30 #if __FLINT_RELEASE >= 20503
31 #include <flint/fmpq_mpoly.h>
38#define OVERFLOW_MAX LONG_MAX
39#define OVERFLOW_MIN LONG_MIN
41#define OVERFLOW_MAX (((int64)LONG_MAX)<<30)
42#define OVERFLOW_MIN (-OVERFLOW_MAX)
384 mpz_set_ui(dummy, 1);
386 mpz_set_si(dummy, -1);
387 mpz_add(ec, ec, dummy);
400 int i,howmanyvarinp = 0;
420 poly notsqrfree =
NULL;
437 if(notsqrfree !=
NULL)
510static void rouneslice(ideal I, ideal S, poly q, poly
x,
int &
prune,
int &moreprune,
int &steps,
int &NNN, mpz_ptr &hilbertcoef,
int* &hilbpower)
612 hilbertcoef = (mpz_ptr)
omAlloc((NNN+1)*
sizeof(mpz_t));
613 hilbpower = (
int*)
omAlloc((NNN+1)*
sizeof(
int));
614 mpz_init_set( &hilbertcoef[NNN], ec);
626 mpz_add(&hilbertcoef[
i],&hilbertcoef[
i],ec_ptr);
631 hilbertcoef = (mpz_ptr)
omRealloc(hilbertcoef, (NNN+1)*
sizeof(mpz_t));
632 hilbpower = (
int*)
omRealloc(hilbpower, (NNN+1)*
sizeof(
int));
633 mpz_init(&hilbertcoef[NNN]);
634 for(
j = NNN;
j>
i;
j--)
636 mpz_set(&hilbertcoef[
j],&hilbertcoef[
j-1]);
637 hilbpower[
j] = hilbpower[
j-1];
639 mpz_set( &hilbertcoef[
i], ec);
657 rouneslice(Ip, Sp, pq,
x,
prune, moreprune, steps, NNN, hilbertcoef,hilbpower);
670 int steps = 0,
prune = 0, moreprune = 0;
687 rouneslice(I,S,q,X->m[0],
prune, moreprune, steps, NNN, hilbertcoef, hilbpower);
693 printf(
"\n// %8d t^0",1);
694 for(
i = 0;
i<NNN;
i++)
696 if(mpz_sgn(&hilbertcoef[
i])!=0)
698 gmp_printf(
"\n// %8Zd t^%d",&hilbertcoef[
i],hilbpower[
i]);
712 if (hseries1 ==
NULL)
714 work =
new intvec(hseries1);
717 for (
i =
k-1;
i >= 0;
i--)
721 if ((
s != 0) || (
k == 1))
726 for (
i =
k-1;
i >= 0;
i--)
735 for (
i =
k-1;
i >= 0;
i--)
736 (*hseries2)[
i] = (*work)[
i];
737 (*hseries2)[
k] = (*work)[
l];
754 for(
k=
j-2;
k>=0;
k--)
767#if defined(HAVE_FLINT) && (__FLINT_RELEASE >= 20503)
769 fmpq_mpoly_ctx_t ctx;
770 convSingRFlintR(ctx,Qt);
773 di2=Flint_Divide_MP(di1,0,o_t,0,ctx,Qt);
774 if (di2==
NULL)
break;
789 if (dummy!=Di1)
break;
802 if ((modul_weight!=
NULL)&&(modul_weight->
compare(0)!=0))
805 Print(
"module weights:%s\n",
s);
812 if (hseries==
NULL) di=0;
824 Print(
"// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1,
mu);
826 Print(
"// dimension (affine) = 0\n// degree (affine) = %d\n",
mu);
829 Print(
"// dimension (local) = %d\n// multiplicity = %d\n", di,
mu);
841 Qt->block0 = (
int *)
omAlloc0(3 *
sizeof(
int *));
842 Qt->block1 = (
int *)
omAlloc0(3 *
sizeof(
int *));
872 if ((modulweight!=
NULL)&&(modulweight->
compare(0)!=0))
875 Print(
"module weights:%s\n",
s);
902 while ((
j >= 0) && (I->m[
j] ==
NULL))
931 if(JCount != ObCount)
936 for(
i = 0;
i < JCount;
i++)
987 if(JCount != ObCount)
997 for(
i = 0;
i< JCount;
i++)
1021 int orbCount = idorb.size();
1047 for(
i = 1;
i < orbCount;
i++)
1068 dtrp = trInd - degp;
1097 int OrbCount = idorb.size();
1104 for(
i = 1;
i < OrbCount;
i++)
1129 int OrbCount = idorb.size();
1130 int dtr=0;
int IwCount, ObCount;
1135 for(
i = 1;
i < OrbCount;
i++)
1158 for(
i = 1;
i < OrbCount;
i++)
1171 for(
i = 1;
i < OrbCount;
i++)
1226 for(
k = ICount - 1;
k >=1;
k--)
1228 for(
i = 0;
i <
k;
i++)
1250 poly smon =
p_One(r);
1254 int *e=(
int *)
omAlloc((r->N+1)*
sizeof(
int));
1255 int *
s=(
int *)
omAlloc0((r->N+1)*
sizeof(
int));
1258 for(
j = 1;
j <= cnt;
j++)
1285 int *e = (
int *)
omAlloc((r->N+1)*
sizeof(
int));
1286 int *
s=(
int *)
omAlloc0((r->N+1)*
sizeof(
int));
1295 for(
j = (cnt+1);
j < (r->N+1);
j++)
1310static void TwordMap(poly
p, poly
w,
int lV,
int d, ideal Jwi,
bool &flag)
1326 for(
i = 0;
i <= d - 1;
i++)
1371static ideal
colonIdeal(ideal S, poly
w,
int lV, ideal Jwi,
int trunDegHs)
1386 if(trunDegHs !=0 && d >= trunDegHs)
1393 for(
i = 0;
i < SCount;
i++)
1429 PrintS(
"Hilbert Series:\n 0\n");
1432 int (*POS)(ideal, poly, std::vector<ideal>, std::vector<poly>, int, int);
1435 Print(
"\nTruncation degree = %d\n",trunDegHs);
1444 WerrorS(
"wrong input: it is not an infinitely gen. case");
1453 std::vector<ideal > idorb;
1454 std::vector< poly > polist;
1456 ideal orb_init =
idInit(1, 1);
1457 idorb.push_back(orb_init);
1461 std::vector< std::vector<int> > posMat;
1462 std::vector<int> posRow(lV,0);
1466 unsigned long lpcnt = 0;
1471 while(lpcnt < idorb.size())
1475 if(lpcnt >= 1 &&
idIs0(idorb[lpcnt]) ==
FALSE)
1492 for(is = 1; is <= lV; is++)
1513 ps = (*POS)(Jwi, wi, idorb, polist, trInd, trunDegHs);
1517 posRow[is-1] = idorb.size();
1519 idorb.push_back(Jwi);
1520 polist.push_back(wi);
1529 posMat.push_back(posRow);
1530 posRow.resize(lV,0);
1535 Print(
"\nlength of the Orbit = %d", lO);
1540 Print(
"words description of the Orbit: \n");
1541 for(is = 0; is < lO; is++)
1547 PrintS(
"\nmaximal degree, #(sum_j R(w,w_j))");
1549 for(is = 0; is < lO; is++)
1551 if(
idIs0(idorb[is]))
1562 for(is = idorb.size()-1; is >= 0; is--)
1566 for(is = polist.size()-1; is >= 0; is--)
1574 int adjMatrix[lO][lO];
1575 memset(adjMatrix, 0, lO*lO*
sizeof(
int));
1576 int rowCount, colCount;
1580 for(rowCount = 0; rowCount < lO; rowCount++)
1582 for(colCount = 0; colCount < lV; colCount++)
1584 tm = posMat[rowCount][colCount];
1585 adjMatrix[rowCount][tm] = adjMatrix[rowCount][tm] + 1;
1596 tt=(
char**)
omAlloc(
sizeof(
char*));
1602 tt=(
char**)
omalloc(lV*
sizeof(
char*));
1603 for(is = 0; is < lV; is++)
1605 tt[is] = (
char*)
omAlloc(7*
sizeof(
char));
1606 snprintf (tt[is],7,
"t%d", is+1);
1613 char** xx = (
char**)
omAlloc(
sizeof(
char*));
1626 for(rowCount = 0; rowCount < lO; rowCount++)
1628 for(colCount = 0; colCount < lO; colCount++)
1630 if(adjMatrix[rowCount][colCount] != 0)
1632 MATELEM(mR, rowCount + 1, colCount + 1) =
p_ISet(adjMatrix[rowCount][colCount],
R);
1640 for(rowCount = 0; rowCount < lO; rowCount++)
1642 for(colCount = 0; colCount < lV; colCount++)
1647 MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1)=
p_Add_q(rc,
MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1),
R);
1652 for(rowCount = 0; rowCount < lO; rowCount++)
1654 if(C[rowCount] != 0)
1668 PrintS(
"\nlinear system:\n");
1671 for(rowCount = 0; rowCount < lO; rowCount++)
1673 Print(
"H(%d) = ", rowCount+1);
1674 for(colCount = 0; colCount < lV; colCount++)
1679 Print(
"H(%d) + ", posMat[rowCount][colCount] + 1);
1681 Print(
" %d\n", C[rowCount] );
1683 PrintS(
"where H(1) represents the series corresp. to input ideal\n");
1684 PrintS(
"and i^th summand in the rhs of an eqn. is according\n");
1685 PrintS(
"to the right colon map corresp. to the i^th variable\n");
1689 for(rowCount = 0; rowCount < lO; rowCount++)
1691 Print(
"H(%d) = ", rowCount+1);
1692 for(colCount = 0; colCount < lV; colCount++)
1697 Print(
"H(%d) + ", posMat[rowCount][colCount] + 1);
1699 Print(
" %d\n", C[rowCount] );
1701 PrintS(
"where H(1) represents the series corresp. to input ideal\n");
1733 Print(
"Hilbert series:");
1742 for(is = lV-1; is >= 0; is--)
1791 for(
int i=src->N;
i>0;
i--)
1808#if defined(__APPLE__) || defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__CYGWIN__)
1809static int compare_rp(
void *arg,
const void *pp1,
const void *pp2)
1811static int compare_rp(
const void *pp1,
const void *pp2,
void* arg)
1814 poly p1=*(poly*)pp1;
1815 poly p2=*(poly*)pp2;
1817 for(
int i=src->N;
i>0;
i--)
1821 if(e1<e2)
return -1;
1829 poly p1=*(poly*)pp1;
1830 poly p2=*(poly*)pp2;
1835 if(e1<e2)
return -1;
1844 while(id->m[
k]==
NULL)
k--;
1846 long *sev=(
long*)
omAlloc0(kk*
sizeof(
long));
1847 BOOLEAN only_lm=r->cf->has_simple_Alloc;
1850 for (
int i=
k;
i>=0;
i--)
1858 for (
int i=
k;
i>=0;
i--)
1865 for (
int i=
k;
i>=0;
i--)
1872 for (
int i=0;
i<
k;
i++)
1878 for (
int j=
i+1;
j<=
k;
j++)
1898 for (
int i=0;
i<
k;
i++)
1904 for (
int j=
i+1;
j<=
k;
j++)
1937 int*
exp=(
int*)
omAlloc((src->N+1)*
sizeof(
int));
1943 for(
int j=src->N;
j>0;
j--)
1945 int w=(*wdegree)[
j-1];
1948 WerrorS(
"weights must be positive");
1965 int *exp_q=(
int*)
omAlloc((src->N+1)*
sizeof(
int));
1967 for (
int i=1;
i<r;
i++)
1970 for(
int ii=src->N;ii>0;ii--)
1973 for(
int ii=0;ii<
i;ii++)
1981 for (
int ii=
IDELEMS(J)-1;ii>=0;ii--)
2045 #if defined(__APPLE__) || defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__CYGWIN__)
2046 qsort_r(AA->m,
IDELEMS(AA),
sizeof(poly),src,compare_rp);
2048 qsort_r(AA->m,
IDELEMS(AA),
sizeof(poly),compare_rp,src);
2067 for(
int i=1;
i<=rk;
i++)
2071 for(
int ii=0;ii<
IDELEMS(AA);ii++)
2073 if (AA->m[ii]!=
NULL)
2101 int sh=(*shifts)[
i-1]-
m;
2128 if((
l==0)||(
l<=-INT_MAX)||(
l>INT_MAX))
2132 else (*ss)[
i]=(int)
l;
2159 while(
prod<(1<<15) && (a>1))
2165 if (a==1)
b=(1<<15);
2203 int w_max=0,w_min=0;
2206 w_max=module_w->
max_in();
2207 w_min=module_w->
min_in();
2209 for(
int c=1;c<=
A->rank;c++)
2217 if ((module_w==
NULL) || ((*module_w)[c-1]==0)) tmp=
ivAdd(
res,res_c);
2226 (*res)[
res->length()-1]=w_min;
2233 if(modulweight==
NULL)
return 0;
2234 return modulweight->
min_in();
2244 x = (*wdegree)[
i-1];
2260 memcpy(pon, pol,
l *
sizeof(
int64));
2263 for (
i =
x;
i <
l;
i++)
2265 #ifndef __SIZEOF_INT128__
2273 __int128 t2=pol[
i -
x];
2275 if ((t>=LONG_MIN)&&(t<=LONG_MAX)) pon[
i]=t;
2279 for (
i =
l;
i < ln;
i++)
2281 #ifndef __SIZEOF_INT128__
2286 __int128 t= -pol[
i -
x];
2287 if ((t>=LONG_MIN)&&(t<=LONG_MAX)) pon[
i]=t;
2294 for (
i =
l;
i <
x;
i++)
2296 for (
i =
x;
i < ln;
i++)
2297 pon[
i] = -pol[
i -
x];
2304 int l = lp,
x,
i,
j;
2308 for (
i = Nv;
i>0;
i--)
2310 x = pure[var[
i + 1]];
2316 for (
i = 0;
i <
l;
i++)
2318 #ifndef __SIZEOF_INT128__
2328 if ((t>=LONG_MIN)&&(t<=LONG_MAX)) pl[
i+
j]=t;
2336 for (
i = 0;
i <
l;
i++)
2338 #ifndef __SIZEOF_INT128__
2348 if ((t>=LONG_MIN)&&(t<=LONG_MAX)) pl[
i+
j]=t;
2363 for (
i = Nvar;
i>0;
i--)
2366 for (
j = 0;
j < Nstc;
j++)
2378 WerrorS(
"internal arrays too big");
2390 for (
x =
Ql[
j];
x < z;
x++)
2400 int Nvar,
int64 *pol,
int Lpol)
2402 int iv = Nvar -1, ln, a, a0, a1,
b,
i;
2415 hStepS(sn, Nstc, var, Nvar, &a, &
x);
2421 x = pure[var[Nvar]];
2439 hStepS(sn, Nstc, var, Nvar, &a, &
x);
2440 hElimS(sn, &
b, a0, a, var, iv);
2442 hPure(sn, a0, &a1, var, iv, pn, &
i);
2453 x = pure[var[Nvar]];
2470 int i,
j,
k,
l, ii, mw;
2509 if (modulweight !=
NULL)
2510 j = (*modulweight)[mc-1]-mw;
2545 while ((
i > 0) && ((*
Qpol)[
i - 1] == 0))
2553 for (ii=0; ii<
k; ii++)
2554 (*work)[ii] = (*hseries1)[ii];
2555 if (hseries1 !=
NULL)
2562 (*hseries1)[
i +
j - 1] += (*Qpol)[
i - 1];
2581 while ((*hseries1)[
l-2]==0)
l--;
2585 for (ii=
l-2; ii>=0; ii--)
2586 (*work)[ii] = (*hseries1)[ii];
2590 (*hseries1)[
l-1] = mw;
2645 for(
int d=0;d<
b->rows()-1;d++)
2717 for(
int i=0;
i<h1->cols();
i++)
2727 hseries2 = hseries1;
2732 if ((
l == 1) &&(
mu == 0))
#define BIMATELEM(M, I, J)
const CanonicalForm CFMap CFMap & N
CanonicalForm convSingPFactoryP(poly p, const ring r)
poly convFactoryPSingP(const CanonicalForm &f, const ring r)
int compare(const intvec *o) const
char * ivString(int not_mat=1, int spaces=0, int dim=2) const
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
static FORCE_INLINE number n_Param(const int iParameter, const coeffs r)
return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1....
static FORCE_INLINE long n_Int(number &n, const coeffs r)
conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 ....
@ n_Q
rational (GMP) numbers
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
const CanonicalForm int s
const CanonicalForm int const CFList const Variable & y
void FACTORY_PUBLIC prune(Variable &alpha)
static int max(int a, int b)
VAR void(* WerrorS_callback)(const char *s)
void WerrorS(const char *s)
This file is work in progress and currently not part of the official Singular.
void scPrintDegree(int co, int mu)
static void idInsertMonomial(ideal I, poly p)
static int comapreMonoIdBases_IG_Case(ideal J, int JCount, ideal Ob, int ObCount)
poly hBIV2Poly(bigintmat *b, const ring Qt, const coeffs biv_cf)
static void rouneslice(ideal I, ideal S, poly q, poly x, int &prune, int &moreprune, int &steps, int &NNN, mpz_ptr &hilbertcoef, int *&hilbpower)
poly hFirstSeries0m(ideal A, ideal Q, intvec *wdegree, intvec *shifts, const ring src, const ring Qt)
static poly hilbert_series(ideal A, const ring src, const intvec *wdegree, const ring Qt)
poly hFirstSeries0p(ideal A, ideal Q, intvec *wdegree, const ring src, const ring Qt)
static poly SqFree(ideal I)
static void idAddMon(ideal I, ideal p)
static int comapreMonoIdBases(ideal J, ideal Ob)
static void TwordMap(poly p, poly w, int lV, int d, ideal Jwi, bool &flag)
static poly ChooseP(ideal I)
static poly deleteInMon(poly w, int i, int lV, const ring r)
intvec * hSecondSeries(intvec *hseries1)
static void hLastHilb(scmon pure, int Nv, varset var, int64 *pol, int lp)
static int CountOnIdUptoTruncationIndex(ideal I, int tr)
static poly ChoosePJL(ideal I)
static int monCompare(const void *m, const void *n)
static void hHilbEst(scfmon stc, int Nstc, varset var, int Nvar)
static int positionInOrbitTruncationCase(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int, int trunDegHs)
static intvec * hSeries(ideal S, intvec *modulweight, intvec *wdegree, ideal Q)
static poly LCMmon(ideal I)
void HilbertSeries_OrbitData(ideal S, int lV, bool IG_CASE, bool mgrad, bool odp, int trunDegHs)
static ideal colonIdeal(ideal S, poly w, int lV, ideal Jwi, int trunDegHs)
intvec * hFirstSeries(ideal A, intvec *module_w, ideal Q, intvec *wdegree)
static int hMinModulweight(intvec *modulweight)
static poly shiftInMon(poly p, int i, int lV, const ring r)
static ideal getModuleComp(ideal A, int c, const ring src)
poly hFirst2Second(poly h, const ring Qt, int &co)
intvec * hFirstSeries0(ideal A, ideal Q, intvec *wdegree, const ring src, const ring Qt)
static void hPrintHilb(poly hseries, const ring Qt, intvec *modul_weight)
static poly ChoosePVar(ideal I)
static int positionInOrbit_FG_Case(ideal I, poly, std::vector< ideal > idorb, std::vector< poly >, int, int)
static void sortMonoIdeal_pCompare(ideal I)
bigintmat * hPoly2BIV(poly h, const ring Qt, const coeffs biv_cf)
static ideal SortByDeg(ideal I)
static bool IsIn(poly p, ideal I)
static void eulerchar(ideal I, int variables, mpz_ptr ec)
ideal RightColonOperation(ideal S, poly w, int lV)
static void hHilbStep(scmon pure, scfmon stc, int Nstc, varset var, int Nvar, int64 *pol, int Lpol)
bigintmat * hFirstSeries0b(ideal I, ideal Q, intvec *wdegree, intvec *shifts, const ring src, const coeffs biv_cf)
static void hWDegree(intvec *wdegree)
static BOOLEAN p_Div_hi(poly p, const int *exp_q, const ring src)
bigintmat * hSecondSeries0b(ideal I, ideal Q, intvec *wdegree, intvec *shifts, const ring src, const coeffs biv_cf)
static int positionInOrbit_IG_Case(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int trInd, int)
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
static poly SearchP(ideal I)
searches for a monomial of degree d>=2 and divides it by a variable (result monomial of deg d-1)
static int64 * hAddHilb(int Nv, int x, int64 *pol, int *lp)
static ideal minimalMonomialGenSet(ideal I)
intvec * hFirstSeries1(ideal S, intvec *modulweight, ideal Q, intvec *wdegree)
ideal idQuotMon(ideal Iorig, ideal p)
static void SortByDeg_p(ideal I, poly p)
void scDegree(ideal S, intvec *modulweight, ideal Q)
static bool JustVar(ideal I)
void hLookSeries(ideal S, intvec *modulweight, ideal Q, intvec *wdegree)
static void id_DelDiv_hi(ideal id, BOOLEAN *bad, const ring r)
static int compare_rp_currRing(const void *pp1, const void *pp2)
void hComp(scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
void hLex2S(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
void hKill(monf xmem, int Nvar)
void hElimS(scfmon stc, int *e1, int a2, int e2, varset var, int Nvar)
void hLexS(scfmon stc, int Nstc, varset var, int Nvar)
void hDelete(scfmon ev, int ev_length)
scfmon hGetmem(int lm, scfmon old, monp monmem)
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
void hStepS(scfmon stc, int Nstc, varset var, int Nvar, int *a, int *x)
void hStaircase(scfmon stc, int *Nstc, varset var, int Nvar)
void hOrdSupp(scfmon stc, int Nstc, varset var, int Nvar)
scfmon hInit(ideal S, ideal Q, int *Nexist)
#define idDelete(H)
delete an ideal
BOOLEAN idInsertPoly(ideal h1, poly h2)
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted
ideal id_Copy(ideal h1, const ring r)
copy an ideal
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
intvec * ivAddShift(intvec *a, intvec *b, int s)
intvec * ivAdd(intvec *a, intvec *b)
static void WerrorS_dummy(const char *)
bool unitMatrix(const int n, matrix &unitMat, const ring R)
Creates a new matrix which is the (nxn) unit matrix, and returns true in case of success.
void luDecomp(const matrix aMat, matrix &pMat, matrix &lMat, matrix &uMat, const ring R)
LU-decomposition of a given (m x n)-matrix.
bool luSolveViaLUDecomp(const matrix pMat, const matrix lMat, const matrix uMat, const matrix bVec, matrix &xVec, matrix &H)
Solves the linear system A * x = b, where A is an (m x n)-matrix which is given by its LU-decompositi...
void mp_Delete(matrix *a, const ring r)
static matrix mu(matrix A, const ring R)
matrix mp_Sub(matrix a, matrix b, const ring R)
matrix mpNew(int r, int c)
create a r x c zero-matrix
#define MATELEM(mat, i, j)
1-based access to matrix
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
gmp_float exp(const gmp_float &a)
The main handler for Singular numbers which are suitable for Singular polynomials.
#define omFreeSize(addr, size)
#define omRealloc(addr, size)
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
poly p_Power(poly p, int i, const ring r)
unsigned long p_GetShortExpVector0(const poly p, const ring r)
poly p_MDivide(poly a, poly b, const ring r)
int p_Compare(const poly a, const poly b, const ring R)
unsigned long p_GetShortExpVector(const poly p, const ring r)
void pEnlargeSet(poly **p, int l, int increment)
unsigned long p_GetShortExpVector1(const poly p, const ring r)
static poly p_Neg(poly p, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
static void p_LmDelete(poly p, const ring r)
static poly p_Mult_q(poly p, poly q, const ring r)
#define p_LmEqual(p1, p2, r)
static void p_SetExpV(poly p, int *ev, const ring r)
static poly pp_Mult_mm(poly p, poly m, const ring r)
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
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
static void p_Setm(poly p, const ring r)
static number p_SetCoeff(poly p, number n, ring r)
static poly p_Head(const poly p, const ring r)
copy the (leading) term of p
static BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
static poly p_New(const ring, omBin bin)
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
static void p_Delete(poly *p, const ring r)
static void p_GetExpV(poly p, int *ev, const ring r)
void p_Write0(poly p, ring lmRing, ring tailRing)
static void p_LmFree(poly p, ring)
static poly p_Init(const ring r, omBin bin)
static poly p_Copy(poly p, const ring r)
returns a copy of p
static long p_Totaldegree(poly p, const ring r)
void rChangeCurrRing(ring r)
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
#define pLmDivisibleBy(a, b)
like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced
#define pCopy(p)
return a copy of the poly
void StringSetS(const char *st)
void PrintS(const char *s)
void Werror(const char *fmt,...)
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...
ring rDefault(const coeffs cf, int N, char **n, int ord_size, rRingOrder_t *ord, int *block0, int *block1, int **wvhdl, unsigned long bitmask)
static short rVar(const ring r)
#define rVar(r) (r->N)
int status int void size_t count
ideal idInit(int idsize, int rank)
initialise an ideal / module
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
BOOLEAN id_IsModule(ideal A, const ring src)
int idSkipZeroes0(ideal ide)
void id_Delete0(ideal *h, ring r)
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
void id_DelDiv(ideal id, const ring r)
delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., delete id[i], if LT(i) == coeff*mon*L...
ideal id_Mult(ideal h1, ideal h2, const ring R)
h1 * h2 one h_i must be an ideal (with at least one column) the other h_i may be a module (with no co...
ideal id_CopyFirstK(const ideal ide, const int k, const ring r)
copies the first k (>= 1) entries of the given ideal/module and returns these as a new ideal/module (...
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
struct for passing initialization parameters to naInitChar