#include "kernel/polys.h"
#include "kernel/GBEngine/kstd1.h"
#include "kernel/GBEngine/kutil.h"
#include "kernel/GBEngine/tgb.h"
#include "kernel/GBEngine/syz.h"
#include "Singular/ipshell.h" // iiCallLibProc1
#include "Singular/ipid.h" // ggetid
#if 0
#include "Singular/ipprint.h" // ipPrint_MA0
#endif
/* #define WITH_OLD_MINOR */
/*0 implementation*/
/*2
*returns a minimized set of generators of h1
*/
ideal idMinBase (ideal h1, ideal *SB)
{
ideal h2, h3,h4,e;
int j,k;
int i,l,ll;
intvec * wth;
BOOLEAN homog;
if(rField_is_Ring(currRing))
{
WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
e=idCopy(h1);
return e;
}
homog = idHomModule(h1,currRing->qideal,&wth);
if (rHasGlobalOrdering(currRing))
{
if(!homog)
{
WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
e=idCopy(h1);
return e;
}
else
{
ideal re=kMin_std2(h1,currRing->qideal,(tHomog)homog,&wth,h2,(bigintmat*)NULL,0,3);
idDelete(&re);
return h2;
}
}
e=idInit(1,h1->rank);
if (idIs0(h1))
{
return e;
}
h2 = kStd2(h1,currRing->qideal,isNotHomog,NULL,(bigintmat*)NULL);
if (SB!=NULL) *SB=h2;
h3 = idMaxIdeal(1);
h4=idMult(h2,h3);
idDelete(&h3);
h3=kStd2(h4,currRing->qideal,isNotHomog,NULL,(bigintmat*)NULL);
k = IDELEMS(h3);
while ((k > 0) && (h3->m[k-1] == NULL)) k--;
j = -1;
l = IDELEMS(h2);
while ((l > 0) && (h2->m[l-1] == NULL)) l--;
for (i=l-1; i>=0; i--)
{
if (h2->m[i] != NULL)
{
ll = 0;
while ((ll < k) && ((h3->m[ll] == NULL)
|| !pDivisibleBy(h3->m[ll],h2->m[i])))
ll++;
if (ll >= k)
{
j++;
if (j > IDELEMS(e)-1)
{
pEnlargeSet(&(e->m),IDELEMS(e),16);
IDELEMS(e) += 16;
}
e->m[j] = pCopy(h2->m[i]);
}
}
}
if (SB==NULL) idDelete(&h2);
idDelete(&h3);
idDelete(&h4);
if (currRing->qideal!=NULL)
{
h3=idInit(1,e->rank);
h2=kNF(h3,currRing->qideal,e);
idDelete(&h3);
idDelete(&e);
e=h2;
}
idSkipZeroes(e);
return e;
}
static ideal idSectWithElim (ideal h1,ideal h2, GbVariant alg)
// does not destroy h1,h2
{
if (TEST_OPT_PROT) PrintS("intersect by elimination method\n");
assume(!idIs0(h1));
assume(!idIs0(h2));
assume(IDELEMS(h1)<=IDELEMS(h2));
assume(id_RankFreeModule(h1,currRing)==0);
assume(id_RankFreeModule(h2,currRing)==0);
// add a new variable:
int j;
ring origRing=currRing;
ring r=rCopy0(origRing);
r->N++;
r->block0[0]=1;
r->block1[0]= r->N;
omFree(r->order);
r->order=(rRingOrder_t*)omAlloc0(3*sizeof(rRingOrder_t));
r->order[0]=ringorder_dp;
r->order[1]=ringorder_C;
char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr));
for (j=0;j<r->N-1;j++) names[j]=r->names[j];
names[r->N-1]=omStrDup("@");
omFree(r->names);
r->names=names;
rComplete(r,TRUE);
// fetch h1, h2
ideal h;
h1=idrCopyR(h1,origRing,r);
h2=idrCopyR(h2,origRing,r);
// switch to temp. ring r
rChangeCurrRing(r);
// create 1-t, t
poly omt=p_One(currRing);
p_SetExp(omt,r->N,1,currRing);
p_Setm(omt,currRing);
poly t=p_Copy(omt,currRing);
omt=p_Neg(omt,currRing);
omt=p_Add_q(omt,pOne(),currRing);
// compute (1-t)*h1
h1=(ideal)mp_MultP((matrix)h1,omt,currRing);
// compute t*h2
h2=(ideal)mp_MultP((matrix)h2,pCopy(t),currRing);
// (1-t)h1 + t*h2
h=idInit(IDELEMS(h1)+IDELEMS(h2),1);
int l;
for (l=IDELEMS(h1)-1; l>=0; l--)
{
h->m[l] = h1->m[l]; h1->m[l]=NULL;
}
j=IDELEMS(h1);
for (l=IDELEMS(h2)-1; l>=0; l--)
{
h->m[l+j] = h2->m[l]; h2->m[l]=NULL;
}
idDelete(&h1);
idDelete(&h2);
// eliminate t:
ideal res=idElimination2(h,t,NULL,alg);
// cleanup
idDelete(&h);
pDelete(&t);
if (res!=NULL) res=idrMoveR(res,r,origRing);
rChangeCurrRing(origRing);
rDelete(r);
return res;
}
static ideal idGroebner(ideal temp,int syzComp,GbVariant alg, bigintmat* hilb=NULL, intvec* w=NULL, tHomog hom=testHomog)
{
//Print("syz=%d\n",syzComp);
//PrintS(showOption());
//PrintLn();
ideal res=NULL;
if (w==NULL)
{
if (hom==testHomog)
hom=(tHomog)idHomModule(temp,currRing->qideal,&w); //sets w to weight vector or NULL
}
else
{
w=ivCopy(w);
hom=isHomog;
}
#ifdef HAVE_SHIFTBBA
if (rIsLPRing(currRing)) alg = GbStd;
#endif
if ((alg==GbStd)||(alg==GbDefault))
{
if (TEST_OPT_PROT &&(alg==GbStd)) { PrintS("std:"); mflush(); }
res = kStd2(temp,currRing->qideal,hom,&w,hilb,syzComp);
idDelete(&temp);
}
else if (alg==GbSlimgb)
{
if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); }
res = t_rep_gb(currRing, temp, syzComp);
idDelete(&temp);
}
else if (alg==GbGroebner)
{
if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); }
BOOLEAN err;
res=(ideal)iiCallLibProc1("groebner",temp,MODUL_CMD,err);
if (err)
{
Werror("error %d in >>groebner<<",err);
res=idInit(1,1);
}
}
else if (alg==GbModstd)
{
if (TEST_OPT_PROT) { PrintS("modStd:"); mflush(); }
BOOLEAN err;
void *args[]={temp,(void*)1,NULL};
int arg_t[]={MODUL_CMD,INT_CMD,0};
leftv temp0=ii_CallLibProcM("modStd",args,arg_t,currRing,err);
res=(ideal)temp0->data;
omFreeBin((ADDRESS)temp0,sleftv_bin);
if (err)
{
Werror("error %d in >>modStd<<",err);
res=idInit(1,1);
}
}
else if (alg==GbSba)
{
if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); }
res = kSba(temp,currRing->qideal,hom,&w,1,0,NULL);
if (w!=NULL) delete w;
}
else if (alg==GbStdSat)
{
if (TEST_OPT_PROT) { PrintS("std:sat:"); mflush(); }
BOOLEAN err;
// search for 2nd block of vars
int i=0;
int block=-1;
loop
{
if ((currRing->order[i]!=ringorder_c)
&& (currRing->order[i]!=ringorder_C)
&& (currRing->order[i]!=ringorder_s))
{
if (currRing->order[i]==0) { err=TRUE;break;}
block++;
if (block==1) { block=i; break;}
}
i++;
}
if (block>0)
{
if (TEST_OPT_PROT)
{
Print("sat(%d..%d)\n",currRing->block0[block],currRing->block1[block]);
mflush();
}
ideal v=idInit(currRing->block1[block]-currRing->block0[block]+1,1);
for(i=currRing->block0[block];i<=currRing->block1[block];i++)
{
v->m[i-currRing->block0[block]]=pOne();
pSetExp(v->m[i-currRing->block0[block]],i,1);
pSetm(v->m[i-currRing->block0[block]]);
}
void *args[]={temp,v,NULL};
int arg_t[]={MODUL_CMD,IDEAL_CMD,0};
leftv temp0=ii_CallLibProcM("satstd",args,arg_t,currRing,err);
res=(ideal)temp0->data;
omFreeBin((ADDRESS)temp0, sleftv_bin);
}
if (err)
{
Werror("error %d in >>satstd<<",err);
res=idInit(1,1);
}
}
if (w!=NULL) delete w;
return res;
}
/*2
* h3 := h1 intersect h2
*/
ideal idSect (ideal h1,ideal h2, GbVariant alg)
{
int i,j,k;
unsigned length;
int flength = id_RankFreeModule(h1,currRing);
int slength = id_RankFreeModule(h2,currRing);
int rank=si_max(h1->rank,h2->rank);
if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank);
BITSET save_opt;
SI_SAVE_OPT1(save_opt);
si_opt_1 |= Sy_bit(OPT_REDTAIL_SYZ);
ideal first,second,temp,temp1,result;
poly p,q;
if (IDELEMS(h1)<IDELEMS(h2))
{
first = h1;
second = h2;
}
else
{
first = h2;
second = h1;
int t=flength; flength=slength; slength=t;
}
length = si_max(flength,slength);
if (length==0)
{
if ((currRing->qideal==NULL)
&& (currRing->OrdSgn==1)
&& (!rIsPluralRing(currRing))
&& ((TEST_V_INTERSECT_ELIM) || (!TEST_V_INTERSECT_SYZ)))
return idSectWithElim(first,second,alg);
else length = 1;
}
if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n");
j = IDELEMS(first);
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
rSetSyzComp(length,syz_ring);
rChangeCurrRing(syz_ring);
si_opt_1 |= Sy_bit(OPT_REDTAIL_SYZ);
while ((j>0) && (first->m[j-1]==NULL)) j--;
temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j);
k = 0;
for (i=0;i<j;i++)
{
if (first->m[i]!=NULL)
{
if (syz_ring==orig_ring)
temp->m[k] = pCopy(first->m[i]);
else
temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring);
q = pOne();
pSetComp(q,i+1+length);
pSetmComp(q);
if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
p = temp->m[k];
while (pNext(p)!=NULL) pIter(p);
pNext(p) = q;
k++;
}
}
for (i=0;i<IDELEMS(second);i++)
{
if (second->m[i]!=NULL)
{
if (syz_ring==orig_ring)
temp->m[k] = pCopy(second->m[i]);
else
temp->m[k] = prCopyR(second->m[i], orig_ring,currRing);
if (slength==0) p_Shift(&(temp->m[k]),1,currRing);
k++;
}
}
intvec *w=NULL;
if ((alg!=GbDefault)
&& (alg!=GbGroebner)
&& (alg!=GbModstd)
&& (alg!=GbSlimgb)
&& (alg!=GbStd))
{
WarnS("wrong algorithm for GB");
alg=GbDefault;
}
temp1=idGroebner(temp,length,alg);
if(syz_ring!=orig_ring)
rChangeCurrRing(orig_ring);
result = idInit(IDELEMS(temp1),rank);
j = 0;
for (i=0;i<IDELEMS(temp1);i++)
{
if ((temp1->m[i]!=NULL)
&& (__p_GetComp(temp1->m[i],syz_ring)>length))
{
if(syz_ring==orig_ring)
{
p = temp1->m[i];
}
else
{
p = prMoveR(temp1->m[i], syz_ring,orig_ring);
}
temp1->m[i]=NULL;
while (p!=NULL)
{
q = pNext(p);
pNext(p) = NULL;
k = pGetComp(p)-1-length;
pSetComp(p,0);
pSetmComp(p);
/* Warning! multiply only from the left! it's very important for Plural */
result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k])));
p = q;
}
j++;
}
}
if(syz_ring!=orig_ring)
{
rChangeCurrRing(syz_ring);
idDelete(&temp1);
rChangeCurrRing(orig_ring);
rDelete(syz_ring);
}
else
{
idDelete(&temp1);
}
idSkipZeroes(result);
SI_RESTORE_OPT1(save_opt);
if (TEST_OPT_RETURN_SB)
{
w=NULL;
temp1=kStd2(result,currRing->qideal,testHomog,&w,(bigintmat*)NULL);
if (w!=NULL) delete w;
idDelete(&result);
idSkipZeroes(temp1);
return temp1;
}
//else
// temp1=kInterRed(result,currRing->qideal);
return result;
}
/*2
* ideal/module intersection for a list of objects
* given as 'resolvente'
*/
ideal idMultSect(resolvente arg, int length, GbVariant alg)
{
int i,j=0,k=0,l,maxrk=-1,realrki;
unsigned syzComp;
ideal bigmat,tempstd,result;
poly p;
int isIdeal=0;
/* find 0-ideals and max rank -----------------------------------*/
for (i=0;i<length;i++)
{
if (!idIs0(arg[i]))
{
realrki=id_RankFreeModule(arg[i],currRing);
k++;
j += IDELEMS(arg[i]);
if (realrki>maxrk) maxrk = realrki;
}
else
{
if (arg[i]!=NULL)
{
return idInit(1,arg[i]->rank);
}
}
}
if (maxrk == 0)
{
isIdeal = 1;
maxrk = 1;
}
/* init -----------------------------------------------------------*/
j += maxrk;
syzComp = k*maxrk;
BITSET save_opt;
SI_SAVE_OPT1(save_opt);
si_opt_1 |= Sy_bit(OPT_REDTAIL_SYZ);
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
rSetSyzComp(syzComp,syz_ring);
rChangeCurrRing(syz_ring);
bigmat = idInit(j,(k+1)*maxrk);
/* create unit matrices ------------------------------------------*/
for (i=0;i<maxrk;i++)
{
for (j=0;j<=k;j++)
{
p = pOne();
pSetComp(p,i+1+j*maxrk);
pSetmComp(p);
bigmat->m[i] = pAdd(bigmat->m[i],p);
}
}
/* enter given ideals ------------------------------------------*/
i = maxrk;
k = 0;
for (j=0;j<length;j++)
{
if (arg[j]!=NULL)
{
for (l=0;l<IDELEMS(arg[j]);l++)
{
if (arg[j]->m[l]!=NULL)
{
if (syz_ring==orig_ring)
bigmat->m[i] = pCopy(arg[j]->m[l]);
else
bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing);
p_Shift(&(bigmat->m[i]),k*maxrk+isIdeal,currRing);
i++;
}
}
k++;
}
}
/* std computation --------------------------------------------*/
if ((alg!=GbDefault)
&& (alg!=GbGroebner)
&& (alg!=GbModstd)
&& (alg!=GbSlimgb)
&& (alg!=GbStd))
{
WarnS("wrong algorithm for GB");
alg=GbDefault;
}
tempstd=idGroebner(bigmat,syzComp,alg);
if(syz_ring!=orig_ring)
rChangeCurrRing(orig_ring);
/* interpret result ----------------------------------------*/
result = idInit(IDELEMS(tempstd),maxrk);
k = 0;
for (j=0;j<IDELEMS(tempstd);j++)
{
if ((tempstd->m[j]!=NULL) && (__p_GetComp(tempstd->m[j],syz_ring)>syzComp))
{
if (syz_ring==orig_ring)
p = pCopy(tempstd->m[j]);
else
p = prCopyR(tempstd->m[j], syz_ring,currRing);
p_Shift(&p,-syzComp-isIdeal,currRing);
result->m[k] = p;
k++;
}
}
/* clean up ----------------------------------------------------*/
if(syz_ring!=orig_ring)
rChangeCurrRing(syz_ring);
idDelete(&tempstd);
if(syz_ring!=orig_ring)
{
rChangeCurrRing(orig_ring);
rDelete(syz_ring);
}
SI_RESTORE_OPT1(save_opt);
idSkipZeroes(result);
return result;
}
/*2
*computes syzygies of h1,
*if quot != NULL it computes in the quotient ring modulo "quot"
*works always in a ring with ringorder_s
*/
/* construct a "matrix" (h11 may be NULL)
* h1 h11
* E_n 0
* and compute a (column) GB of it, with a syzComp=rows(h1)=rows(h11)
* currRing must be a syz-ring with syzComp set
* result is a "matrix":
* G 0
* T S
* where G: GB of (h1+h11)
* T: G/h11=h1*T
* S: relative syzygies(h1) modulo h11
* if V_IDLIFT is set, ignore/do not return S
*/
static ideal idPrepare (ideal h1, ideal h11, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
{
ideal h2,h22;
int j,k;
poly p,q;
assume(!idIs0(h1));
k = id_RankFreeModule(h1,currRing);
if (h11!=NULL)
{
k = si_max(k,(int)id_RankFreeModule(h11,currRing));
h22=idCopy(h11);
}
h2=idCopy(h1);
int i = IDELEMS(h2);
if (h11!=NULL) i+=IDELEMS(h22);
if (k == 0)
{
id_Shift(h2,1,currRing);
if (h11!=NULL) id_Shift(h22,1,currRing);
k = 1;
}
if (syzcomp<k)
{
Warn("syzcomp too low, should be %d instead of %d",k,syzcomp);
syzcomp = k;
rSetSyzComp(k,currRing);
}
h2->rank = syzcomp+i;
//if (hom==testHomog)
//{
// if(idHomIdeal(h1,currRing->qideal))
// {
// hom=TRUE;
// }
//}
for (j=0; j<IDELEMS(h2); j++)
{
p = h2->m[j];
q = pOne();
#ifdef HAVE_SHIFTBBA
// non multiplicative variable
if (rIsLPRing(currRing))
{
pSetExp(q, currRing->isLPring - currRing->LPncGenCount + j + 1, 1);
p_Setm(q, currRing);
}
#endif
pSetComp(q,syzcomp+1+j);
pSetmComp(q);
if (p!=NULL)
{
#ifdef HAVE_SHIFTBBA
if (rIsLPRing(currRing))
{
h2->m[j] = pAdd(p, q);
}
else
#endif
{
while (pNext(p)) pIter(p);
p->next = q;
}
}
else
h2->m[j]=q;
}
if (h11!=NULL)
{
ideal h=id_SimpleAdd(h2,h22,currRing);
id_Delete(&h2,currRing);
id_Delete(&h22,currRing);
h2=h;
}
idTest(h2);
#if 0
matrix TT=id_Module2Matrix(idCopy(h2),currRing);
PrintS(" --------------before std------------------------\n");
ipPrint_MA0(TT,"T");
PrintLn();
idDelete((ideal*)&TT);
#endif
if ((alg!=GbDefault)
&& (alg!=GbGroebner)
&& (alg!=GbModstd)
&& (alg!=GbSlimgb)
&& (alg!=GbStd))
{
WarnS("wrong algorithm for GB");
alg=GbDefault;
}
ideal h3;
if (w!=NULL) h3=idGroebner(h2,syzcomp,alg,NULL,*w,hom);
else h3=idGroebner(h2,syzcomp,alg,NULL,NULL,hom);
return h3;
}
ideal idExtractG_T_S(ideal s_h3,matrix *T,ideal *S,long syzComp,
int h1_size,BOOLEAN inputIsIdeal,const ring oring, const ring sring)
{
// now sort the result, SB : leave in s_h3
// T: put in s_h2 (*T as a matrix)
// syz: put in *S
idSkipZeroes(s_h3);
ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); // will become T
#if 0
matrix TT=id_Module2Matrix(idCopy(s_h3),currRing);
Print("after std: --------------syzComp=%d------------------------\n",syzComp);
ipPrint_MA0(TT,"T");
PrintLn();
idDelete((ideal*)&TT);
#endif
int j, i=0;
for (j=0; j<IDELEMS(s_h3); j++)
{
if (s_h3->m[j] != NULL)
{
if (pGetComp(s_h3->m[j]) <= syzComp) // syz_ring == currRing
{
i++;
poly q = s_h3->m[j];
while (pNext(q) != NULL)
{
if (pGetComp(pNext(q)) > syzComp)
{
s_h2->m[i-1] = pNext(q);
pNext(q) = NULL;
}
else
{
pIter(q);
}
}
if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing);
}
else
{
// we a syzygy here:
if (S!=NULL)
{
p_Shift(&s_h3->m[j], -syzComp,currRing);
(*S)->m[j]=s_h3->m[j];
s_h3->m[j]=NULL;
}
else
p_Delete(&(s_h3->m[j]),currRing);
}
}
}
idSkipZeroes(s_h3);
#if 0
TT=id_Module2Matrix(idCopy(s_h2),currRing);
PrintS("T: ----------------------------------------\n");
ipPrint_MA0(TT,"T");
PrintLn();
idDelete((ideal*)&TT);
#endif
if (S!=NULL) idSkipZeroes(*S);
if (sring!=oring)
{
rChangeCurrRing(oring);
}
if (T!=NULL)
{
*T = mpNew(h1_size,i);
for (j=0; j<i; j++)
{
if (s_h2->m[j] != NULL)
{
poly q = prMoveR( s_h2->m[j], sring,oring);
s_h2->m[j] = NULL;
if (q!=NULL)
{
q=pReverse(q);
while (q != NULL)
{
poly p = q;
pIter(q);
pNext(p) = NULL;
int t=pGetComp(p);
pSetComp(p,0);
pSetmComp(p);
MATELEM(*T,t-syzComp,j+1) = pAdd(MATELEM(*T,t-syzComp,j+1),p);
}
}
}
}
}
id_Delete(&s_h2,sring);
for (i=0; i<IDELEMS(s_h3); i++)
{
s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], sring,oring);
}
if (S!=NULL)
{
for (i=0; i<IDELEMS(*S); i++)
{
(*S)->m[i] = prMoveR_NoSort((*S)->m[i], sring,oring);
}
}
return s_h3;
}
/*2
* compute the syzygies of h1 in R/quot,
* weights of components are in w
* if setRegularity, return the regularity in deg
* do not change h1, w
*/
ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp,
BOOLEAN setRegularity, int *deg, GbVariant alg)
{
ideal s_h1;
int j, k, length=0,reg;
BOOLEAN isMonomial=TRUE;
int ii, idElemens_h1;
assume(h1 != NULL);
idElemens_h1=IDELEMS(h1);
#ifdef PDEBUG
for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]);
#endif
if (idIs0(h1))
{
ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/);
return result;
}
int slength=(int)id_RankFreeModule(h1,currRing);
k=si_max(1,slength /*id_RankFreeModule(h1)*/);
assume(currRing != NULL);
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzComp(orig_ring,TRUE);
if (setSyzComp) rSetSyzComp(k,syz_ring);
if (orig_ring != syz_ring)
{
rChangeCurrRing(syz_ring);
s_h1=idrCopyR_NoSort(h1,orig_ring,syz_ring);
}
else
{
s_h1 = h1;
}
idTest(s_h1);
BITSET save_opt;
SI_SAVE_OPT1(save_opt);
si_opt_1|=Sy_bit(OPT_REDTAIL_SYZ);
ideal s_h3=idPrepare(s_h1,NULL,h,k,w,alg); // main (syz) GB computation
SI_RESTORE_OPT1(save_opt);
if (orig_ring != syz_ring)
{
idDelete(&s_h1);
for (j=0; j<IDELEMS(s_h3); j++)
{
if (s_h3->m[j] != NULL)
{
if (p_MinComp(s_h3->m[j],syz_ring) > k)
p_Shift(&s_h3->m[j], -k,syz_ring);
else
p_Delete(&s_h3->m[j],syz_ring);
}
}
idSkipZeroes(s_h3);
s_h3->rank -= k;
rChangeCurrRing(orig_ring);
s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
rDelete(syz_ring);
#ifdef HAVE_PLURAL
if (rIsPluralRing(orig_ring))
{
id_DelMultiples(s_h3,orig_ring);
idSkipZeroes(s_h3);
}
#endif
idTest(s_h3);
return s_h3;
}
ideal e = idInit(IDELEMS(s_h3), s_h3->rank);
for (j=IDELEMS(s_h3)-1; j>=0; j--)
{
if (s_h3->m[j] != NULL)
{
if (p_MinComp(s_h3->m[j],syz_ring) <= k)
{
e->m[j] = s_h3->m[j];
isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL);
p_Delete(&pNext(s_h3->m[j]),syz_ring);
s_h3->m[j] = NULL;
}
}
}
idSkipZeroes(s_h3);
idSkipZeroes(e);
if ((deg != NULL)
&& (!isMonomial)
&& (!TEST_OPT_NOTREGULARITY)
&& (setRegularity)
&& (h==isHomog)
&& (!rIsPluralRing(currRing))
&& (!rField_is_Ring(currRing))
)
{
assume(orig_ring==syz_ring);
ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later
if (dp_C_ring != syz_ring)
{
rChangeCurrRing(dp_C_ring);
e = idrMoveR_NoSort(e, syz_ring, dp_C_ring);
}
resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE);
intvec * dummy = syBetti(res,length,&reg, *w);
*deg = reg+2;
delete dummy;
for (j=0;j<length;j++)
{
if (res[j]!=NULL) idDelete(&(res[j]));
}
omFreeSize((ADDRESS)res,length*sizeof(ideal));
idDelete(&e);
if (dp_C_ring != orig_ring)
{
rChangeCurrRing(orig_ring);
rDelete(dp_C_ring);
}
}
else
{
idDelete(&e);
}
assume(orig_ring==currRing);
idTest(s_h3);
if (currRing->qideal != NULL)
{
ideal ts_h3=kStd2(s_h3,currRing->qideal,h,w,(bigintmat*)NULL);
idDelete(&s_h3);
s_h3 = ts_h3;
}
return s_h3;
}
/*
*computes a standard basis for h1 and stores the transformation matrix
* in ma
*/
ideal idLiftStd (ideal h1, matrix* T, tHomog hi, ideal * S, GbVariant alg,
ideal h11)
{
int inputIsIdeal=id_RankFreeModule(h1,currRing);
long k;
intvec *w=NULL;
idDelete((ideal*)T);
BOOLEAN lift3=FALSE;
if (S!=NULL) { lift3=TRUE; idDelete(S); }
if (idIs0(h1))
{
*T=mpNew(1,IDELEMS(h1));
if (lift3)
{
*S=idFreeModule(IDELEMS(h1));
}
return idInit(1,h1->rank);
}
BITSET saveOpt1,saveOpt2;
SI_SAVE_OPT(saveOpt1,saveOpt2);
si_opt_2|=Sy_bit(V_PURE_GB);
k=si_max(1,inputIsIdeal);
if ((!lift3)&&(!TEST_OPT_RETURN_SB)) si_opt_2 |=Sy_bit(V_IDLIFT);
ring orig_ring = currRing;
ring syz_ring = rAssure_SyzOrder(orig_ring,TRUE);
rSetSyzComp(k,syz_ring);
rChangeCurrRing(syz_ring);
ideal s_h1;
if (orig_ring != syz_ring)
s_h1 = idrCopyR_NoSort(h1,orig_ring,syz_ring);
else
s_h1 = h1;
ideal s_h11=NULL;
if (h11!=NULL)
{
s_h11=idrCopyR_NoSort(h11,orig_ring,syz_ring);
}
ideal s_h3=idPrepare(s_h1,s_h11,hi,k,&w,alg); // main (syz) GB computation
if (w!=NULL) delete w;
if (syz_ring!=orig_ring)
{
idDelete(&s_h1);
if (s_h11!=NULL) idDelete(&s_h11);
}
if (S!=NULL) (*S)=idInit(IDELEMS(s_h3),IDELEMS(h1));
s_h3=idExtractG_T_S(s_h3,T,S,k,IDELEMS(h1),inputIsIdeal,orig_ring,syz_ring);
if (syz_ring!=orig_ring) rDelete(syz_ring);
s_h3->rank=h1->rank;
SI_RESTORE_OPT(saveOpt1,saveOpt2);
return s_h3;
}
static void idPrepareStd(ideal s_temp, int k)
{
int j,rk=id_RankFreeModule(s_temp,currRing);
poly p,q;
if (rk == 0)
{
for (j=0; j<IDELEMS(s_temp); j++)
{
if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1);
}
k = si_max(k,1);
}
for (j=0; j<IDELEMS(s_temp); j++)
{
if (s_temp->m[j]!=NULL)
{
p = s_temp->m[j];
q = pOne();
//pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1
pSetComp(q,k+1+j);
pSetmComp(q);
#ifdef HAVE_SHIFTBBA
// non multiplicative variable
if (rIsLPRing(currRing))
{
pSetExp(q, currRing->isLPring - currRing->LPncGenCount + j + 1, 1);
p_Setm(q, currRing);
s_temp->m[j] = pAdd(p, q);
}
else
#endif
{
while (pNext(p)) pIter(p);
pNext(p) = q;
}
}
}
s_temp->rank = k+IDELEMS(s_temp);
}
static void idLift_setUnit(int e_mod, matrix *unit)
{
if (unit!=NULL)
{
*unit=mpNew(e_mod,e_mod);
// make sure that U is a diagonal matrix of units
for(int i=e_mod;i>0;i--)
{
MATELEM(*unit,i,i)=pOne();
}
}
}
/*2
*computes a representation of the generators of submod with respect to those
* of mod
*/
/// represents the generators of submod in terms of the generators of mod
/// (Matrix(SM)*U-Matrix(rest)) = Matrix(M)*Matrix(result)
/// goodShape: maximal non-zero index in generators of SM <= that of M
/// isSB: generators of M form a Groebner basis
/// divide: allow SM not to be a submodule of M
/// U is an diagonal matrix of units (non-constant only in local rings)
/// rest is: 0 if SM in M, SM if not divide, NF(SM,std(M)) if divide
ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape,
BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
{
int lsmod =id_RankFreeModule(submod,currRing), j, k;
int comps_to_add=0;
int idelems_mod=IDELEMS(mod);
int idelems_submod=IDELEMS(submod);
poly p;
if (idIs0(submod))
{
if (rest!=NULL)
{
*rest=idInit(1,mod->rank);
}
idLift_setUnit(idelems_submod,unit);
return idInit(1,idelems_mod);
}
if (idIs0(mod)) /* and not idIs0(submod) */
{
if (rest!=NULL)
{
*rest=idCopy(submod);
idLift_setUnit(idelems_submod,unit);
return idInit(1,idelems_mod);
}
else
{
WerrorS("2nd module does not lie in the first");
return NULL;
}
}
if (unit!=NULL)
{
comps_to_add = idelems_submod;
while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL))
comps_to_add--;
}
k=si_max(id_RankFreeModule(mod,currRing),id_RankFreeModule(submod,currRing));
if ((k!=0) && (lsmod==0)) lsmod=1;
k=si_max(k,(int)mod->rank);
if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; }
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
rSetSyzComp(k,syz_ring);
rChangeCurrRing(syz_ring);
ideal s_mod, s_temp;
if (orig_ring != syz_ring)
{
s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring);
s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring);
}
else
{
s_mod = idCopy(mod);
s_temp = idCopy(submod);
}
BITSET save2;
SI_SAVE_OPT2(save2);
if ((rest==NULL)
&& (!rField_is_Ring(currRing))
&& (!rIsNCRing(currRing))
&& (!TEST_OPT_RETURN_SB))
si_opt_2 |=Sy_bit(V_IDLIFT);
else
si_opt_2 &=~Sy_bit(V_IDLIFT);
ideal s_h3;
if (isSB && !TEST_OPT_IDLIFT)
{
s_h3 = idCopy(s_mod);
idPrepareStd(s_h3, k+comps_to_add);
}
else
{
s_h3 = idPrepare(s_mod,NULL,(tHomog)FALSE,k+comps_to_add,NULL,alg);
}
SI_RESTORE_OPT2(save2);
if (errorreported)
{
rChangeCurrRing(orig_ring);
return NULL;
}
if (!goodShape)
{
for (j=0;j<IDELEMS(s_h3);j++)
{
if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k))
p_Delete(&(s_h3->m[j]),currRing);
}
}
idSkipZeroes(s_h3);
if (lsmod==0)
{
id_Shift(s_temp,1,currRing);
}
if (unit!=NULL)
{
for(j = 0;j<comps_to_add;j++)
{
p = s_temp->m[j];
if (p!=NULL)
{
while (pNext(p)!=NULL) pIter(p);
pNext(p) = pOne();
pIter(p);
pSetComp(p,1+j+k);
pSetmComp(p);
p = pNeg(p);
}
}
s_temp->rank += (k+comps_to_add);
}
ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k);
s_result->rank = s_h3->rank;
ideal s_rest = idInit(IDELEMS(s_result),k);
idDelete(&s_h3);
idDelete(&s_temp);
for (j=0;j<IDELEMS(s_result);j++)
{
if (s_result->m[j]!=NULL)
{
if (pGetComp(s_result->m[j])<=k)
{
if (!divide)
{
if (rest==NULL)
{
if (isSB)
{
WarnS("first module not a standardbasis\n"
"// ** or second not a proper submodule");
}
else
WerrorS("2nd module does not lie in the first");
}
idDelete(&s_result);
idDelete(&s_rest);
if(syz_ring!=orig_ring)
{
idDelete(&s_mod);
rChangeCurrRing(orig_ring);
rDelete(syz_ring);
}
if (unit!=NULL)
{
idLift_setUnit(idelems_submod,unit);
}
if (rest!=NULL) *rest=idCopy(submod);
s_result=idInit(idelems_submod,idelems_mod);
return s_result;
}
else
{
p = s_rest->m[j] = s_result->m[j];
while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p);
s_result->m[j] = pNext(p);
pNext(p) = NULL;
}
}
p_Shift(&(s_result->m[j]),-k,currRing);
pNeg(s_result->m[j]);
}
}
if ((lsmod==0) && (s_rest!=NULL))
{
for (j=IDELEMS(s_rest);j>0;j--)
{
if (s_rest->m[j-1]!=NULL)
{
p_Shift(&(s_rest->m[j-1]),-1,currRing);
}
}
}
if(syz_ring!=orig_ring)
{
idDelete(&s_mod);
rChangeCurrRing(orig_ring);
s_result = idrMoveR_NoSort(s_result, syz_ring, orig_ring);
s_rest = idrMoveR_NoSort(s_rest, syz_ring, orig_ring);
rDelete(syz_ring);
}
if (rest!=NULL)
{
s_rest->rank=mod->rank;
*rest = s_rest;
}
else
idDelete(&s_rest);
if (unit!=NULL)
{
*unit=mpNew(idelems_submod,idelems_submod);
int i;
for(i=0;i<IDELEMS(s_result);i++)
{
poly p=s_result->m[i];
poly q=NULL;
while(p!=NULL)
{
if(pGetComp(p)<=comps_to_add)
{
pSetComp(p,0);
if (q!=NULL)
{
pNext(q)=pNext(p);
}
else
{
pIter(s_result->m[i]);
}
pNext(p)=NULL;
MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p);
if(q!=NULL) p=pNext(q);
else p=s_result->m[i];
}
else
{
q=p;
pIter(p);
}
}
p_Shift(&s_result->m[i],-comps_to_add,currRing);
}
}
s_result->rank=idelems_mod;
return s_result;
}
/*2
*computes division of P by Q with remainder up to (w-weighted) degree n
*P, Q, and w are not changed
*/
void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,int *w)
{
long N=0;
int i;
for(i=IDELEMS(Q)-1;i>=0;i--)
if(w==NULL)
N=si_max(N,p_Deg(Q->m[i],currRing));
else
N=si_max(N,p_DegW(Q->m[i],w,currRing));
N+=n;
T=mpNew(IDELEMS(Q),IDELEMS(P));
R=idInit(IDELEMS(P),P->rank);
for(i=IDELEMS(P)-1;i>=0;i--)
{
poly p;
if(w==NULL)
p=ppJet(P->m[i],N);
else
p=ppJetW(P->m[i],N,w);
int j=IDELEMS(Q)-1;
while(p!=NULL)
{
if(pDivisibleBy(Q->m[j],p))
{
poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing);
if(w==NULL)
p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N);
else
p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w);
pNormalize(p);
if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
p_Delete(&p0,currRing);
else
MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0);
j=IDELEMS(Q)-1;
}
else
{
if(j==0)
{
poly p0=p;
pIter(p);
pNext(p0)=NULL;
if(((w==NULL)&&(p_Deg(p0,currRing)>n))
||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
p_Delete(&p0,currRing);
else
R->m[i]=pAdd(R->m[i],p0);
j=IDELEMS(Q)-1;
}
else
j--;
}
}
}
}
/*2
*computes the quotient of h1,h2 : internal routine for idQuot
*BEWARE: the returned ideals may contain incorrectly ordered polys !
*
*/
static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
{
idTest(h1);
idTest(h2);
ideal temph1;
poly p,q = NULL;
int i,l,ll,k,kkk,kmax;
int j = 0;
int k1 = id_RankFreeModule(h1,currRing);
int k2 = id_RankFreeModule(h2,currRing);
tHomog hom=isNotHomog;
k=si_max(k1,k2);
if (k==0)
k = 1;
if ((k2==0) && (k>1)) *addOnlyOne = FALSE;
intvec * weights;
hom = (tHomog)idHomModule(h1,currRing->qideal,&weights);
if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/)
temph1 = kStd2(h1,currRing->qideal,hom,&weights,(bigintmat*)NULL);
else
temph1 = idCopy(h1);
if (weights!=NULL) delete weights;
if (currRing->qideal!=NULL)
{
int kk=si_max(k1,k2);
if (kk==0)
{
ideal tmp=id_SimpleAdd(temph1,currRing->qideal,currRing);
id_Delete(&temph1,currRing);
temph1=tmp;
}
else
{
for(int i=1;i<=kk;i++)
{
ideal q=id_Copy(currRing->qideal,currRing);
id_Shift(q,i,currRing); q->rank=i;
ideal tmp=id_SimpleAdd(temph1,q,currRing);
id_Delete(&q,currRing);
id_Delete(&temph1,currRing);
temph1=tmp;
}
}
}
idTest(temph1);
/*--- making a single vector from h2 ---------------------*/
for (i=0; i<IDELEMS(h2); i++)
{
if (h2->m[i] != NULL)
{
p = pCopy(h2->m[i]);
if (k2 == 0)
p_Shift(&p,j*k+1,currRing);
else
p_Shift(&p,j*k,currRing);
q = pAdd(q,p);
j++;
}
}
*kkmax = kmax = j*k+1;
/*--- adding a monomial for the result (syzygy) ----------*/
p = q;
while (pNext(p)!=NULL) pIter(p);
pNext(p) = pOne();
pIter(p);
pSetComp(p,kmax);
pSetmComp(p);
/*--- constructing the big matrix ------------------------*/
ideal h4 = idInit(k,kmax+k-1);
h4->m[0] = q;
if (k2 == 0)
{
for (i=1; i<k; i++)
{
if (h4->m[i-1]!=NULL)
{
p = p_Copy_noCheck(h4->m[i-1], currRing); /*h4->m[i-1]!=NULL*/
p_Shift(&p,1,currRing);
h4->m[i] = p;
}
else break;
}
}
idSkipZeroes(h4);
kkk = IDELEMS(h4);
i = IDELEMS(temph1);
for (l=0; l<i; l++)
{
if(temph1->m[l]!=NULL)
{
for (ll=0; ll<j; ll++)
{
p = pCopy(temph1->m[l]);
if (k1 == 0)
p_Shift(&p,ll*k+1,currRing);
else
p_Shift(&p,ll*k,currRing);
if (kkk >= IDELEMS(h4))
{
pEnlargeSet(&(h4->m),IDELEMS(h4),16);
IDELEMS(h4) += 16;
}
h4->m[kkk] = p;
kkk++;
}
}
}
/*--- if h2 goes in as single vector - the h1-part is just SB ---*/
if (*addOnlyOne)
{
idSkipZeroes(h4);
p = h4->m[0];
for (i=0;i<IDELEMS(h4)-1;i++)
{
h4->m[i] = h4->m[i+1];
}
h4->m[IDELEMS(h4)-1] = p;
}
idDelete(&temph1);
//idTest(h4);//see remark at the beginning
return h4;
}
/*2
*computes the quotient of h1,h2
*/
ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
{
// first check for special case h1:(0)
if (idIs0(h2))
{
ideal res;
if (resultIsIdeal)
{
res = idInit(1,1);
res->m[0] = pOne();
}
else
res = idFreeModule(h1->rank);
return res;
}
int i, kmax;
BOOLEAN addOnlyOne=TRUE;
tHomog hom=isNotHomog;
intvec * weights1;
ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax);
hom = (tHomog)idHomModule(s_h4,currRing->qideal,&weights1);
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
rSetSyzComp(kmax-1,syz_ring);
rChangeCurrRing(syz_ring);
if (orig_ring!=syz_ring)
// s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring);
s_h4 = idrMoveR(s_h4,orig_ring, syz_ring);
idTest(s_h4);
#if 0
matrix m=idModule2Matrix(idCopy(s_h4));
PrintS("start:\n");
ipPrint_MA0(m,"Q");
idDelete((ideal *)&m);
PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn();
#endif
ideal s_h3;
BITSET old_test1;
SI_SAVE_OPT1(old_test1);
if (TEST_OPT_RETURN_SB) si_opt_1 |= Sy_bit(OPT_REDTAIL_SYZ);
if (addOnlyOne)
{
if(!rField_is_Ring(currRing)) si_opt_1 |= Sy_bit(OPT_SB_1);
s_h3 = kStd2(s_h4,currRing->qideal,hom,&weights1,(bigintmat*)NULL,0/*kmax-1*/,IDELEMS(s_h4)-1);
}
else
{
//s_h3 = kStd2(s_h4,currRing->qideal,hom,&weights1,(bigintmat*)NULL,kmax-1);
// qideal added in idInitializeQuotient
s_h3 = kStd2(s_h4,NULL,hom,&weights1,(bigintmat*)NULL,kmax-1);
}
SI_RESTORE_OPT1(old_test1);
#if 0
// only together with the above debug stuff
idSkipZeroes(s_h3);
m=idModule2Matrix(idCopy(s_h3));
Print("result, kmax=%d:\n",kmax);
ipPrint_MA0(m,"S");
idDelete((ideal *)&m);
#endif
idTest(s_h3);
if (weights1!=NULL) delete weights1;
idDelete(&s_h4);
for (i=0;i<IDELEMS(s_h3);i++)
{
if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax))
{
if (resultIsIdeal)
p_Shift(&s_h3->m[i],-kmax,currRing);
else
p_Shift(&s_h3->m[i],-kmax+1,currRing);
}
else
p_Delete(&s_h3->m[i],currRing);
}
if (resultIsIdeal)
s_h3->rank = 1;
else
s_h3->rank = h1->rank;
if(syz_ring!=orig_ring)
{
rChangeCurrRing(orig_ring);
s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
rDelete(syz_ring);
}
idSkipZeroes(s_h3);
idTest(s_h3);
return s_h3;
}
/*2
* eliminate delVar (product of vars) in h1
*/
ideal idElimination2 (ideal h1,poly delVar,bigintmat *hilb, GbVariant alg)
{
int i,j=0,k,l;
ideal h,hh, h3;
rRingOrder_t *ord;
int *block0,*block1;
int ordersize=2;
int **wv;
tHomog hom;
intvec * w;
ring tmpR;
ring origR = currRing;
if (delVar==NULL)
{
return idCopy(h1);
}
if ((currRing->qideal!=NULL) && rIsPluralRing(origR))
{
WerrorS("cannot eliminate in a qring");
return NULL;
}
if (idIs0(h1)) return idInit(1,h1->rank);
#ifdef HAVE_PLURAL
if (rIsPluralRing(origR))
/* in the NC case, we have to check the admissibility of */
/* the subalgebra to be intersected with */
{
if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */
{
if (nc_CheckSubalgebra(delVar,origR))
{
WerrorS("no elimination is possible: subalgebra is not admissible");
return NULL;
}
}
}
#endif
hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL
h3=idInit(16,h1->rank);
ordersize=rBlocks(origR)+1;
#if 0
if (rIsPluralRing(origR)) // we have too keep the ordering: it may be needed
// for G-algebra
{
for (k=0;k<ordersize-1; k++)
{
block0[k+1] = origR->block0[k];
block1[k+1] = origR->block1[k];
ord[k+1] = origR->order[k];
if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
}
}
else
{
block0[1] = 1;
block1[1] = (currRing->N);
if (origR->OrdSgn==1) ord[1] = ringorder_wp;
else ord[1] = ringorder_ws;
wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int));
double wNsqr = (double)2.0 / (double)(currRing->N);
wFunctional = wFunctionalBuch;
int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int));
int sl=IDELEMS(h1) - 1;
wCall(h1->m, sl, x, wNsqr);
for (sl = (currRing->N); sl!=0; sl--)
wv[1][sl-1] = x[sl + (currRing->N) + 1];
omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int));
ord[2]=ringorder_C;
ord[3]=0;
}
#else
#endif
if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR)))
{
#if 1
// we change to an ordering:
// aa(1,1,1,...,0,0,0),wp(...),C
// this seems to be better than version 2 below,
// according to Tst/../elimiate_[3568].tat (- 17 %)
ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t));
block0=(int*)omAlloc0(4*sizeof(int));
block1=(int*)omAlloc0(4*sizeof(int));
wv=(int**) omAlloc0(4*sizeof(int**));
block0[0] = block0[1] = 1;
block1[0] = block1[1] = rVar(origR);
wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
// use this special ordering: like ringorder_a, except that pFDeg, pWeights
// ignore it
ord[0] = ringorder_aa;
for (j=0;j<rVar(origR);j++)
if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
BOOLEAN wp=FALSE;
for (j=0;j<rVar(origR);j++)
if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; }
if (wp)
{
wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
for (j=0;j<rVar(origR);j++)
wv[1][j]=p_Weight(j+1,origR);
ord[1] = ringorder_wp;
}
else
ord[1] = ringorder_dp;
#else
// we change to an ordering:
// a(w1,...wn),wp(1,...0.....),C
ord=(int*)omAlloc0(4*sizeof(int));
block0=(int*)omAlloc0(4*sizeof(int));
block1=(int*)omAlloc0(4*sizeof(int));
wv=(int**) omAlloc0(4*sizeof(int**));
block0[0] = block0[1] = 1;
block1[0] = block1[1] = rVar(origR);
wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
ord[0] = ringorder_a;
for (j=0;j<rVar(origR);j++)
wv[0][j]=pWeight(j+1,origR);
ord[1] = ringorder_wp;
for (j=0;j<rVar(origR);j++)
if (pGetExp(delVar,j+1)!=0) wv[1][j]=1;
#endif
ord[2] = ringorder_C;
ord[3] = (rRingOrder_t)0;
}
else
{
// we change to an ordering:
// aa(....),orig_ordering
ord=(rRingOrder_t*)omAlloc0(ordersize*sizeof(rRingOrder_t));
block0=(int*)omAlloc0(ordersize*sizeof(int));
block1=(int*)omAlloc0(ordersize*sizeof(int));
wv=(int**) omAlloc0(ordersize*sizeof(int**));
for (k=0;k<ordersize-1; k++)
{
block0[k+1] = origR->block0[k];
block1[k+1] = origR->block1[k];
ord[k+1] = origR->order[k];
if (origR->wvhdl[k]!=NULL)
#ifdef HAVE_OMALLOC
wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
#else
{
int l=(origR->block1[k]-origR->block0[k]+1)*sizeof(int);
if (origR->order[k]==ringorder_a64) l*=2;
wv[k+1]=(int*)omalloc(l);
memcpy(wv[k+1],origR->wvhdl[k],l);
}
#endif
}
block0[0] = 1;
block1[0] = rVar(origR);
wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
for (j=0;j<rVar(origR);j++)
if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
// use this special ordering: like ringorder_a, except that pFDeg, pWeights
// ignore it
ord[0] = ringorder_aa;
}
// fill in tmp ring to get back the data later on
tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL
//rUnComplete(tmpR);
tmpR->p_Procs=NULL;
tmpR->order = ord;
tmpR->block0 = block0;
tmpR->block1 = block1;
tmpR->wvhdl = wv;
rComplete(tmpR, 1);
#ifdef HAVE_PLURAL
/* update nc structure on tmpR */
if (rIsPluralRing(origR))
{
if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal!
{
WerrorS("no elimination is possible: ordering condition is violated");
// cleanup
rDelete(tmpR);
if (w!=NULL)
delete w;
return NULL;
}
}
#endif
// change into the new ring
//pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv);
rChangeCurrRing(tmpR);
//h = idInit(IDELEMS(h1),h1->rank);
// fetch data from the old ring
//for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR);
h=idrCopyR(h1,origR,currRing);
if (origR->qideal!=NULL)
{
WarnS("eliminate in q-ring: experimental");
ideal q=idrCopyR(origR->qideal,origR,currRing);
ideal s=idSimpleAdd(h,q);
idDelete(&h);
idDelete(&q);
h=s;
}
// compute GB
if ((alg!=GbDefault)
&& (alg!=GbGroebner)
&& (alg!=GbModstd)
&& (alg!=GbSlimgb)
&& (alg!=GbSba)
&& (alg!=GbStd))
{
WarnS("wrong algorithm for GB");
alg=GbDefault;
}
hh=idGroebner(h,0,alg,hilb);
// go back to the original ring
rChangeCurrRing(origR);
i = IDELEMS(hh)-1;
while ((i >= 0) && (hh->m[i] == NULL)) i--;
j = -1;
// fetch data from temp ring
for (k=0; k<=i; k++)
{
l=(currRing->N);
while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--;
if (l==0)
{
j++;
if (j >= IDELEMS(h3))
{
pEnlargeSet(&(h3->m),IDELEMS(h3),16);
IDELEMS(h3) += 16;
}
h3->m[j] = prMoveR( hh->m[k], tmpR,origR);
hh->m[k] = NULL;
}
}
id_Delete(&hh, tmpR);
idSkipZeroes(h3);
rDelete(tmpR);
if (w!=NULL)
delete w;
return h3;
}
ideal idElimination(ideal h1,poly delVar,intvec *hilb, GbVariant alg)
{
bigintmat *hh=iv2biv(hilb,coeffs_BIGINT);
ideal res=idElimination2(h1,delVar,hh,alg);
if (hh!=NULL) delete hh;
return res;
}
#ifdef WITH_OLD_MINOR
/*2
* compute the which-th ar-minor of the matrix a
*/
poly idMinor(matrix a, int ar, unsigned long which, ideal R)
{
int i,j/*,k,size*/;
unsigned long curr;
int *rowchoise,*colchoise;
BOOLEAN rowch,colch;
// ideal result;
matrix tmp;
poly p,q;
rowchoise=(int *)omAlloc(ar*sizeof(int));
colchoise=(int *)omAlloc(ar*sizeof(int));
tmp=mpNew(ar,ar);
curr = 0; /* index of current minor */
idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
while (!rowch)
{
idInitChoise(ar,1,a->cols(),&colch,colchoise);
while (!colch)
{
if (curr == which)
{
for (i=1; i<=ar; i++)
{
for (j=1; j<=ar; j++)
{
MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
}
}
p = mp_DetBareiss(tmp,currRing);
if (p!=NULL)
{
if (R!=NULL)
{
q = p;
p = kNF(R,currRing->qideal,q);
p_Delete(&q,currRing);
}
}
/*delete the matrix tmp*/
for (i=1; i<=ar; i++)
{
for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
}
idDelete((ideal*)&tmp);
omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
return (p);
}
curr++;
idGetNextChoise(ar,a->cols(),&colch,colchoise);
}
idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
}
return (poly) 1;
}
/*2
* compute all ar-minors of the matrix a
*/
ideal idMinors(matrix a, int ar, ideal R)
{
int i,j,/*k,*/size;
int *rowchoise,*colchoise;
BOOLEAN rowch,colch;
ideal result;
matrix tmp;
poly p,q;
i = binom(a->rows(),ar);
j = binom(a->cols(),ar);
size=i*j;
rowchoise=(int *)omAlloc(ar*sizeof(int));
colchoise=(int *)omAlloc(ar*sizeof(int));
result=idInit(size,1);
tmp=mpNew(ar,ar);
// k = 0; /* the index in result*/
idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
while (!rowch)
{
idInitChoise(ar,1,a->cols(),&colch,colchoise);
while (!colch)
{
for (i=1; i<=ar; i++)
{
for (j=1; j<=ar; j++)
{
MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
}
}
p = mp_DetBareiss(tmp,currRing);
if (p!=NULL)
{
if (R!=NULL)
{
q = p;
p = kNF(R,currRing->qideal,q);
p_Delete(&q,currRing);
}
}
if (k>=size)
{
pEnlargeSet(&result->m,size,32);
size += 32;
}
result->m[k] = p;
k++;
idGetNextChoise(ar,a->cols(),&colch,colchoise);
}
idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
}
/*delete the matrix tmp*/
for (i=1; i<=ar; i++)
{
for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
}
idDelete((ideal*)&tmp);
if (k==0)
{
k=1;
result->m[0]=NULL;
}
omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
pEnlargeSet(&result->m,size,k-size);
IDELEMS(result) = k;
return (result);
}
#else
/// compute all ar-minors of the matrix a
/// the caller of mpRecMin
/// the elements of the result are not in R (if R!=NULL)
ideal idMinors(matrix a, int ar, ideal R)
{
const ring origR=currRing;
id_Test((ideal)a, origR);
const int r = a->nrows;
const int c = a->ncols;
if((ar<=0) || (ar>r) || (ar>c))
{
Werror("%d-th minor, matrix is %dx%d",ar,r,c);
return NULL;
}
ideal h = id_Matrix2Module(mp_Copy(a,origR),origR);
long bound = sm_ExpBound(h,c,r,ar,origR);
id_Delete(&h, origR);
ring tmpR = sm_RingChange(origR,bound);
matrix b = mpNew(r,c);
for (int i=r*c-1;i>=0;i--)
if (a->m[i] != NULL)
b->m[i] = prCopyR(a->m[i],origR,tmpR);
id_Test( (ideal)b, tmpR);
if (R!=NULL)
{
R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak?
//if (ar>1) // otherwise done in mpMinorToResult
//{
// matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b);
// bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols;
// idDelete((ideal*)&b); b=bb;
//}
id_Test( R, tmpR);
}
int size=binom(r,ar)*binom(c,ar);
ideal result = idInit(size,1);
int elems = 0;
if(ar>1)
mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR);
else
mp_MinorToResult(result,elems,b,r,c,R,tmpR);
id_Test( (ideal)b, tmpR);
id_Delete((ideal *)&b, tmpR);
if (R!=NULL) id_Delete(&R,tmpR);
rChangeCurrRing(origR);
result = idrMoveR(result,tmpR,origR);
sm_KillModifiedRing(tmpR);
idTest(result);
return result;
}
#endif
/*2
*returns TRUE if id1 is a submodule of id2
*/
BOOLEAN idIsSubModule(ideal id1,ideal id2)
{
int i;
poly p;
if (idIs0(id1)) return TRUE;
for (i=0;i<IDELEMS(id1);i++)
{
if (id1->m[i] != NULL)
{
p = kNF(id2,currRing->qideal,id1->m[i]);
if (p != NULL)
{
p_Delete(&p,currRing);
return FALSE;
}
}
}
return TRUE;
}
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
{
if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
if (idIs0(m)) return TRUE;
int cmax=-1;
int i;
poly p=NULL;
int length=IDELEMS(m);
polyset P=m->m;
for (i=length-1;i>=0;i--)
{
p=P[i];
if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
}
if (w != NULL)
if (w->length()+1 < cmax)
{
// Print("length: %d - %d \n", w->length(),cmax);
return FALSE;
}
if(w!=NULL)
p_SetModDeg(w, currRing);
for (i=length-1;i>=0;i--)
{
p=P[i];
if (p!=NULL)
{
int d=currRing->pFDeg(p,currRing);
loop
{
pIter(p);
if (p==NULL) break;
if (d!=currRing->pFDeg(p,currRing))
{
//pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
if(w!=NULL)
p_SetModDeg(NULL, currRing);
return FALSE;
}
}
}
}
if(w!=NULL)
p_SetModDeg(NULL, currRing);
return TRUE;
}
ideal idSeries(int n,ideal M,matrix U,intvec *w)
{
for(int i=IDELEMS(M)-1;i>=0;i--)
{
if(U==NULL)
M->m[i]=pSeries(n,M->m[i],NULL,w);
else
{
M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w);
MATELEM(U,i+1,i+1)=NULL;
}
}
if(U!=NULL)
idDelete((ideal*)&U);
return M;
}
matrix idDiff(matrix i, int k)
{
int e=MATCOLS(i)*MATROWS(i);
matrix r=mpNew(MATROWS(i),MATCOLS(i));
r->rank=i->rank;
int j;
for(j=0; j<e; j++)
{
r->m[j]=pDiff(i->m[j],k);
}
return r;
}
matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply)
{
matrix r=mpNew(IDELEMS(I),IDELEMS(J));
int i,j;
for(i=0; i<IDELEMS(I); i++)
{
for(j=0; j<IDELEMS(J); j++)
{
MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply);
}
}
return r;
}
/*3
*handles for some ideal operations the ring/syzcomp management
*returns all syzygies (componentwise-)shifted by -syzcomp
*or -syzcomp-1 (in case of ideals as input)
static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE)
{
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring);
rSetSyzComp(length, syz_ring);
ideal s_temp;
if (orig_ring!=syz_ring)
s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring);
else
s_temp=arg;
ideal s_temp1 = kStd2(s_temp,currRing->qideal,testHomog,&w,NULL,length);
if (w!=NULL) delete w;
if (syz_ring!=orig_ring)
{
idDelete(&s_temp);
rChangeCurrRing(orig_ring);
}
idDelete(&temp);
ideal temp1=idRingCopy(s_temp1,syz_ring);
if (syz_ring!=orig_ring)
{
rChangeCurrRing(syz_ring);
idDelete(&s_temp1);
rChangeCurrRing(orig_ring);
rDelete(syz_ring);
}
for (i=0;i<IDELEMS(temp1);i++)
{
if ((temp1->m[i]!=NULL)
&& (pGetComp(temp1->m[i])<=length))
{
pDelete(&(temp1->m[i]));
}
else
{
p_Shift(&(temp1->m[i]),-length,currRing);
}
}
temp1->rank = rk;
idSkipZeroes(temp1);
return temp1;
}
*/
#ifdef HAVE_SHIFTBBA
ideal idModuloLP (ideal h2,ideal h1, tHomog, intvec ** w, matrix *T, GbVariant alg)
{
intvec *wtmp=NULL;
if (T!=NULL) idDelete((ideal*)T);
int i,k,rk,flength=0,slength,length;
poly p,q;
if (idIs0(h2))
return idFreeModule(si_max(1,h2->ncols));
if (!idIs0(h1))
flength = id_RankFreeModule(h1,currRing);
slength = id_RankFreeModule(h2,currRing);
length = si_max(flength,slength);
if (length==0)
{
length = 1;
}
ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2));
if ((w!=NULL)&&((*w)!=NULL))
{
//Print("input weights:");(*w)->show(1);PrintLn();
int d;
int k;
wtmp=new intvec(length+IDELEMS(h2));
for (i=0;i<length;i++)
((*wtmp)[i])=(**w)[i];
for (i=0;i<IDELEMS(h2);i++)
{
poly p=h2->m[i];
if (p!=NULL)
{
d = p_Deg(p,currRing);
k= pGetComp(p);
if (slength>0) k--;
d +=((**w)[k]);
((*wtmp)[i+length]) = d;
}
}
//Print("weights:");wtmp->show(1);PrintLn();
}
for (i=0;i<IDELEMS(h2);i++)
{
temp->m[i] = pCopy(h2->m[i]);
q = pOne();
// non multiplicative variable
pSetExp(q, currRing->isLPring - currRing->LPncGenCount + i + 1, 1);
p_Setm(q, currRing);
pSetComp(q,i+1+length);
pSetmComp(q);
if(temp->m[i]!=NULL)
{
if (slength==0) p_Shift(&(temp->m[i]),1,currRing);
p = temp->m[i];
temp->m[i] = pAdd(p, q);
}
else
temp->m[i]=q;
}
rk = k = IDELEMS(h2);
if (!idIs0(h1))
{
pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1));
IDELEMS(temp) += IDELEMS(h1);
for (i=0;i<IDELEMS(h1);i++)
{
if (h1->m[i]!=NULL)
{
temp->m[k] = pCopy(h1->m[i]);
if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
k++;
}
}
}
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE);
rSetSyzComp(length,syz_ring);
rChangeCurrRing(syz_ring);
// we can use OPT_RETURN_SB only, if syz_ring==orig_ring,
// therefore we disable OPT_RETURN_SB for modulo:
// (see tr. #701)
//if (TEST_OPT_RETURN_SB)
// rSetSyzComp(IDELEMS(h2)+length, syz_ring);
//else
// rSetSyzComp(length, syz_ring);
ideal s_temp;
if (syz_ring != orig_ring)
{
s_temp = idrMoveR_NoSort(temp, orig_ring, syz_ring);
}
else
{
s_temp = temp;
}
idTest(s_temp);
BITSET save_opt,save_opt2;
SI_SAVE_OPT(save_opt,save_opt2);
if (T==NULL) si_opt_1 |= Sy_bit(OPT_REDTAIL_SYZ);
si_opt_1 |= Sy_bit(OPT_REDTAIL);
ideal s_temp1 = idGroebner(s_temp,length,alg);
SI_RESTORE_OPT(save_opt,save_opt2);
//if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
{
delete *w;
*w=new intvec(IDELEMS(h2));
for (i=0;i<IDELEMS(h2);i++)
((**w)[i])=(*wtmp)[i+length];
}
if (wtmp!=NULL) delete wtmp;
if (T==NULL)
{
for (i=0;i<IDELEMS(s_temp1);i++)
{
if (s_temp1->m[i]!=NULL)
{
if (((int)pGetComp(s_temp1->m[i]))<=length)
{
p_Delete(&(s_temp1->m[i]),currRing);
}
else
{
p_Shift(&(s_temp1->m[i]),-length,currRing);
}
}
}
}
else
{
*T=mpNew(IDELEMS(s_temp1),IDELEMS(h2));
for (i=0;i<IDELEMS(s_temp1);i++)
{
if (s_temp1->m[i]!=NULL)
{
if (((int)pGetComp(s_temp1->m[i]))<=length)
{
do
{
p_LmDelete(&(s_temp1->m[i]),currRing);
} while((int)pGetComp(s_temp1->m[i])<=length);
poly q = prMoveR( s_temp1->m[i], syz_ring,orig_ring);
s_temp1->m[i] = NULL;
if (q!=NULL)
{
q=pReverse(q);
do
{
poly p = q;
long t=pGetComp(p);
pIter(q);
pNext(p) = NULL;
pSetComp(p,0);
pSetmComp(p);
pTest(p);
MATELEM(*T,(int)t-length,i) = pAdd(MATELEM(*T,(int)t-length,i),p);
} while (q != NULL);
}
}
else
{
p_Shift(&(s_temp1->m[i]),-length,currRing);
}
}
}
}
s_temp1->rank = rk;
idSkipZeroes(s_temp1);
if (syz_ring!=orig_ring)
{
rChangeCurrRing(orig_ring);
s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring, orig_ring);
rDelete(syz_ring);
// Hmm ... here seems to be a memory leak
// However, simply deleting it causes memory trouble
// idDelete(&s_temp);
}
idTest(s_temp1);
return s_temp1;
}
#endif
/*2
* represents (h1+h2)/h2=h1/(h1 intersect h2)
*/
//ideal idModulo (ideal h2,ideal h1)
ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w, matrix *T, GbVariant alg)
{
#ifdef HAVE_SHIFTBBA
if (rIsLPRing(currRing))
return idModuloLP(h2,h1,hom,w,T,alg);
#endif
intvec *wtmp=NULL;
if (T!=NULL) idDelete((ideal*)T);
int i,flength=0,slength,length;
if (idIs0(h2))
return idFreeModule(si_max(1,h2->ncols));
if (!idIs0(h1))
flength = id_RankFreeModule(h1,currRing);
slength = id_RankFreeModule(h2,currRing);
length = si_max(flength,slength);
BOOLEAN inputIsIdeal=FALSE;
if (length==0)
{
length = 1;
inputIsIdeal=TRUE;
}
if ((w!=NULL)&&((*w)!=NULL))
{
//Print("input weights:");(*w)->show(1);PrintLn();
int d;
int k;
wtmp=new intvec(length+IDELEMS(h2));
for (i=0;i<length;i++)
((*wtmp)[i])=(**w)[i];
for (i=0;i<IDELEMS(h2);i++)
{
poly p=h2->m[i];
if (p!=NULL)
{
d = p_Deg(p,currRing);
k= pGetComp(p);
if (slength>0) k--;
d +=((**w)[k]);
((*wtmp)[i+length]) = d;
}
}
//Print("weights:");wtmp->show(1);PrintLn();
}
ideal s_temp1;
ring orig_ring=currRing;
ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE);
rSetSyzComp(length,syz_ring);
{
rChangeCurrRing(syz_ring);
ideal s1,s2;
if (syz_ring != orig_ring)
{
s1 = idrCopyR_NoSort(h1, orig_ring, syz_ring);
s2 = idrCopyR_NoSort(h2, orig_ring, syz_ring);
}
else
{
s1=idCopy(h1);
s2=idCopy(h2);
}
BITSET save_opt,save_opt2;
SI_SAVE_OPT(save_opt,save_opt2);
if (T==NULL) si_opt_1 |= Sy_bit(OPT_REDTAIL);
si_opt_1 |= Sy_bit(OPT_REDTAIL_SYZ);
s_temp1 = idPrepare(s2,s1,testHomog,length,w,alg);
SI_RESTORE_OPT(save_opt,save_opt2);
}
//if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
{
delete *w;
*w=new intvec(IDELEMS(h2));
for (i=0;i<IDELEMS(h2);i++)
((**w)[i])=(*wtmp)[i+length];
}
if (wtmp!=NULL) delete wtmp;
ideal result=idInit(IDELEMS(s_temp1),IDELEMS(h2));
s_temp1=idExtractG_T_S(s_temp1,T,&result,length,IDELEMS(h2),inputIsIdeal,orig_ring,syz_ring);
idDelete(&s_temp1);
if (syz_ring!=orig_ring)
{
rDelete(syz_ring);
}
idTest(h2);
idTest(h1);
idTest(result);
if (T!=NULL) idTest((ideal)*T);
return result;
}
/*
*computes module-weights for liftings of homogeneous modules
*/
#if 0
static intvec * idMWLift(ideal mod,intvec * weights)
{
if (idIs0(mod)) return new intvec(2);
int i=IDELEMS(mod);
while ((i>0) && (mod->m[i-1]==NULL)) i--;
intvec *result = new intvec(i+1);
while (i>0)
{
(*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])];
}
return result;
}
#endif
/*2
*sorts the kbase for idCoef* in a special way (lexicographically
*with x_max,...,x_1)
*/
ideal idCreateSpecialKbase(ideal kBase,intvec ** convert)
{
int i;
ideal result;
if (idIs0(kBase)) return NULL;
result = idInit(IDELEMS(kBase),kBase->rank);
*convert = idSort(kBase,FALSE);
for (i=0;i<(*convert)->length();i++)
{
result->m[i] = pCopy(kBase->m[(**convert)[i]-1]);
}
return result;
}
/*2
*returns the index of a given monom in the list of the special kbase
*/
int idIndexOfKBase(poly monom, ideal kbase)
{
int j=IDELEMS(kbase);
while ((j>0) && (kbase->m[j-1]==NULL)) j--;
if (j==0) return -1;
int i=(currRing->N);
while (i>0)
{
loop
{
if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1;
if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break;
j--;
if (j==0) return -1;
}
if (i==1)
{
while(j>0)
{
if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1;
if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1;
j--;
}
}
i--;
}
return -1;
}
/*2
*decomposes the monom in a part of coefficients described by the
*complement of how and a monom in variables occurring in how, the
*index of which in kbase is returned as integer pos (-1 if it don't
*exists)
*/
poly idDecompose(poly monom, poly how, ideal kbase, int * pos)
{
int i;
poly coeff=pOne(), base=pOne();
for (i=1;i<=(currRing->N);i++)
{
if (pGetExp(how,i)>0)
{
pSetExp(base,i,pGetExp(monom,i));
}
else
{
pSetExp(coeff,i,pGetExp(monom,i));
}
}
pSetComp(base,pGetComp(monom));
pSetm(base);
pSetCoeff(coeff,nCopy(pGetCoeff(monom)));
pSetm(coeff);
*pos = idIndexOfKBase(base,kbase);
if (*pos<0)
p_Delete(&coeff,currRing);
p_Delete(&base,currRing);
return coeff;
}
/*2
*returns a matrix A of coefficients with kbase*A=arg
*if all monomials in variables of how occur in kbase
*the other are deleted
*/
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
{
matrix result;
ideal tempKbase;
poly p,q;
intvec * convert;
int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos;
#if 0
while ((i>0) && (kbase->m[i-1]==NULL)) i--;
if (idIs0(arg))
return mpNew(i,1);
while ((j>0) && (arg->m[j-1]==NULL)) j--;
result = mpNew(i,j);
#else
result = mpNew(i, j);
while ((j>0) && (arg->m[j-1]==NULL)) j--;
#endif
tempKbase = idCreateSpecialKbase(kbase,&convert);
for (k=0;k<j;k++)
{
p = arg->m[k];
while (p!=NULL)
{
q = idDecompose(p,how,tempKbase,&pos);
if (pos>=0)
{
MATELEM(result,(*convert)[pos],k+1) =
pAdd(MATELEM(result,(*convert)[pos],k+1),q);
}
else
p_Delete(&q,currRing);
pIter(p);
}
}
idDelete(&tempKbase);
return result;
}
static void idDeleteComps(ideal arg,int* red_comp,int del)
// red_comp is an array [0..args->rank]
{
int i,j;
poly p;
for (i=IDELEMS(arg)-1;i>=0;i--)
{
p = arg->m[i];
while (p!=NULL)
{
j = pGetComp(p);
if (red_comp[j]!=j)
{
pSetComp(p,red_comp[j]);
pSetmComp(p);
}
pIter(p);
}
}
(arg->rank) -= del;
}
/*3
* searches for the next unit in the components of the module arg and
* returns the first one;
*/
static int id_ReadOutPivot(ideal arg,int* comp, const ring r)
{
int i=0,j, generator=-1;
int rk_arg=arg->rank; //idRankFreeModule(arg);
int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int));
poly p;
while ((generator<0) && (i<IDELEMS(arg)))
{
memset(componentIsUsed,0,(rk_arg+1)*sizeof(int));
p = arg->m[i];
if (rField_is_Ring(r))
{
while (p!=NULL)
{
j = __p_GetComp(p,r);
if (componentIsUsed[j]==0)
{
if (p_LmIsConstantComp(p,r) &&
n_IsUnit(pGetCoeff(p),r->cf))
{
generator = i;
componentIsUsed[j] = 1;
}
else
{
componentIsUsed[j] = -1;
}
}
else if (componentIsUsed[j]>0)
{
(componentIsUsed[j])++;
}
pIter(p);
}
}
else
{
while (p!=NULL)
{
j = __p_GetComp(p,r);
if (componentIsUsed[j]==0)
{
if (p_LmIsConstantComp(p,r))
{
generator = i;
componentIsUsed[j] = 1;
}
else
{
componentIsUsed[j] = -1;
}
}
else if (componentIsUsed[j]>0)
{
(componentIsUsed[j])++;
}
pIter(p);
}
}
i++;
}
i = 0;
*comp = -1;
for (j=0;j<=rk_arg;j++)
{
if (componentIsUsed[j]>0)
{
if ((*comp==-1) || (componentIsUsed[j]<i))
{
*comp = j;
i= componentIsUsed[j];
}
}
}
omFree(componentIsUsed);
return generator;
}
/*2
* returns the presentation of an isomorphic, minimally
* embedded module (arg represents the quotient!)
*/
static ideal idMinEmbedding1(ideal arg,BOOLEAN inPlace, intvec **w,
int* red_comp, int &del)
{
if (idIs0(arg)) return idInit(1,arg->rank);
int i,next_gen,next_comp;
ideal res=arg;
if (!inPlace) res = idCopy(arg);
res->rank=si_max(res->rank,id_RankFreeModule(res,currRing));
for (i=res->rank;i>=0;i--) red_comp[i]=i;
loop
{
next_gen = id_ReadOutPivot(res, &next_comp, currRing);
if (next_gen<0) break;
del++;
syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res));
for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--;
if ((w !=NULL)&&(*w!=NULL))
{
for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i];
}
}
idSkipZeroes(res);
if ((w !=NULL)&&(*w!=NULL) &&(del>0))
{
int nl=si_max((*w)->length()-del,1);
intvec *wtmp=new intvec(nl);
for(i=0;i<nl;i++) (*wtmp)[i]=(**w)[i];
delete *w;
*w=wtmp;
}
return res;
}
ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w)
{
int *red_comp=(int*)omAlloc((arg->rank+1)*sizeof(int));
int del=0;
ideal res=idMinEmbedding1(arg,inPlace,w,red_comp,del);
idDeleteComps(res,red_comp,del);
omFree(red_comp);
return res;
}
ideal idMinEmbedding_with_map(ideal arg,intvec **w, ideal &trans)
{
int *red_comp=(int*)omAlloc((arg->rank+1)*sizeof(int));
int del=0;
ideal res=idMinEmbedding1(arg,FALSE,w,red_comp,del);
trans=idLift(arg,res,NULL,TRUE,FALSE,FALSE,NULL);
//idDeleteComps(res,red_comp,del);
omFree(red_comp);
return res;
}
ideal idMinEmbedding_with_map_v(ideal arg,intvec **w, ideal &trans, int* g)
{
if (idIs0(arg))
{
trans=idFreeModule(arg->rank);
if (g!=NULL)
{
for(int i=0;i<arg->rank;i++) g[i]=i+1;
}
return arg;
}
int *red_comp=(int*)omAlloc((arg->rank+1)*sizeof(int));
int del=0;
ideal res=idMinEmbedding1(arg,FALSE,w,red_comp,del);
trans=idLift(arg,res,NULL,TRUE,FALSE,FALSE,NULL);
for(int i=1;i<=arg->rank;i++)
{
g[i-1]=red_comp[i];
}
idDeleteComps(res,red_comp,del);
return res;
}
extern void ipPrint_MA0(matrix m, const char *name);
#if 0 // unused
ideal idMinEmbedding_with_map0(ideal arg,intvec **w, ideal &trans)
{
ideal a=idCopy(arg);
// add unit matrix to a
int k=a->rank+1;
const int rk=a->rank;
poly p;
int i;
for(i=0;i<IDELEMS(a);i++,k++)
{
p=pOne();
pSetComp(p,k);pSetmComp(p);
a->m[i]=p_Add_q(a->m[i],p,currRing);
}
// search a unit in orig part of a
// and subtract, start at start
int start=0;
loop
{
PrintS("matrix:\n");
ipPrint_MA0((matrix)a,"a");
i=start;
if (i>=IDELEMS(a)) break;
p=a->m[i];
start=IDELEMS(a);
while((p!=NULL)&&(pGetComp(p)<=rk)&&(p_Totaldegree(p,currRing)>0)) pIter(p);
if ((p!=NULL)&&(pGetComp(p)<=rk)&&(p_Totaldegree(p,currRing)==0))
{ // found const in vector i, comp k
k=pGetComp(p);
// normalize:
number n=nCopy(pGetCoeff(p));
n=nInpNeg(n);
a->m[i]=p_Div_nn(p,n,currRing);
// subtract
BOOLEAN changed=FALSE;
for(int j=IDELEMS(a)-1;j>=0;j--)
{
if (j!=i)
{
poly q=p_Vec2Poly(a->m[j],k,currRing);
if (q!=NULL)
{
start=j; // changed entries start at j
changed=TRUE;
poly s=p_Mult_q(a->m[i],q,currRing);
a->m[j]=p_Add_q(a->m[j],s,currRing);
}
}
}
if(changed) continue;
}
else i++;
}
// a -> result,trans
trans=idInit(IDELEMS(a),IDELEMS(a));
ideal result=idInit(IDELEMS(a),rk);
for(i=0;i<IDELEMS(a);i++)
{
while(a->m[i]!=NULL)
{
poly p=a->m[i];
a->m[i]=p->next;
p->next=NULL;
if(pGetComp(p)<=rk)
{
result->m[i]=p_Add_q(result->m[i],p,currRing);
}
else
{
p_Shift(&p,-rk,currRing);
trans->m[i]=p_Add_q(trans->m[i],p,currRing);
}
}
}
PrintS("prune:\n");
ipPrint_MA0((matrix)result,"R");
PrintS("trans:\n");
ipPrint_MA0((matrix)trans,"T");
idDelete(&a);
return result;
}
#endif
#include "polys/clapsing.h"
#if 0
poly id_GCD(poly f, poly g, const ring r)
{
ring save_r=currRing;
rChangeCurrRing(r);
ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
intvec *w = NULL;
ideal S=idSyzygies(I,testHomog,&w);
if (w!=NULL) delete w;
poly gg=pTakeOutComp(&(S->m[0]),2);
idDelete(&S);
poly gcd_p=singclap_pdivide(f,gg,r);
p_Delete(&gg,r);
rChangeCurrRing(save_r);
return gcd_p;
}
#else
poly id_GCD(poly f, poly g, const ring r)
{
ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
intvec *w = NULL;
ring save_r = currRing;
rChangeCurrRing(r);
ideal S=idSyzygies(I,testHomog,&w);
rChangeCurrRing(save_r);
if (w!=NULL) delete w;
poly gg=p_TakeOutComp(&(S->m[0]), 2, r);
id_Delete(&S, r);
poly gcd_p=singclap_pdivide(f,gg, r);
p_Delete(&gg, r);
return gcd_p;
}
#endif
#if 0
/*2
* xx,q: arrays of length 0..rl-1
* xx[i]: SB mod q[i]
* assume: char=0
* assume: q[i]!=0
* destroys xx
*/
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R)
{
int cnt=IDELEMS(xx[0])*xx[0]->nrows;
ideal result=idInit(cnt,xx[0]->rank);
result->nrows=xx[0]->nrows; // for lifting matrices
result->ncols=xx[0]->ncols; // for lifting matrices
int i,j;
poly r,h,hh,res_p;
number *x=(number *)omAlloc(rl*sizeof(number));
for(i=cnt-1;i>=0;i--)
{
res_p=NULL;
loop
{
r=NULL;
for(j=rl-1;j>=0;j--)
{
h=xx[j]->m[i];
if ((h!=NULL)
&&((r==NULL)||(p_LmCmp(r,h,R)==-1)))
r=h;
}
if (r==NULL) break;
h=p_Head(r, R);
for(j=rl-1;j>=0;j--)
{
hh=xx[j]->m[i];
if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0))
{
x[j]=p_GetCoeff(hh, R);
hh=p_LmFreeAndNext(hh, R);
xx[j]->m[i]=hh;
}
else
x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes!
}
number n=n_ChineseRemainder(x,q,rl, R->cf);
for(j=rl-1;j>=0;j--)
{
x[j]=NULL; // nlInit(0...) takes no memory
}
if (n_IsZero(n, R->cf)) p_Delete(&h, R);
else
{
p_SetCoeff(h,n, R);
//Print("new mon:");pWrite(h);
res_p=p_Add_q(res_p, h, R);
}
}
result->m[i]=res_p;
}
omFree(x);
for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R);
omFree(xx);
return result;
}
#endif
/* currently unused:
ideal idChineseRemainder(ideal *xx, intvec *iv)
{
int rl=iv->length();
number *q=(number *)omAlloc(rl*sizeof(number));
int i;
for(i=0; i<rl; i++)
{
q[i]=nInit((*iv)[i]);
}
return idChineseRemainder(xx,q,rl);
}
*/
/*
* lift ideal with coeffs over Z (mod N) to Q via Farey
*/
ideal id_Farey(ideal x, number N, const ring r)
{
int cnt=IDELEMS(x)*x->nrows;
ideal result=idInit(cnt,x->rank);
result->nrows=x->nrows; // for lifting matrices
result->ncols=x->ncols; // for lifting matrices
int i;
for(i=cnt-1;i>=0;i--)
{
result->m[i]=p_Farey(x->m[i],N,r);
}
return result;
}
// uses glabl vars via pSetModDeg
/*
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
{
if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
if (idIs0(m)) return TRUE;
int cmax=-1;
int i;
poly p=NULL;
int length=IDELEMS(m);
poly* P=m->m;
for (i=length-1;i>=0;i--)
{
p=P[i];
if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
}
if (w != NULL)
if (w->length()+1 < cmax)
{
// Print("length: %d - %d \n", w->length(),cmax);
return FALSE;
}
if(w!=NULL)
p_SetModDeg(w, currRing);
for (i=length-1;i>=0;i--)
{
p=P[i];
poly q=p;
if (p!=NULL)
{
int d=p_FDeg(p,currRing);
loop
{
pIter(p);
if (p==NULL) break;
if (d!=p_FDeg(p,currRing))
{
//pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
if(w!=NULL)
p_SetModDeg(NULL, currRing);
return FALSE;
}
}
}
}
if(w!=NULL)
p_SetModDeg(NULL, currRing);
return TRUE;
}
*/
/// keeps the first k (>= 1) entries of the given ideal
/// (Note that the kept polynomials may be zero.)
void idKeepFirstK(ideal id, const int k)
{
for (int i = IDELEMS(id)-1; i >= k; i--)
{
if (id->m[i] != NULL) pDelete(&id->m[i]);
}
int kk=k;
if (k==0) kk=1; /* ideals must have at least one element(0)*/
pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id));
IDELEMS(id) = kk;
}
typedef struct
{
poly p;
int index;
} poly_sort;
int pCompare_qsort(const void *a, const void *b)
{
return (p_Compare(((poly_sort *)a)->p, ((poly_sort *)b)->p,currRing));
}
void idSort_qsort(poly_sort *id_sort, int idsize)
{
qsort(id_sort, idsize, sizeof(poly_sort), pCompare_qsort);
}
/*2
* ideal id = (id[i])
* if id[i] = id[j] then id[j] is deleted for j > i
*/
void idDelEquals(ideal id)
{
int idsize = IDELEMS(id);
poly_sort *id_sort = (poly_sort *)omAlloc0(idsize*sizeof(poly_sort));
for (int i = 0; i < idsize; i++)
{
id_sort[i].p = id->m[i];
id_sort[i].index = i;
}
idSort_qsort(id_sort, idsize);
int index, index_i, index_j;
int i = 0;
for (int j = 1; j < idsize; j++)
{
if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p))
{
index_i = id_sort[i].index;
index_j = id_sort[j].index;
if (index_j > index_i)
{
index = index_j;
}
else
{
index = index_i;
i = j;
}
pDelete(&id->m[index]);
}
else
{
i = j;
}
}
omFreeSize((ADDRESS)(id_sort), idsize*sizeof(poly_sort));
}
STATIC_VAR int * id_satstdSaturatingVariables=NULL;
static BOOLEAN id_sat_vars_sp(kStrategy strat)
{
BOOLEAN b = FALSE; // set b to TRUE, if spoly was changed,
// let it remain FALSE otherwise
if (strat->P.t_p==NULL)
{
poly p=strat->P.p;
// iterate over all terms of p and
// compute the minimum mm of all exponent vectors
int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
p_GetExpV(p,mm,currRing);
bool nonTrivialSaturationToBeDone=true;
for (; p!=NULL; pIter(p))
{
nonTrivialSaturationToBeDone=false;
p_GetExpV(p,m0,currRing);
for (int i=rVar(currRing); i>0; i--)
{
if (id_satstdSaturatingVariables[i]!=0)
{
mm[i]=si_min(mm[i],m0[i]);
if (mm[i]>0) nonTrivialSaturationToBeDone=true;
}
else mm[i]=0;
}
// abort if the minimum is zero in each component
if (!nonTrivialSaturationToBeDone) break;
}
if (nonTrivialSaturationToBeDone)
{
// std::cout << "simplifying!" << std::endl;
if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
p=p_Copy(strat->P.p,currRing);
//pWrite(p);
// for (int i=rVar(currRing); i>0; i--)
// if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
//PrintLn();
strat->P.Init(strat->tailRing);
//memset(&strat->P,0,sizeof(strat->P));
//strat->P.tailRing = strat->tailRing; // done by Init
strat->P.p=p;
while(p!=NULL)
{
for (int i=rVar(currRing); i>0; i--)
{
p_SubExp(p,i,mm[i],currRing);
}
p_Setm(p,currRing);
pIter(p);
}
b = TRUE;
}
omFree(mm);
omFree(m0);
}
else
{
poly p=strat->P.t_p;
// iterate over all terms of p and
// compute the minimum mm of all exponent vectors
int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
p_GetExpV(p,mm,strat->tailRing);
bool nonTrivialSaturationToBeDone=true;
for (; p!=NULL; pIter(p))
{
nonTrivialSaturationToBeDone=false;
p_GetExpV(p,m0,strat->tailRing);
for(int i=rVar(currRing); i>0; i--)
{
if(id_satstdSaturatingVariables[i]!=0)
{
mm[i]=si_min(mm[i],m0[i]);
if (mm[i]>0) nonTrivialSaturationToBeDone = true;
}
else mm[i]=0;
}
// abort if the minimum is zero in each component
if (!nonTrivialSaturationToBeDone) break;
}
if (nonTrivialSaturationToBeDone)
{
if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
p=p_Copy(strat->P.t_p,strat->tailRing);
//p_Write(p,strat->tailRing);
// for (int i=rVar(currRing); i>0; i--)
// if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
//PrintLn();
strat->P.Init(strat->tailRing);
//memset(&strat->P,0,sizeof(strat->P));
//strat->P.tailRing = strat->tailRing;// done by Init
strat->P.t_p=p;
while(p!=NULL)
{
for(int i=rVar(currRing); i>0; i--)
{
p_SubExp(p,i,mm[i],strat->tailRing);
}
p_Setm(p,strat->tailRing);
pIter(p);
}
strat->P.GetP();
b = TRUE;
}
omFree(mm);
omFree(m0);
}
return b; // return TRUE if sp was changed, FALSE if not
}
ideal id_Satstd(const ideal I, ideal J, const ring r)
{
ring save=currRing;
if (currRing!=r) rChangeCurrRing(r);
idSkipZeroes(J);
id_satstdSaturatingVariables=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
int k=IDELEMS(J);
if (k>1)
{
for (int i=0; i<k; i++)
{
poly x = J->m[i];
int li = p_Var(x,r);
if (li>0)
id_satstdSaturatingVariables[li]=1;
else
{
if (currRing!=save) rChangeCurrRing(save);
WerrorS("ideal generators must be variables");
return NULL;
}
}
}
else
{
poly x = J->m[0];
if (pNext(x)!=NULL)
{
Werror("generator must be a monomial");
if (currRing!=save) rChangeCurrRing(save);
return NULL;
}
for (int i=1; i<=r->N; i++)
{
int li = p_GetExp(x,i,r);
if (li==1)
id_satstdSaturatingVariables[i]=1;
else if (li>1)
{
if (currRing!=save) rChangeCurrRing(save);
Werror("exponent(x(%d)^%d) must be 0 or 1",i,li);
return NULL;
}
}
}
ideal res=kStd2(I,r->qideal,testHomog,NULL,(bigintmat*)NULL,0,0,NULL,id_sat_vars_sp);
omFreeSize(id_satstdSaturatingVariables,(1+rVar(currRing))*sizeof(int));
id_satstdSaturatingVariables=NULL;
if (currRing!=save) rChangeCurrRing(save);
return res;
}
ideal id_Sat_principal(ideal I, ideal J, const ring origR)
{
rRingOrder_t *ord;
int *block0,*block1;
int **wv;
// construction extension ring
ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t));
block0=(int*)omAlloc0(4*sizeof(int));
block1=(int*)omAlloc0(4*sizeof(int));
wv=(int**) omAlloc0(4*sizeof(int**));
wv[0]=(int*)omAlloc0((rVar(origR) + 2)*sizeof(int));
block0[0] = block0[1] = 1;
block1[0] = block1[1] = rVar(origR)+1;
// use this special ordering: like ringorder_a, except that pFDeg, pWeights
// ignore it
ord[0] = ringorder_aa;
wv[0][rVar(origR)]=1;
BOOLEAN wp=FALSE;
for (int j=0;j<rVar(origR);j++)
if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; }
if (wp)
{
wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
for (int j=0;j<rVar(origR);j++)
wv[1][j]=p_Weight(j+1,origR);
ord[1] = ringorder_wp;
}
else
ord[1] = ringorder_dp;
ord[2] = ringorder_C;
ord[3] = (rRingOrder_t)0;
char **names=(char**)omAlloc0((origR->N+1) * sizeof(char *));
for (int j=0;j<rVar(origR);j++)
names[j]=origR->names[j];
names[rVar(origR)]=(char*)"@";
ring tmpR=rDefault(nCopyCoeff(origR->cf),rVar(origR)+1,names,4,ord,block0,block1,wv);
omFree(names);
rComplete(tmpR, 1);
rChangeCurrRing(tmpR);
// map I
ideal II=idrCopyR(I,origR,tmpR);
// map J
ideal JJ=idrCopyR(J,origR,tmpR);
// J[1]*t-1
poly t=pOne();
p_SetExp(t,rVar(tmpR),1,tmpR);
p_Setm(t,tmpR);
poly p=JJ->m[0];
p_Norm(p,currRing);
p=p_Mult_q(p,t,tmpR);
p=p_Sub(p,pOne(),tmpR);
JJ->m[0]=p;
ideal T=id_SimpleAdd(II,JJ,tmpR);
idTest(T);
id_Delete(&II,tmpR);
id_Delete(&JJ,tmpR);
// elimination
t=pOne();
p_SetExp(t,rVar(tmpR),1,tmpR);
p_Setm(t,tmpR);
ideal TT=idGroebner(T,0,GbStd);
p_Delete(&t,tmpR);
for(int j=0;j<IDELEMS(TT);j++)
{
if ((TT->m[j]!=NULL)
&& (p_GetExp(TT->m[j],rVar(tmpR),tmpR)>0))
{
p_Delete(&TT->m[j],tmpR);
}
}
// map back
ideal TTT=idrCopyR(TT,tmpR,origR);
id_Delete(&TT,tmpR);
rChangeCurrRing(origR);
rDelete(tmpR);
idSkipZeroes(TTT);
return TTT;
}
ideal idSaturate_intern(ideal I, ideal J, int &k, BOOLEAN isIdeal, BOOLEAN isSB)
{
if(idIs0(J))
{
ideal res;
if(isIdeal)
{
res=idInit(1,1);
res->m[0]=pOne();
}
else
{
res=idFreeModule(I->rank);
}
k=1;
return(res);
}
BITSET save_opt;SI_SAVE_OPT2(save_opt);
//if (idElem(J)==1)
//{
// idSkipZeroes(J);
// return id_Sat_principal(I,J,currRing);
//}
//---------------------------------------------------
if (!rField_is_Ring(currRing))
{
BOOLEAN only_vars=TRUE; // enabled for I:x_i
if (idElem(J)==1)
{
for(int j=IDELEMS(J)-1;j>=0;j--)
{
poly p=J->m[j];
if (p!=NULL)
{
if (pVar(p)==0)
{
only_vars=FALSE;
break;
}
}
}
}
if (only_vars && isIdeal && rOrd_is_Totaldegree_Ordering(currRing)
&& (idElem(J)==1))
{
ideal Iquot,Istd;
intvec *w=NULL;
Istd=id_Satstd(I,J,currRing);
si_opt_2|=Sy_bit(V_PURE_GB);
k=0;
loop
{
k++;
Iquot=idQuot(Istd,J,TRUE,isIdeal);
ideal tmp=kNF(Istd,currRing->qideal,Iquot,5);
int elem=idElem(tmp);
id_Delete(&tmp,currRing);
id_Delete(&Istd,currRing);
Istd=Iquot;
w=NULL;
Istd=kStd2(Iquot,currRing->qideal,testHomog,&w,(bigintmat*)NULL);
if (w!=NULL) delete w;
id_Delete(&Iquot,currRing);
if (elem==0) break;
}
k--;
idSkipZeroes(Istd);
//PrintS("\nSatstd:\n");
//iiWriteMatrix((matrix)I,"I",1,currRing,0); PrintLn();
//iiWriteMatrix((matrix)J,"J",1,currRing,0); PrintLn();
//iiWriteMatrix((matrix)Istd,"res",1,currRing,0);PrintLn();
//id_Delete(&Istd,currRing);
SI_RESTORE_OPT2(save_opt);
return Istd;
}
}
//--------------------------------------------------
ideal Iquot,Istd;
intvec *w=NULL;
Istd=idCopy(I);
k=0;
loop
{
k++;
Iquot=idQuot(Istd,J,isSB,isIdeal);
isSB=FALSE;
si_opt_2|=Sy_bit(V_PURE_GB); // used from 2nd loop on
ideal tmp=kNF(Istd,currRing->qideal,Iquot,5);
int elem=idElem(tmp);
id_Delete(&tmp,currRing);
id_Delete(&Istd,currRing);
Istd=Iquot;
if (elem==0) break;
}
k--;
Istd=kStd2(Iquot,currRing->qideal,testHomog,&w,(bigintmat*)NULL);
idSkipZeroes(Istd);
SI_RESTORE_OPT2(save_opt);
//if (only_vars)
//{
// iiWriteMatrix((matrix)Istd,"org",1,currRing,0);
//}
return Istd;
}
ideal idSaturate(ideal I, ideal J, int &k, BOOLEAN isIdeal)
{
return idSaturate_intern(I,J,k,isIdeal,FALSE);
}
ideal idSaturateGB(ideal I, ideal J, int &k, BOOLEAN isIdeal)
{
return idSaturate_intern(I,J,k,isIdeal,TRUE);
}
ideal id_Homogenize(ideal I, int var_num, const ring r)
{
ideal II=id_Copy(I,r);
if (var_num==1)
{
ring tmpR=rAssure_Dp_C(r);
if (tmpR!=r)
{
rChangeCurrRing(tmpR);
II=idrMoveR(II,r,tmpR);
}
ideal III=id_Homogen(II,1,tmpR);
id_Delete(&II,tmpR);
intvec *ww=NULL;
II=kStd2(III,currRing->qideal,(tHomog)TRUE,&ww,(bigintmat*)NULL);
if (ww!=NULL) delete ww;
id_Delete(&III,tmpR);
if (tmpR!=r)
{
rChangeCurrRing(r);
II=idrMoveR(II,tmpR,r);
}
return II;
}
ideal III=idInit(IDELEMS(II),1);
int *perm=(int*)omAlloc0((rVar(r)+1)*sizeof(int));
for(int i=rVar(r)-1; i>0; i--) perm[i]=i;
perm[var_num]=1;
perm[1]=var_num;
for(int i=IDELEMS(II)-1; i>=0;i--)
{
III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
}
id_Delete(&II,r);
II=id_Homogenize(III,1,r);
id_Delete(&III,r);
III=idInit(IDELEMS(II),1);
for(int i=IDELEMS(II)-1; i>=0;i--)
{
III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
}
id_Delete(&II,r);
return III;
}
ideal id_HomogenizeW(ideal I, int var_num, intvec *w,const ring r)
{
ideal II=id_Copy(I,r);
if (var_num==1)
{
ring tmpR=rAssure_Wp_C(r,w);
if (tmpR!=r)
{
rChangeCurrRing(tmpR);
II=idrMoveR(II,r,tmpR);
}
ideal III=id_Homogen(II,1,tmpR);
id_Delete(&II,tmpR);
intvec *ww=NULL;
II=kStd2(III,currRing->qideal,(tHomog)TRUE,&ww,(bigintmat*)NULL);
if (ww!=NULL) delete ww;
id_Delete(&III,tmpR);
if (tmpR!=r)
{
rChangeCurrRing(r);
II=idrMoveR(II,tmpR,r);
}
return II;
}
ideal III=idInit(IDELEMS(II),1);
int *perm=(int*)omAlloc0((rVar(r)+1)*sizeof(int));
for(int i=rVar(r)-1; i>0; i--) perm[i]=i;
perm[var_num]=1;
perm[1]=var_num;
for(int i=IDELEMS(II)-1; i>=0;i--)
{
III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
}
id_Delete(&II,r);
II=id_HomogenizeW(III,1,w,r);
id_Delete(&III,r);
III=idInit(IDELEMS(II),1);
for(int i=IDELEMS(II)-1; i>=0;i--)
{
III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
}
id_Delete(&II,r);
return III;
}
GbVariant syGetAlgorithm(char *n, const ring r, const ideal /*M*/)
{
GbVariant alg=GbDefault;
if (strcmp(n,"default")==0) alg=GbDefault;
else if (strcmp(n,"slimgb")==0) alg=GbSlimgb;
else if (strcmp(n,"std")==0) alg=GbStd;
else if (strcmp(n,"sba")==0) alg=GbSba;
else if (strcmp(n,"singmatic")==0) alg=GbSingmatic;
else if (strcmp(n,"groebner")==0) alg=GbGroebner;
else if (strcmp(n,"modstd")==0) alg=GbModstd;
else if (strcmp(n,"ffmod")==0) alg=GbFfmod;
else if (strcmp(n,"nfmod")==0) alg=GbNfmod;
else if (strcmp(n,"std:sat")==0) alg=GbStdSat;
else Warn(">>%s<< is an unknown algorithm",n);
if (alg==GbSlimgb) // test conditions for slimgb
{
if(rHasGlobalOrdering(r)
&&(!rIsNCRing(r))
&&(r->qideal==NULL)
&&(!rField_is_Ring(r)))
{
return GbSlimgb;
}
if (TEST_OPT_PROT)
WarnS("requires: coef:field, commutative, global ordering, not qring");
}
else if (alg==GbSba) // cond. for sba
{
if(rField_is_Domain(r)
&&(!rIsNCRing(r))
&&(rHasGlobalOrdering(r)))
{
return GbSba;
}
if (TEST_OPT_PROT)
WarnS("requires: coef:domain, commutative, global ordering");
}
else if (alg==GbGroebner) // cond. for groebner
{
return GbGroebner;
}
else if(alg==GbModstd) // cond for modstd: Q or Q(a)
{
if(ggetid("modStd")==NULL)
{
WarnS(">>modStd<< not found");
}
else if(rField_is_Q(r)
&&(!rIsNCRing(r))
&&(rHasGlobalOrdering(r)))
{
return GbModstd;
}
if (TEST_OPT_PROT)
WarnS("requires: coef:QQ, commutative, global ordering");
}
else if(alg==GbStdSat) // cond for std:sat: 2 blocks of variables
{
if(ggetid("satstd")==NULL)
{
WarnS(">>satstd<< not found");
}
else
{
return GbStdSat;
}
}
return GbStd; // no conditions for std
}
//----------------------------------------------------------------------------
// GB-algorithms and their pre-conditions
// std slimgb sba singmatic modstd ffmod nfmod groebner
// + + + - + - - + coeffs: QQ
// + + + + - - - + coeffs: ZZ/p
// + + + - ? - + + coeffs: K[a]/f
// + + + - ? + - + coeffs: K(a)
// + - + - - - - + coeffs: domain, not field
// + - - - - - - + coeffs: zero-divisors
// + + + + - ? ? + also for modules: C
// + + - + - ? ? + also for modules: all orderings
// + + - - - - - + exterior algebra
// + + - - - - - + G-algebra
// + + + + + + + + degree ordering
// + - + + + + + + non-degree ordering
// - - - + + + + + parallel
BITSET
#define BITSET
Definition auxiliary.h:85
si_max
static int si_max(const int a, const int b)
Definition auxiliary.h:125
BOOLEAN
int BOOLEAN
Definition auxiliary.h:88
TRUE
#define TRUE
Definition auxiliary.h:101
FALSE
#define FALSE
Definition auxiliary.h:97
ADDRESS
void * ADDRESS
Definition auxiliary.h:120
si_min
static int si_min(const int a, const int b)
Definition auxiliary.h:126
size
int size(const CanonicalForm &f, const Variable &v)
int size ( const CanonicalForm & f, const Variable & v )
Definition cf_ops.cc:600
mod
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
N
const CanonicalForm CFMap CFMap & N
Definition cfEzgcd.cc:56
l
int l
Definition cfEzgcd.cc:100
m
int m
Definition cfEzgcd.cc:128
i
int i
Definition cfEzgcd.cc:132
k
int k
Definition cfEzgcd.cc:99
x
Variable x
Definition cfModGcd.cc:4090
p
int p
Definition cfModGcd.cc:4086
g
g
Definition cfModGcd.cc:4098
b
CanonicalForm b
Definition cfModGcd.cc:4111
bound
static CanonicalForm bound(const CFMatrix &M)
Definition cf_linsys.cc:460
f
FILE * f
Definition checklibs.c:9
singclap_pdivide
poly singclap_pdivide(poly f, poly g, const ring r)
Definition clapsing.cc:649
clapsing.h
bigintmat
Matrices of numbers.
Definition bigintmat.h:51
intvec
Definition intvec.h:24
ip_smatrix::nrows
int nrows
Definition matpol.h:20
ip_smatrix::rank
long rank
Definition matpol.h:19
ip_smatrix::ncols
int ncols
Definition matpol.h:21
ip_smatrix::m
poly * m
Definition matpol.h:18
ip_smatrix::cols
int & cols()
Definition matpol.h:24
ip_smatrix::rows
int & rows()
Definition matpol.h:23
skStrategy::tailRing
ring tailRing
Definition kutil.h:342
skStrategy::P
LObject P
Definition kutil.h:301
sleftv::data
void * data
Definition subexpr.h:88
coeffs.h
Coefficient rings, fields and other domains suitable for Singular polynomials.
ndCopyMap
number ndCopyMap(number a, const coeffs src, const coeffs dst)
Definition numbers.cc:293
n_IsUnit
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:521
n_IsZero
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition coeffs.h:470
nCopyCoeff
static FORCE_INLINE coeffs nCopyCoeff(const coeffs r)
"copy" coeffs, i.e. increment ref
Definition coeffs.h:439
n_Init
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition coeffs.h:541
Print
#define Print
Definition emacs.cc:80
Warn
#define Warn
Definition emacs.cc:77
WarnS
#define WarnS
Definition emacs.cc:78
result
return result
Definition facAbsBiFact.cc:76
s
const CanonicalForm int s
Definition facAbsFact.cc:51
res
CanonicalForm res
Definition facAbsFact.cc:60
w
const CanonicalForm & w
Definition facAbsFact.cc:51
divide
CanonicalForm divide(const CanonicalForm &ff, const CanonicalForm &f, const CFList &as)
Definition facAlgFuncUtil.cc:496
v
const Variable & v
< [in] a sqrfree bivariate poly
Definition facBivar.h:39
j
int j
Definition facHensel.cc:110
comp
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
Definition facSparseHensel.h:25
name
char name(const Variable &v)
Definition factory.h:189
errorreported
VAR short errorreported
Definition feFopen.cc:23
WerrorS
void WerrorS(const char *s)
Definition feFopen.cc:24
STATIC_VAR
#define STATIC_VAR
Definition globaldefs.h:7
IDEAL_CMD
@ IDEAL_CMD
Definition grammar.cc:285
MODUL_CMD
@ MODUL_CMD
Definition grammar.cc:288
syGetAlgorithm
GbVariant syGetAlgorithm(char *n, const ring r, const ideal)
Definition ideals.cc:3698
idMinEmbedding1
static ideal idMinEmbedding1(ideal arg, BOOLEAN inPlace, intvec **w, int *red_comp, int &del)
Definition ideals.cc:2817
poly_sort::index
int index
Definition ideals.cc:3194
idPrepareStd
static void idPrepareStd(ideal s_temp, int k)
Definition ideals.cc:1047
idCoeffOfKBase
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
Definition ideals.cc:2668
idLiftW
void idLiftW(ideal P, ideal Q, int n, matrix &T, ideal &R, int *w)
Definition ideals.cc:1347
idLift_setUnit
static void idLift_setUnit(int e_mod, matrix *unit)
Definition ideals.cc:1088
idSyzygies
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp, BOOLEAN setRegularity, int *deg, GbVariant alg)
Definition ideals.cc:836
poly_sort::p
poly p
Definition ideals.cc:3193
idDiff
matrix idDiff(matrix i, int k)
Definition ideals.cc:2189
id_Sat_principal
ideal id_Sat_principal(ideal I, ideal J, const ring origR)
Definition ideals.cc:3415
idSaturateGB
ideal idSaturateGB(ideal I, ideal J, int &k, BOOLEAN isIdeal)
Definition ideals.cc:3603
idGroebner
static ideal idGroebner(ideal temp, int syzComp, GbVariant alg, bigintmat *hilb=NULL, intvec *w=NULL, tHomog hom=testHomog)
Definition ideals.cc:200
idTestHomModule
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
Definition ideals.cc:2120
id_Homogenize
ideal id_Homogenize(ideal I, int var_num, const ring r)
Definition ideals.cc:3608
idLiftStd
ideal idLiftStd(ideal h1, matrix *T, tHomog hi, ideal *S, GbVariant alg, ideal h11)
Definition ideals.cc:982
idDelEquals
void idDelEquals(ideal id)
Definition ideals.cc:3211
pCompare_qsort
int pCompare_qsort(const void *a, const void *b)
Definition ideals.cc:3197
idQuot
ideal idQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
Definition ideals.cc:1539
id_HomogenizeW
ideal id_HomogenizeW(ideal I, int var_num, intvec *w, const ring r)
Definition ideals.cc:3653
idMinors
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 ...
Definition ideals.cc:2031
idSaturate
ideal idSaturate(ideal I, ideal J, int &k, BOOLEAN isIdeal)
Definition ideals.cc:3599
ipPrint_MA0
void ipPrint_MA0(matrix m, const char *name)
Definition ipprint.cc:57
idIsSubModule
BOOLEAN idIsSubModule(ideal id1, ideal id2)
Definition ideals.cc:2099
idSeries
ideal idSeries(int n, ideal M, matrix U, intvec *w)
Definition ideals.cc:2172
idMinEmbedding_with_map_v
ideal idMinEmbedding_with_map_v(ideal arg, intvec **w, ideal &trans, int *g)
Definition ideals.cc:2874
idCreateSpecialKbase
ideal idCreateSpecialKbase(ideal kBase, intvec **convert)
Definition ideals.cc:2582
idPrepare
static ideal idPrepare(ideal h1, ideal h11, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
Definition ideals.cc:613
id_GCD
poly id_GCD(poly f, poly g, const ring r)
Definition ideals.cc:3000
idIndexOfKBase
int idIndexOfKBase(poly monom, ideal kbase)
Definition ideals.cc:2600
idDecompose
poly idDecompose(poly monom, poly how, ideal kbase, int *pos)
Definition ideals.cc:2636
idSaturate_intern
ideal idSaturate_intern(ideal I, ideal J, int &k, BOOLEAN isIdeal, BOOLEAN isSB)
Definition ideals.cc:3495
idElimination2
ideal idElimination2(ideal h1, poly delVar, bigintmat *hilb, GbVariant alg)
Definition ideals.cc:1640
idDiffOp
matrix idDiffOp(ideal I, ideal J, BOOLEAN multiply)
Definition ideals.cc:2202
idSort_qsort
void idSort_qsort(poly_sort *id_sort, int idsize)
Definition ideals.cc:3202
idInitializeQuot
static ideal idInitializeQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
Definition ideals.cc:1412
idElimination
ideal idElimination(ideal h1, poly delVar, intvec *hilb, GbVariant alg)
Definition ideals.cc:1884
idSectWithElim
static ideal idSectWithElim(ideal h1, ideal h2, GbVariant alg)
Definition ideals.cc:132
idSect
ideal idSect(ideal h1, ideal h2, GbVariant alg)
Definition ideals.cc:315
idMultSect
ideal idMultSect(resolvente arg, int length, GbVariant alg)
Definition ideals.cc:472
idKeepFirstK
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....
Definition ideals.cc:3179
idLift
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
represents the generators of submod in terms of the generators of mod (Matrix(SM)*U-Matrix(rest)) = M...
Definition ideals.cc:1111
id_satstdSaturatingVariables
STATIC_VAR int * id_satstdSaturatingVariables
Definition ideals.cc:3248
idExtractG_T_S
ideal idExtractG_T_S(ideal s_h3, matrix *T, ideal *S, long syzComp, int h1_size, BOOLEAN inputIsIdeal, const ring oring, const ring sring)
Definition ideals.cc:715
idDeleteComps
static void idDeleteComps(ideal arg, int *red_comp, int del)
Definition ideals.cc:2707
idModulo
ideal idModulo(ideal h2, ideal h1, tHomog hom, intvec **w, matrix *T, GbVariant alg)
Definition ideals.cc:2463
idMinEmbedding_with_map
ideal idMinEmbedding_with_map(ideal arg, intvec **w, ideal &trans)
Definition ideals.cc:2863
idMinBase
ideal idMinBase(ideal h1, ideal *SB)
Definition ideals.cc:51
id_Farey
ideal id_Farey(ideal x, number N, const ring r)
Definition ideals.cc:3103
id_Satstd
ideal id_Satstd(const ideal I, ideal J, const ring r)
Definition ideals.cc:3363
id_ReadOutPivot
static int id_ReadOutPivot(ideal arg, int *comp, const ring r)
Definition ideals.cc:2734
idModuloLP
ideal idModuloLP(ideal h2, ideal h1, tHomog, intvec **w, matrix *T, GbVariant alg)
Definition ideals.cc:2272
id_sat_vars_sp
static BOOLEAN id_sat_vars_sp(kStrategy strat)
Definition ideals.cc:3250
idMinEmbedding
ideal idMinEmbedding(ideal arg, BOOLEAN inPlace, intvec **w)
Definition ideals.cc:2853
poly_sort
Definition ideals.cc:3192
ideals.h
binom
int binom(int n, int r)
Definition simpleideals.cc:1212
GbVariant
GbVariant
Definition ideals.h:119
GbGroebner
@ GbGroebner
Definition ideals.h:126
GbModstd
@ GbModstd
Definition ideals.h:127
GbStdSat
@ GbStdSat
Definition ideals.h:130
GbSlimgb
@ GbSlimgb
Definition ideals.h:123
GbFfmod
@ GbFfmod
Definition ideals.h:128
GbNfmod
@ GbNfmod
Definition ideals.h:129
GbDefault
@ GbDefault
Definition ideals.h:120
GbStd
@ GbStd
Definition ideals.h:122
GbSingmatic
@ GbSingmatic
Definition ideals.h:131
GbSba
@ GbSba
Definition ideals.h:124
idDelete
#define idDelete(H)
delete an ideal
Definition ideals.h:29
idSimpleAdd
#define idSimpleAdd(A, B)
Definition ideals.h:42
idGetNextChoise
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
Definition simpleideals.cc:1154
id_Copy
ideal id_Copy(ideal h1, const ring r)
copy an ideal
Definition simpleideals.cc:542
idIs0
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
Definition simpleideals.cc:960
idHomModule
static BOOLEAN idHomModule(ideal m, ideal Q, intvec **w)
Definition ideals.h:96
idTest
#define idTest(id)
Definition ideals.h:47
idHomIdeal
static BOOLEAN idHomIdeal(ideal id, ideal Q=NULL)
Definition ideals.h:91
idMult
static ideal idMult(ideal h1, ideal h2)
hh := h1 * h2
Definition ideals.h:84
idCopy
ideal idCopy(ideal A)
Definition ideals.h:60
idMaxIdeal
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
Definition ideals.h:33
resolvente
ideal * resolvente
Definition ideals.h:18
idInitChoise
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
Definition simpleideals.cc:1132
idSort
static intvec * idSort(ideal id, BOOLEAN nolex=TRUE)
Definition ideals.h:188
idFreeModule
ideal idFreeModule(int i)
Definition ideals.h:111
length
static BOOLEAN length(leftv result, leftv arg)
Definition interval.cc:257
iv2biv
bigintmat * iv2biv(intvec *hilb, const coeffs cf)
Definition intvec.cc:851
intvec.h
ivCopy
intvec * ivCopy(const intvec *o)
Definition intvec.h:146
ggetid
idhdl ggetid(const char *n)
Definition ipid.cc:581
ipid.h
sleftv_bin
EXTERN_VAR omBin sleftv_bin
Definition ipid.h:145
ii_CallLibProcM
leftv ii_CallLibProcM(const char *n, void **args, int *arg_types, const ring R, BOOLEAN &err)
args: NULL terminated array of arguments arg_types: 0 terminated array of corresponding types
Definition iplib.cc:710
iiCallLibProc1
void * iiCallLibProc1(const char *n, void *arg, int arg_type, BOOLEAN &err)
Definition iplib.cc:636
ipprint.h
ipshell.h
T
STATIC_VAR jList * T
Definition janet.cc:30
h
STATIC_VAR Poly * h
Definition janet.cc:971
p_TakeOutComp
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition p_polys.cc:3620
kMin_std2
ideal kMin_std2(ideal F, ideal Q, tHomog h, intvec **w, ideal &M, bigintmat *hilb, int syzComp, int reduced)
Definition kstd1.cc:3069
kStd2
ideal kStd2(ideal F, ideal Q, tHomog h, intvec **w, bigintmat *hilb, int syzComp, int newIdeal, intvec *vw, s_poly_proc_t sp)
generic interface to GB/SB computations, large hilbert vectors
Definition kstd1.cc:2607
kSba
ideal kSba(ideal F, ideal Q, tHomog h, intvec **w, int sbaOrder, int arri, bigintmat *hilb, int syzComp, int newIdeal, intvec *vw)
Definition kstd1.cc:2668
kNF
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
Definition kstd1.cc:3229
kstd1.h
kutil.h
nc.h
nc_skew
@ nc_skew
Definition nc.h:16
nc_exterior
@ nc_exterior
Definition nc.h:21
ncRingType
static nc_type & ncRingType(nc_struct *p)
Definition nc.h:159
nc_CheckSubalgebra
BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r)
Definition old.gring.cc:2578
mpNew
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition matpol.cc:37
mp_MultP
matrix mp_MultP(matrix a, poly p, const ring R)
multiply a matrix 'a' by a poly 'p', destroy the args
Definition matpol.cc:141
mp_Copy
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
Definition matpol.cc:57
mp_MinorToResult
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)
Definition matpol.cc:1501
mp_RecMin
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
Definition matpol.cc:1597
mp_DetBareiss
poly mp_DetBareiss(matrix a, const ring r)
returns the determinant of the matrix m; uses Bareiss algorithm
Definition matpol.cc:1670
matpol.h
MATELEM
#define MATELEM(mat, i, j)
1-based access to matrix
Definition matpol.h:29
matrix
ip_smatrix * matrix
Definition matpol.h:43
MATROWS
#define MATROWS(i)
Definition matpol.h:26
MATCOLS
#define MATCOLS(i)
Definition matpol.h:27
mod2.h
assume
#define assume(x)
Definition mod2.h:389
pIter
#define pIter(p)
Definition monomials.h:37
pNext
#define pNext(p)
Definition monomials.h:36
p_GetCoeff
#define p_GetCoeff(p, r)
Definition monomials.h:50
pGetCoeff
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
__p_GetComp
#define __p_GetComp(p, r)
Definition monomials.h:63
numbers.h
nInpNeg
#define nInpNeg(n)
Definition numbers.h:21
nCopy
#define nCopy(n)
Definition numbers.h:15
omStrDup
#define omStrDup(s)
Definition omAllocDecl.h:263
omFreeSize
#define omFreeSize(addr, size)
Definition omAllocDecl.h:260
omAlloc
#define omAlloc(size)
Definition omAllocDecl.h:210
omalloc
#define omalloc(size)
Definition omAllocDecl.h:228
omFree
#define omFree(addr)
Definition omAllocDecl.h:261
omAlloc0
#define omAlloc0(size)
Definition omAllocDecl.h:211
omFreeBin
#define omFreeBin(addr, bin)
Definition omAllocDecl.h:259
omMemDup
#define omMemDup(s)
Definition omAllocDecl.h:264
NULL
#define NULL
Definition omList.c:12
si_opt_2
VAR unsigned si_opt_2
Definition options.c:6
si_opt_1
VAR unsigned si_opt_1
Definition options.c:5
options.h
SI_SAVE_OPT
#define SI_SAVE_OPT(A, B)
Definition options.h:20
TEST_OPT_IDLIFT
#define TEST_OPT_IDLIFT
Definition options.h:131
SI_SAVE_OPT2
#define SI_SAVE_OPT2(A)
Definition options.h:22
OPT_REDTAIL_SYZ
#define OPT_REDTAIL_SYZ
Definition options.h:88
OPT_REDTAIL
#define OPT_REDTAIL
Definition options.h:92
OPT_SB_1
#define OPT_SB_1
Definition options.h:96
SI_SAVE_OPT1
#define SI_SAVE_OPT1(A)
Definition options.h:21
SI_RESTORE_OPT1
#define SI_RESTORE_OPT1(A)
Definition options.h:24
SI_RESTORE_OPT2
#define SI_RESTORE_OPT2(A)
Definition options.h:25
Sy_bit
#define Sy_bit(x)
Definition options.h:31
TEST_OPT_RETURN_SB
#define TEST_OPT_RETURN_SB
Definition options.h:114
V_PURE_GB
#define V_PURE_GB
Definition options.h:71
TEST_V_INTERSECT_ELIM
#define TEST_V_INTERSECT_ELIM
Definition options.h:146
TEST_V_INTERSECT_SYZ
#define TEST_V_INTERSECT_SYZ
Definition options.h:147
TEST_OPT_NOTREGULARITY
#define TEST_OPT_NOTREGULARITY
Definition options.h:122
TEST_OPT_PROT
#define TEST_OPT_PROT
Definition options.h:105
V_IDLIFT
#define V_IDLIFT
Definition options.h:63
SI_RESTORE_OPT
#define SI_RESTORE_OPT(A, B)
Definition options.h:23
index
static int index(p_Length length, p_Ord ord)
Definition p_Procs_Impl.h:592
p_DivideM
poly p_DivideM(poly a, poly b, const ring r)
Definition p_polys.cc:1582
p_Farey
poly p_Farey(poly p, number N, const ring r)
Definition p_polys.cc:54
p_Weight
int p_Weight(int i, const ring r)
Definition p_polys.cc:706
p_Shift
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition p_polys.cc:4860
p_PermPoly
poly p_PermPoly(poly p, const int *perm, const ring oldRing, const ring dst, nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult)
Definition p_polys.cc:4256
p_Div_nn
poly p_Div_nn(poly p, const number n, const ring r)
Definition p_polys.cc:1506
p_Norm
void p_Norm(poly p1, const ring r)
Definition p_polys.cc:3844
p_Compare
int p_Compare(const poly a, const poly b, const ring R)
Definition p_polys.cc:5050
p_DegW
long p_DegW(poly p, const int *w, const ring R)
Definition p_polys.cc:691
p_Vec2Poly
poly p_Vec2Poly(poly v, int k, const ring r)
Definition p_polys.cc:3698
p_SetModDeg
void p_SetModDeg(intvec *w, ring r)
Definition p_polys.cc:3798
p_Var
int p_Var(poly m, const ring r)
Definition p_polys.cc:4810
p_One
poly p_One(const ring r)
Definition p_polys.cc:1314
p_Sub
poly p_Sub(poly p1, poly p2, const ring r)
Definition p_polys.cc:1994
pEnlargeSet
void pEnlargeSet(poly **p, int l, int increment)
Definition p_polys.cc:3821
p_Deg
long p_Deg(poly a, const ring r)
Definition p_polys.cc:586
p_Neg
static poly p_Neg(poly p, const ring r)
Definition p_polys.h:1114
p_Add_q
static poly p_Add_q(poly p, poly q, const ring r)
Definition p_polys.h:938
p_LmDelete
static void p_LmDelete(poly p, const ring r)
Definition p_polys.h:725
p_Mult_q
static poly p_Mult_q(poly p, poly q, const ring r)
Definition p_polys.h:1125
p_SubExp
static long p_SubExp(poly p, int v, long ee, ring r)
Definition p_polys.h:615
p_SetExp
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
Definition p_polys.h:490
p_MinComp
static long p_MinComp(poly p, ring lmRing, ring tailRing)
Definition p_polys.h:315
p_Setm
static void p_Setm(poly p, const ring r)
Definition p_polys.h:235
p_Copy_noCheck
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition p_polys.h:838
p_SetCoeff
static number p_SetCoeff(poly p, number n, ring r)
Definition p_polys.h:414
pReverse
static poly pReverse(poly p)
Definition p_polys.h:337
p_LmIsConstantComp
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
Definition p_polys.h:1008
p_Head
static poly p_Head(const poly p, const ring r)
copy the (leading) term of p
Definition p_polys.h:862
p_LmCmp
static int p_LmCmp(poly p, poly q, const ring r)
Definition p_polys.h:1601
p_GetExp
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition p_polys.h:471
p_Delete
static void p_Delete(poly *p, const ring r)
Definition p_polys.h:903
p_GetExpV
static void p_GetExpV(poly p, int *ev, const ring r)
Definition p_polys.h:1541
p_LmFreeAndNext
static poly p_LmFreeAndNext(poly p, ring)
Definition p_polys.h:713
p_Copy
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition p_polys.h:848
p_Totaldegree
static long p_Totaldegree(poly p, const ring r)
Definition p_polys.h:1528
rChangeCurrRing
void rChangeCurrRing(ring r)
Definition polys.cc:16
coeffs_BIGINT
VAR coeffs coeffs_BIGINT
Definition polys.cc:14
currRing
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition polys.cc:13
polys.h
Compatibility layer for legacy polynomial operations (over currRing).
pAdd
#define pAdd(p, q)
Definition polys.h:204
pTest
#define pTest(p)
Definition polys.h:415
pDelete
#define pDelete(p_ptr)
Definition polys.h:187
ppJet
#define ppJet(p, m)
Definition polys.h:367
pHead
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL
Definition polys.h:68
pSetm
#define pSetm(p)
Definition polys.h:272
pNeg
#define pNeg(p)
Definition polys.h:199
ppMult_mm
#define ppMult_mm(p, m)
Definition polys.h:202
pSetCompP
#define pSetCompP(a, i)
Definition polys.h:304
pGetComp
#define pGetComp(p)
Component.
Definition polys.h:38
pDiff
#define pDiff(a, b)
Definition polys.h:297
pSetCoeff
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition polys.h:32
pVar
#define pVar(m)
Definition polys.h:381
pJet
#define pJet(p, m)
Definition polys.h:368
pSub
#define pSub(a, b)
Definition polys.h:288
pWeight
#define pWeight(i)
Definition polys.h:281
ppJetW
#define ppJetW(p, m, iv)
Definition polys.h:369
pMaxComp
#define pMaxComp(p)
Definition polys.h:300
pSetComp
#define pSetComp(p, v)
Definition polys.h:39
wrp
void wrp(poly p)
Definition polys.h:311
pMult
#define pMult(p, q)
Definition polys.h:208
pJetW
#define pJetW(p, m, iv)
Definition polys.h:370
pDiffOp
#define pDiffOp(a, b, m)
Definition polys.h:298
pSeries
#define pSeries(n, p, u, w)
Definition polys.h:372
pGetExp
#define pGetExp(p, i)
Exponent.
Definition polys.h:42
pSetmComp
#define pSetmComp(p)
TODO:
Definition polys.h:274
pNormalize
#define pNormalize(p)
Definition polys.h:318
pEqualPolys
#define pEqualPolys(p1, p2)
Definition polys.h:400
pDivisibleBy
#define pDivisibleBy(a, b)
returns TRUE, if leading monom of a divides leading monom of b i.e., if there exists a expvector c > ...
Definition polys.h:139
pSetExp
#define pSetExp(p, i, v)
Definition polys.h:43
pTakeOutComp
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 ...
Definition polys.h:339
pCopy
#define pCopy(p)
return a copy of the poly
Definition polys.h:186
pOne
#define pOne()
Definition polys.h:316
pMinComp
#define pMinComp(p)
Definition polys.h:301
polyset
poly * polyset
Definition polys.h:260
prMoveR
poly prMoveR(poly &p, ring src_r, ring dest_r)
Definition prCopy.cc:90
idrMoveR
ideal idrMoveR(ideal &id, ring src_r, ring dest_r)
Definition prCopy.cc:248
prCopyR
poly prCopyR(poly p, ring src_r, ring dest_r)
Definition prCopy.cc:34
idrCopyR
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
Definition prCopy.cc:192
idrMoveR_NoSort
ideal idrMoveR_NoSort(ideal &id, ring src_r, ring dest_r)
Definition prCopy.cc:261
prMoveR_NoSort
poly prMoveR_NoSort(poly &p, ring src_r, ring dest_r)
Definition prCopy.cc:101
idrCopyR_NoSort
ideal idrCopyR_NoSort(ideal id, ring src_r, ring dest_r)
Definition prCopy.cc:205
prCopy.h
PrintS
void PrintS(const char *s)
Definition reporter.cc:288
PrintLn
void PrintLn()
Definition reporter.cc:314
Werror
void Werror(const char *fmt,...)
Definition reporter.cc:189
mflush
#define mflush()
Definition reporter.h:58
rComplete
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...
Definition ring.cc:3527
rAssure_SyzComp
ring rAssure_SyzComp(const ring r, BOOLEAN complete)
Definition ring.cc:4527
nc_rComplete
BOOLEAN nc_rComplete(const ring src, ring dest, bool bSetupQuotient)
Definition ring.cc:5833
rAssure_Wp_C
ring rAssure_Wp_C(const ring r, intvec *w)
Definition ring.cc:4942
rAssure_Dp_C
ring rAssure_Dp_C(const ring r)
Definition ring.cc:5124
rOrd_is_Totaldegree_Ordering
BOOLEAN rOrd_is_Totaldegree_Ordering(const ring r)
Definition ring.cc:2043
rAssure_SyzOrder
ring rAssure_SyzOrder(const ring r, BOOLEAN complete)
Definition ring.cc:4522
rCopy0
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
Definition ring.cc:1427
rDelete
void rDelete(ring r)
unconditionally deletes fields in r
Definition ring.cc:454
rDefault
ring rDefault(const coeffs cf, int N, char **n, int ord_size, rRingOrder_t *ord, int *block0, int *block1, int **wvhdl, unsigned long bitmask)
Definition ring.cc:103
rSetSyzComp
void rSetSyzComp(int k, const ring r)
Definition ring.cc:5230
rAssure_dp_C
ring rAssure_dp_C(const ring r)
Definition ring.cc:5119
ring.h
rHasGlobalOrdering
static BOOLEAN rHasGlobalOrdering(const ring r)
Definition ring.h:768
rIsPluralRing
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition ring.h:406
rBlocks
static int rBlocks(const ring r)
Definition ring.h:574
rField_is_Domain
static BOOLEAN rField_is_Domain(const ring r)
Definition ring.h:493
rIsLPRing
static BOOLEAN rIsLPRing(const ring r)
Definition ring.h:417
rRingOrder_t
rRingOrder_t
order stuff
Definition ring.h:69
ringorder_a
@ ringorder_a
Definition ring.h:71
ringorder_a64
@ ringorder_a64
for int64 weights
Definition ring.h:72
ringorder_C
@ ringorder_C
Definition ring.h:74
ringorder_dp
@ ringorder_dp
Definition ring.h:79
ringorder_c
@ ringorder_c
Definition ring.h:73
ringorder_aa
@ ringorder_aa
for idElimination, like a, except pFDeg, pWeigths ignore it
Definition ring.h:93
ringorder_ws
@ ringorder_ws
Definition ring.h:88
ringorder_s
@ ringorder_s
s?
Definition ring.h:77
ringorder_wp
@ ringorder_wp
Definition ring.h:82
rField_is_Q
static BOOLEAN rField_is_Q(const ring r)
Definition ring.h:512
rIsNCRing
static BOOLEAN rIsNCRing(const ring r)
Definition ring.h:427
rVar
static short rVar(const ring r)
define rVar(r) (r->N)
Definition ring.h:598
rField_is_Ring
#define rField_is_Ring(R)
Definition ring.h:491
block
#define block
Definition scanner.cc:646
idInit
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition simpleideals.cc:35
id_Delete
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
Definition simpleideals.cc:123
id_Homogen
ideal id_Homogen(ideal h, int varnum, const ring r)
Definition simpleideals.cc:1503
id_Module2Matrix
matrix id_Module2Matrix(ideal mod, const ring R)
Definition simpleideals.cc:1594
id_RankFreeModule
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
Definition simpleideals.cc:992
id_DelMultiples
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
Definition simpleideals.cc:296
id_Matrix2Module
ideal id_Matrix2Module(matrix mat, const ring R)
converts mat to module, destroys mat
Definition simpleideals.cc:1560
id_SimpleAdd
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
Definition simpleideals.cc:790
idSkipZeroes
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
Definition simpleideals.cc:201
id_Shift
void id_Shift(ideal M, int s, const ring r)
Definition simpleideals.cc:2196
id_ChineseRemainder
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
Definition simpleideals.cc:2147
IDELEMS
#define IDELEMS(i)
Definition simpleideals.h:23
id_Test
#define id_Test(A, lR)
Definition simpleideals.h:89
idElem
static int idElem(const ideal F)
number of non-zero polys in F
Definition simpleideals.h:69
R
#define R
Definition sirandom.c:27
M
#define M
Definition sirandom.c:25
Q
#define Q
Definition sirandom.c:26
sm_ExpBound
long sm_ExpBound(ideal m, int di, int ra, int t, const ring currRing)
Definition sparsmat.cc:188
sm_RingChange
ring sm_RingChange(const ring origR, long bound)
Definition sparsmat.cc:258
sm_KillModifiedRing
void sm_KillModifiedRing(ring r)
Definition sparsmat.cc:289
sparsmat.h
leftv
sleftv * leftv
Definition structs.h:53
char_ptr
char * char_ptr
Definition structs.h:49
tHomog
tHomog
Definition structs.h:31
isHomog
@ isHomog
Definition structs.h:33
testHomog
@ testHomog
Definition structs.h:34
isNotHomog
@ isNotHomog
Definition structs.h:32
kStrategy
skStrategy * kStrategy
Definition structs.h:54
loop
#define loop
Definition structs.h:71
syGaussForOne
void syGaussForOne(ideal syz, int elnum, int ModComp, int from, int till)
Definition syz.cc:218
syBetti
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
Definition syz.cc:787
syz.h
sySchreyerResolvente
resolvente sySchreyerResolvente(ideal arg, int maxlength, int *length, BOOLEAN isMonomial=FALSE, BOOLEAN notReplace=FALSE)
Definition syz0.cc:855
t_rep_gb
ideal t_rep_gb(const ring r, ideal arg_I, int syz_comp, BOOLEAN F4_mode)
Definition tgb.cc:3581
tgb.h
INT_CMD
@ INT_CMD
Definition tok.h:96
wFunctional
THREAD_VAR double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition weight.cc:20
wCall
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
Definition weight.cc:108
wFunctionalBuch
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition weight0.cc:78
weight.h