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)
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--)
737 (*hseries2)[
k] = (*work)[
l];
754 for(
k=
j-2;
k>=0;
k--)
767#if defined(HAVE_FLINT) && (__FLINT_RELEASE >= 20503)
805 Print(
"module weights:%s\n",
s);
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 *));
875 Print(
"module weights:%s\n",
s);
902 while ((
j >= 0) && (
I->m[
j] ==
NULL))
1228 for(
i = 0;
i <
k;
i++)
1258 for(
j = 1;
j <= cnt;
j++)
1285 int *e = (
int *)
omAlloc((r->N+1)*
sizeof(
int));
1295 for(
j = (cnt+1);
j < (r->N+1);
j++)
1326 for(
i = 0;
i <= d - 1;
i++)
1429 PrintS(
"Hilbert Series:\n 0\n");
1444 WerrorS(
"wrong input: it is not an infinitely gen. case");
1453 std::vector<ideal >
idorb;
1454 std::vector< poly >
polist;
1461 std::vector< std::vector<int> >
posMat;
1466 unsigned long lpcnt = 0;
1492 for(is = 1; is <=
lV; is++)
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++)
1562 for(is =
idorb.size()-1; is >= 0; is--)
1566 for(is =
polist.size()-1; is >= 0; is--)
1603 for(is = 0; is <
lV; is++)
1605 tt[is] = (
char*)
omAlloc(7*
sizeof(
char));
1613 char**
xx = (
char**)
omAlloc(
sizeof(
char*));
1668 PrintS(
"\nlinear system:\n");
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");
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__)
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--;
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++)
1943 for(
int j=src->N;
j>0;
j--)
1945 int w=(*wdegree)[
j-1];
1948 WerrorS(
"weights must be positive");
1967 for (
int i=1;
i<r;
i++)
1970 for(
int ii=src->N;
ii>0;
ii--)
2045 #if defined(__APPLE__) || defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__CYGWIN__)
2067 for(
int i=1;
i<=
rk;
i++)
2101 int sh=(*shifts)[
i-1]-
m;
2159 while(
prod<(1<<15) && (a>1))
2165 if (a==1)
b=(1<<15);
2209 for(
int c=1;c<=
A->rank;c++)
2244 x = (*wdegree)[
i-1];
2263 for (
i =
x;
i <
l;
i++)
2265 #ifndef __SIZEOF_INT128__
2281 #ifndef __SIZEOF_INT128__
2294 for (
i =
l;
i <
x;
i++)
2308 for (
i =
Nv;
i>0;
i--)
2316 for (
i = 0;
i <
l;
i++)
2318 #ifndef __SIZEOF_INT128__
2336 for (
i = 0;
i <
l;
i++)
2338 #ifndef __SIZEOF_INT128__
2378 WerrorS(
"internal arrays too big");
2390 for (
x =
Ql[
j];
x < z;
x++)
2510 j = (*modulweight)[mc-1]-
mw;
2545 while ((
i > 0) && ((*Qpol)[
i - 1] == 0))
2562 (*hseries1)[
i +
j - 1] += (*Qpol)[
i - 1];
2590 (*hseries1)[
l-1] =
mw;
2645 for(
int d=0;d<
b->rows()-1;d++)
2717 for(
int i=0;
i<
h1->cols();
i++)
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)
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