54 if(modulweight==
NULL)
return 0;
56 for(i=modulweight->
rows()-1;i!=0;i--)
69 for (i = Nvar; i>0; i--)
72 for (j = 0; j < Nstc; j++)
84 WerrorS(
"internal arrays too big");
87 p = (
int *)
omAlloc((
unsigned long)z *
sizeof(int));
91 memcpy(p,
Qpol[j],
Ql[j] *
sizeof(
int));
96 for (x =
Ql[j]; x < z; x++)
111 memcpy(pon, pol, l *
sizeof(
int));
114 for (i = x; i <
l; i++)
118 if ((t>=INT_MIN)&&(t<=INT_MAX)) pon[
i]=t;
121 for (i = l; i < ln; i++)
124 if ((t>=INT_MIN)&&(t<=INT_MAX)) pon[
i]=t;
130 for (i = l; i <
x; i++)
132 for (i = x; i < ln; i++)
133 pon[i] = -pol[i - x];
144 for (i = Nv; i>0; i--)
146 x = pure[var[i + 1]];
152 for (i = 0; i <
l; i++)
157 if ((t>=INT_MIN)&&(t<=INT_MAX)) pl[i+
j]=t;
164 for (i = 0; i <
l; i++)
169 if ((t>=INT_MIN)&&(t<=INT_MAX)) pl[i+
j]=t;
179 int Nvar,
int *pol,
int Lpol)
181 int iv = Nvar -1, ln, a, a0, a1,
b,
i;
194 hStepS(sn, Nstc, var, Nvar, &a, &x);
218 hStepS(sn, Nstc, var, Nvar, &a, &x);
219 hElimS(sn, &b, a0, a, var, iv);
221 hPure(sn, a0, &a1, var, iv, pn, &i);
227 pon =
hAddHilb(iv, x - x0, pol, &ln);
234 pon =
hAddHilb(iv, x - x0, pol, &ln);
268 static bool idDegSortTest(ideal I)
279 WerrorS(
"Ideal is not deg sorted!!");
366 for(j =
IDELEMS(I)-1; j>=i+1;j--)
377 for(j =
IDELEMS(I)-1; j>=i+2;j--)
399 for(i = 0; i<=
IDELEMS(I)-1;i++)
460 for(i = 0; i<=
IDELEMS(res)-1; i++)
488 for(j=
IDELEMS(I)-1;(j>=0)&&(flag);j--)
513 static poly ChoosePXL(ideal I)
517 for(i =
IDELEMS(I)-1; (i>=0) && (dummy == 0); i--)
519 for(j = 1; (j<=
currRing->N) && (dummy == 0); j++)
548 static poly ChoosePXF(ideal I)
552 for(i =0 ; (i<=
IDELEMS(I)-1) && (dummy == 0); i++)
554 for(j = 1; (j<=
currRing->N) && (dummy == 0); j++)
583 static poly ChoosePOL(ideal I)
615 static poly ChoosePOF(ideal I)
619 for(i = 0 ;i<=
IDELEMS(I)-1;i++)
647 static poly ChoosePVL(ideal I)
652 for(i =
IDELEMS(I)-1;(i>=0) && (flag);i--)
655 for(j=1;(j<=
currRing->N) && (flag);j++)
677 static poly ChoosePVF(ideal I)
682 for(i = 0;(i<=
IDELEMS(I)-1) && (flag);i++)
685 for(j=1;(j<=
currRing->N) && (flag);j++)
711 for(i =
IDELEMS(I)-1;(i>=0) && (flag);i--)
714 for(j=1;(j<=
currRing->N) && (flag);j++)
736 static poly ChoosePJF(ideal I)
741 for(i = 0;(i<=
IDELEMS(I)-1) && (flag);i++)
744 for(j=1;(j<=
currRing->N) && (flag);j++)
848 if((variables % 2) == 0)
849 mpz_set_ui(dummy, 1);
851 mpz_set_si(dummy, -1);
852 mpz_add(ec, ec, dummy);
865 int i,howmanyvarinp = 0;
873 eulerchar(Ip, variables-howmanyvarinp, ec);
885 poly notsqrfree =
NULL;
890 for(i=
IDELEMS(I)-1;(i>=0)&&(flag);i--)
892 for(j=1;(j<=
currRing->N)&&(flag);j++)
902 if(notsqrfree !=
NULL)
933 for(j = 1;(j<=
currRing->N) &&(flag);j++)
975 void rouneslice(ideal I, ideal S, poly q, poly
x,
int &
prune,
int &moreprune,
int &steps,
int &NNN, mpz_ptr &hilbertcoef,
int* &hilbpower)
1072 mpz_ptr ec_ptr = ec;
1077 hilbertcoef = (mpz_ptr)
omAlloc((NNN+1)*
sizeof(mpz_t));
1078 hilbpower = (
int*)
omAlloc((NNN+1)*
sizeof(int));
1079 mpz_init_set( &hilbertcoef[NNN], ec);
1086 for(i = 0;(i<NNN)&&(flag == FALSE)&&(p_Totaldegree(q,currRing)>=hilbpower[
i]);i++)
1091 mpz_add(&hilbertcoef[i],&hilbertcoef[i],ec_ptr);
1096 hilbertcoef = (mpz_ptr)
omRealloc(hilbertcoef, (NNN+1)*
sizeof(mpz_t));
1097 hilbpower = (
int*)
omRealloc(hilbpower, (NNN+1)*
sizeof(int));
1098 mpz_init(&hilbertcoef[NNN]);
1099 for(j = NNN; j>
i; j--)
1101 mpz_set(&hilbertcoef[j],&hilbertcoef[j-1]);
1102 hilbpower[
j] = hilbpower[j-1];
1104 mpz_set( &hilbertcoef[i], ec);
1122 rouneslice(Ip, Sp, pq, x, prune, moreprune, steps, NNN, hilbertcoef,hilbpower);
1135 int steps = 0,
prune = 0, moreprune = 0;
1136 mpz_ptr hilbertcoef;
1152 rouneslice(I,S,q,X->m[0],
prune, moreprune, steps, NNN, hilbertcoef, hilbpower);
1158 printf(
"\n// %8d t^0",1);
1159 for(i = 0; i<NNN; i++)
1161 if(mpz_sgn(&hilbertcoef[i])!=0)
1163 gmp_printf(
"\n// %8Zd t^%d",&hilbertcoef[i],hilbpower[i]);
1167 omFreeSize(hilbertcoef, (NNN)*
sizeof(mpz_t));
1174 int ,
intvec *wdegree, ideal
Q, ring tailRing)
1181 int i,
j,
k,
l, ii, mw;
1192 if (wdegree ==
NULL)
1227 if (modulweight !=
NULL)
1228 j = (*modulweight)[mc-1]-mw;
1233 for (i =
hNvar; i>=0; i--)
1263 while ((i > 0) && ((*Qpol)[i - 1] == 0))
1271 for (ii=0; ii<
k; ii++)
1272 (*work)[ii] = (*hseries1)[ii];
1273 if (hseries1 !=
NULL)
1280 (*hseries1)[i + j - 1] += (*Qpol)[i - 1];
1299 while ((*hseries1)[l-2]==0) l--;
1303 for (ii=l-2; ii>=0; ii--)
1304 (*work)[ii] = (*hseries1)[ii];
1308 (*hseries1)[l-1] = mw;
1310 for (i = 0; i <= (
currRing->N); i++)
1333 return hSeries(S, modulweight, 0, wdegree, Q, tailRing);
1341 intvec *hseries1=
hSeries(S, modulweight, 1, wdegree, Q, tailRing);
1351 if (hseries1 ==
NULL)
1353 work =
new intvec(hseries1);
1354 k = l = work->
length()-1;
1356 for (i = k-1; i >= 0; i--)
1360 if ((s != 0) || (k == 1))
1365 for (i = k-1; i >= 0; i--)
1373 hseries2 =
new intvec(k+1);
1374 for (i = k-1; i >= 0; i--)
1375 (*hseries2)[
i] = (*work)[
i];
1376 (*hseries2)[
k] = (*work)[
l];
1393 for(k=j-2; k>=0; k--)
1402 if (hseries ==
NULL)
1406 for (i = 0; i <
l; i++)
1411 Print(
"// %8d t^%d\n", j, i+k);
1428 const int l = hseries1->
length()-1;
1437 if ((l == 1) &&(mu == 0))
1465 while ((j >= 0) && (I->m[j] ==
NULL))
1494 if(JCount != ObCount)
1499 for(i = 0; i < JCount; i++)
1550 if(JCount != ObCount)
1560 for(i = 0; i< JCount; i++)
1584 int orbCount = idorb.size();
1610 for(i = 1;i < orbCount; i++)
1631 dtrp = trInd - degp;
1660 int OrbCount = idorb.size();
1667 for(i = 1; i < OrbCount; i++)
1692 int OrbCount = idorb.size();
1693 int dtr=0;
int IwCount, ObCount;
1698 for(i = 1; i < OrbCount; i++)
1721 for(i = 1; i < OrbCount; i++)
1734 for(i = 1; i < OrbCount; i++)
1789 for(k = ICount - 1; k >=1; k--)
1791 for(i = 0; i <
k; i++)
1813 poly smon =
p_One(r);
1817 int *e=(
int *)
omAlloc((r->N+1)*
sizeof(int));
1818 int *
s=(
int *)
omAlloc0((r->N+1)*
sizeof(int));
1821 for(j = 1; j <= cnt; j++)
1848 int *e = (
int *)
omAlloc((r->N+1)*
sizeof(int));
1849 int *
s=(
int *)
omAlloc0((r->N+1)*
sizeof(int));
1858 for(j = (cnt+1); j < (r->N+1); j++)
1873 static void TwordMap(poly
p, poly
w,
int lV,
int d, ideal Jwi,
bool &flag)
1889 for(i = 0;i <= d - 1; i++)
1934 static ideal
colonIdeal(ideal S, poly
w,
int lV, ideal Jwi,
int trunDegHs)
1949 if(trunDegHs !=0 && d >= trunDegHs)
1956 for(i = 0; i < SCount; i++)
1958 TwordMap(S->m[i], w, lV, d, Jwi, flag);
1985 PrintS(
"Hilbert Series:\n 0\n");
1988 int (*POS)(ideal, poly, std::vector<ideal>, std::vector<poly>, int, int);
1991 Print(
"\nTruncation degree = %d\n",trunDegHs);
2000 WerrorS(
"wrong input: it is not an infinitely gen. case");
2009 std::vector<ideal > idorb;
2010 std::vector< poly > polist;
2012 ideal orb_init =
idInit(1, 1);
2013 idorb.push_back(orb_init);
2017 std::vector< std::vector<int> > posMat;
2018 std::vector<int> posRow(lV,0);
2027 while(lpcnt < idorb.size())
2031 if(lpcnt >= 1 &&
idIs0(idorb[lpcnt]) ==
FALSE)
2048 for(is = 1; is <= lV; is++)
2069 ps = (*POS)(Jwi, wi, idorb, polist, trInd, trunDegHs);
2073 posRow[is-1] = idorb.size();
2075 idorb.push_back(Jwi);
2076 polist.push_back(wi);
2085 posMat.push_back(posRow);
2086 posRow.resize(lV,0);
2091 Print(
"\nlength of the Orbit = %d", lO);
2096 Print(
"words description of the Orbit: \n");
2097 for(is = 0; is < lO; is++)
2103 PrintS(
"\nmaximal degree, #(sum_j R(w,w_j))");
2105 for(is = 0; is < lO; is++)
2107 if(
idIs0(idorb[is]))
2118 for(is = idorb.size()-1; is >= 0; is--)
2122 for(is = polist.size()-1; is >= 0; is--)
2130 int adjMatrix[lO][lO];
2131 memset(adjMatrix, 0, lO*lO*
sizeof(
int));
2132 int rowCount, colCount;
2136 for(rowCount = 0; rowCount < lO; rowCount++)
2138 for(colCount = 0; colCount < lV; colCount++)
2140 tm = posMat[rowCount][colCount];
2141 adjMatrix[rowCount][tm] = adjMatrix[rowCount][tm] + 1;
2152 tt=(
char**)
omAlloc(
sizeof(
char*));
2158 tt=(
char**)
omalloc(lV*
sizeof(
char*));
2159 for(is = 0; is < lV; is++)
2161 tt[is] = (
char*)
omAlloc(7*
sizeof(
char));
2162 sprintf (tt[is],
"t%d", is+1);
2169 char** xx = (
char**)
omAlloc(
sizeof(
char*));
2182 for(rowCount = 0; rowCount < lO; rowCount++)
2184 for(colCount = 0; colCount < lO; colCount++)
2186 if(adjMatrix[rowCount][colCount] != 0)
2188 MATELEM(mR, rowCount + 1, colCount + 1) =
p_ISet(adjMatrix[rowCount][colCount], R);
2196 for(rowCount = 0; rowCount < lO; rowCount++)
2198 for(colCount = 0; colCount < lV; colCount++)
2203 MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1)=
p_Add_q(rc,
MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1), R);
2208 for(rowCount = 0; rowCount < lO; rowCount++)
2210 if(C[rowCount] != 0)
2224 PrintS(
"\nlinear system:\n");
2227 for(rowCount = 0; rowCount < lO; rowCount++)
2229 Print(
"H(%d) = ", rowCount+1);
2230 for(colCount = 0; colCount < lV; colCount++)
2235 Print(
"H(%d) + ", posMat[rowCount][colCount] + 1);
2237 Print(
" %d\n", C[rowCount] );
2239 PrintS(
"where H(1) represents the series corresp. to input ideal\n");
2240 PrintS(
"and i^th summand in the rhs of an eqn. is according\n");
2241 PrintS(
"to the right colon map corresp. to the i^th variable\n");
2245 for(rowCount = 0; rowCount < lO; rowCount++)
2247 Print(
"H(%d) = ", rowCount+1);
2248 for(colCount = 0; colCount < lV; colCount++)
2253 Print(
"H(%d) + ", posMat[rowCount][colCount] + 1);
2255 Print(
" %d\n", C[rowCount] );
2257 PrintS(
"where H(1) represents the series corresp. to input ideal\n");
2272 luDecomp(gMat, pMat, lMat, uMat, R);
2289 Print(
"Hilbert series:");
2298 for(is = lV-1; is >= 0; is--)
int status int void size_t count
ideal idQuotMon(ideal Iorig, ideal p)
void rouneslice(ideal I, ideal S, poly q, poly x, int &prune, int &moreprune, int &steps, int &NNN, mpz_ptr &hilbertcoef, int *&hilbpower)
#define id_TestTail(A, lR, tR)
const CanonicalForm int s
void hLexS(scfmon stc, int Nstc, varset var, int Nvar)
const CanonicalForm int const CFList const Variable & y
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...
static poly ChoosePVar(ideal I)
void mu(int **points, int sizePoints)
scfmon hGetmem(int lm, scfmon old, monp monmem)
void hElimS(scfmon stc, int *e1, int a2, int e2, varset var, int Nvar)
#define idDelete(H)
delete an ideal
gmp_float exp(const gmp_float &a)
void scPrintDegree(int co, int mu)
static void hHilbStep(scmon pure, scfmon stc, int Nstc, varset var, int Nvar, int *pol, int Lpol)
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
void HilbertSeries_OrbitData(ideal S, int lV, bool IG_CASE, bool mgrad, bool odp, int trunDegHs)
ideal id_Copy(ideal h1, const ring r)
copy an ideal
static int positionInOrbitTruncationCase(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int, int trunDegHs)
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
static void hLastHilb(scmon pure, int Nv, varset var, int *pol, int lp)
static ideal minimalMonomialGenSet(ideal I)
static void p_GetExpV(poly p, int *ev, const ring r)
#define omFreeSize(addr, size)
static void idAddMon(ideal I, ideal p)
static short rVar(const ring r)
#define rVar(r) (r->N)
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
static bool JustVar(ideal I)
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.
static bool IsIn(poly p, ideal I)
static poly pp_Mult_mm(poly p, poly m, const ring r)
static long p_Totaldegree(poly p, const ring r)
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
void WerrorS(const char *s)
static void TwordMap(poly p, poly w, int lV, int d, ideal Jwi, bool &flag)
#define pLmDivisibleBy(a, b)
like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
static number p_SetCoeff(poly p, number n, ring r)
static poly LCMmon(ideal I)
intvec * hHstdSeries(ideal S, intvec *modulweight, intvec *wdegree, ideal Q, ring tailRing)
static void p_SetExpV(poly p, int *ev, const ring r)
static poly p_Copy(poly p, const ring r)
returns a copy of p
void prune(Variable &alpha)
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..n_NumberOfParameters(...)
void hDelete(scfmon ev, int ev_length)
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
void luDecomp(const matrix aMat, matrix &pMat, matrix &lMat, matrix &uMat, const ring R)
LU-decomposition of a given (m x n)-matrix.
static poly p_Head(poly p, const ring r)
Coefficient rings, fields and other domains suitable for Singular polynomials.
void hOrdSupp(scfmon stc, int Nstc, varset var, int Nvar)
const CanonicalForm CFMap CFMap & N
void hKill(monf xmem, int Nvar)
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent : the integer VarOffset encodes:
static poly ChoosePJL(ideal I)
static int * hAddHilb(int Nv, int x, int *pol, int *lp)
The main handler for Singular numbers which are suitable for Singular polynomials.
static void hWDegree(intvec *wdegree)
void StringSetS(const char *st)
static int positionInOrbit_FG_Case(ideal I, poly, std::vector< ideal > idorb, std::vector< poly >, int, int)
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
static int positionInOrbit_IG_Case(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int trInd, int trunDegHs)
void hStaircase(scfmon stc, int *Nstc, varset var, int Nvar)
void sortMonoIdeal_pCompare(ideal I)
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
BOOLEAN idInsertPoly(ideal h1, poly h2)
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted ...
static int comapreMonoIdBases(ideal J, ideal Ob)
static intvec * hSeries(ideal S, intvec *modulweight, int, intvec *wdegree, ideal Q, ring tailRing)
struct for passing initialization parameters to naInitChar
int p_Compare(const poly a, const poly b, const ring R)
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
void hLex2S(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
void PrintS(const char *s)
static void SortByDeg_p(ideal I, poly p)
!!!!!!!!!!!!!!!!!!!! Just for Monomial Ideals !!!!!!!!!!!!!!!!!!!!!!!!!!!!
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
void mp_Delete(matrix *a, const ring r)
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
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 int monCompare(const void *m, const void *n)
void rChangeCurrRing(ring r)
matrix mpNew(int r, int c)
create a r x c zero-matrix
static int CountOnIdUptoTruncationIndex(ideal I, int tr)
static void p_Delete(poly *p, const ring r)
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 idInit(int idsize, int rank)
initialise an ideal / module
#define p_LmEqual(p1, p2, r)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent : VarOffset encodes the position in p->exp
ideal RightColonOperation(ideal S, poly w, int lV)
static ideal SortByDeg(ideal I)
void pEnlargeSet(poly **p, int l, int increment)
void hStepS(scfmon stc, int Nstc, varset var, int Nvar, int *a, int *x)
intvec * hSecondSeries(intvec *hseries1)
static poly shiftInMon(poly p, int i, int lV, const ring r)
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
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 void p_Setm(poly p, const ring r)
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced ...
poly p_MDivide(poly a, poly b, const ring r)
static poly ChooseP(ideal I)
intvec * hFirstSeries(ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
matrix mp_Sub(matrix a, matrix b, const ring R)
void hLookSeries(ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
static poly p_Add_q(poly p, poly q, const ring r)
static int hMinModulweight(intvec *modulweight)
static int comapreMonoIdBases_IG_Case(ideal J, int JCount, ideal Ob, int ObCount)
static ideal colonIdeal(ideal S, poly w, int lV, ideal Jwi, int trunDegHs)
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
#define omRealloc(addr, size)
void hComp(scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
static poly SqFree(ideal I)
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
scfmon hInit(ideal S, ideal Q, int *Nexist, ring tailRing)
static poly deleteInMon(poly w, int i, int lV, const ring r)
static void idInsertMonomial(ideal I, poly p)
static void hHilbEst(scfmon stc, int Nstc, varset var, int Nvar)
#define pCopy(p)
return a copy of the poly
#define MATELEM(mat, i, j)
static void hPrintHilb(intvec *hseries)
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
static void eulerchar(ideal I, int variables, mpz_ptr ec)