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31 int dn, iv, rad0,
b, c,
x;
44 while(pure[
var[iv]]) iv--;
135 int dn, iv, rad0,
b, c,
x;
172 while(pure[
var[iv]]) iv--;
301 for (iv=(
currRing->N); iv!=0 ; iv--)
315 int dn, iv, rad0,
b, c,
x;
328 for (iv = Nvar; iv!=0; iv--)
364 while(pure[
var[iv]]) iv--;
397 while (sm->nx !=
NULL)
403 if (((*Set)[iv-1] == 0) && (pure[iv] == 0))
424 while (sm->nx !=
NULL)
430 if ((pure[iv] == 1) && ((*Set)[iv-1] == 1))
498 int dn, iv, rad0,
b, c,
x;
511 for (iv = Nvar; iv; iv--)
526 while(pure[
var[iv]]) iv--;
554 int iv = Nvar -1, sum, a, a0, a1,
b,
i;
563 for (
i = Nvar;
i;
i--)
613 if ((i0 > 2) && (
i > 10))
624 int dn, iv, rad0,
b, c,
x;
637 for (iv = Nvar; iv; iv--)
673 while(pure[
var[iv]]) iv--;
813 Print(
"// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1,
mu);
815 Print(
"// dimension (affine) = 0\n// degree (affine) = %d\n",
mu);
818 Print(
"// dimension (local) = %d\n// multiplicity = %d\n", di,
mu);
835 if ((
l == 1) &&(
mu == 0))
844 static void hDegree0(ideal S, ideal
Q,
const ring tailRing)
893 memset(
hpur0, 0, ((r->N) + 1) *
sizeof(
int));
906 if (mc <= 0 ||
hMu < 0)
945 int Nstc,
varset var,
int Nvar,poly hEdge)
947 int iv = Nvar -1,
k =
var[Nvar], a, a0, a1,
b,
i;
959 for (
i = Nvar;
i>0;
i--)
1029 printf(
"\nThis is HC:\n");
1030 for(
int ii=0;ii<=
idElem(S);ii++)
1090 int x,
y=stc[0][Nvar];
1102 int x,
y=stc[0][Nvar];
1115 int i,
j, Istc = Nstc;
1118 for (
i=Nstc-1;
i>=0;
i--)
1123 if(stc[
i][
j] != 0)
break;
1137 for (
i=Nstc-1;
i>=0;
i--)
1139 if (stc[
i] && (stc[
i][Nvar] >=
y))
1169 for (
i=Nvar;
i;
i--)
act[
i] = 0;
1182 scAll(Nvar-1, deg-d);
1192 scAll(Nvar-1, deg-ideg);
1194 }
while (ideg >= 0);
1199 int Ivar, Istc,
i,
j;
1205 for (
i=Nstc-1;
i>=0;
i--)
1207 for (
j=Nvar;
j;
j--){
if(stc[
i][
j])
break; }
1210 for (
i=Nvar;
i;
i--)
act[
i] = 0;
1216 for (
i=Nstc-1;
i>=0;
i--)
if(deg >= stc[
i][1])
return;
1231 if (deg <
x) ideg = deg;
1241 x =
scMax(Nstc, sn, Nvar);
1248 if (ideg < 0)
return;
1250 for (
i=Nstc-1;
i>=0;
i--)
1252 if (ideg < sn[
i][Nvar])
1280 int Ivar, Istc,
i,
j;
1286 ideg =
scMin(Nstc, stc, 1);
1302 x =
scMax(Nstc, sn, Nvar);
1309 if (ideg < 0)
return;
1311 for (
i=Nstc-1;
i>=0;
i--)
1313 if (ideg < sn[
i][Nvar])
1392 if (mv!=
NULL) deg_ei -= (*mv)[
i-1];
1393 if ((deg < 0) || (deg_ei>=0))
1418 #if 0 //-- alternative implementation of scComputeHC
void hStaircase(scfmon stc, int *Nstc, varset var, int Nvar)
int idElem(const ideal F)
count non-zero elements
void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void scDegree(ideal S, intvec *modulweight, ideal Q)
void hElimS(scfmon stc, int *e1, int a2, int e2, varset var, int Nvar)
static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar)
void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge, ring tailRing)
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced
static void hHedgeStep(scmon pure, scfmon stc, int Nstc, varset var, int Nvar, poly hEdge)
static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
const CanonicalForm int const CFList const Variable & y
static void scAllKbase(int Nvar, int ideg, int deg)
#define omGetSpecBin(size)
#define pGetExp(p, i)
Exponent.
void hRadical(scfmon rad, int *Nrad, int Nvar)
static int scRestrict(int &Nstc, scfmon stc, int Nvar)
ideal scKBase(int deg, ideal s, ideal Q, intvec *mv)
static ideal scIdKbase(poly q, const int rank)
int scMultInt(ideal S, ideal Q)
scfmon hGetmem(int lm, scfmon old, monp monmem)
static void scInKbase(scfmon stc, int Nstc, int Nvar)
void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
int scDimInt(ideal S, ideal Q)
static void hHedge(poly hEdge)
void mu(int **points, int sizePoints)
static unsigned pLength(poly a)
static void scAll(int Nvar, int deg)
static int scMin(int i, scfmon stc, int Nvar)
static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar)
#define omFreeSize(addr, size)
static void hCheckIndep(scmon pure)
static void hDegree0(ideal S, ideal Q, const ring tailRing)
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
static BOOLEAN rField_is_Ring(const ring r)
void hComp(scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
void hKill(monf xmem, int Nvar)
#define pInit()
allocates a new monomial and initializes everything to 0
void hStepR(scfmon rad, int Nrad, varset var, int Nvar, int *a)
void hDelete(scfmon ev, int ev_length)
void hStepS(scfmon stc, int Nstc, varset var, int Nvar, int *a, int *x)
void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void hLex2R(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
static void scDegKbase(scfmon stc, int Nstc, int Nvar, int deg)
intvec * hSecondSeries(intvec *hseries1)
intvec * scIndIntvec(ideal S, ideal Q)
static int scMax(int i, scfmon stc, int Nvar)
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
void hLex2S(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
static void p_Delete(poly *p, const ring r)
scfmon hInit(ideal S, ideal Q, int *Nexist, ring tailRing)
intvec * hFirstSeries(ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
static void hDegree(ideal S, ideal Q)
static indset hCheck2(indset sm, scmon pure)
void hOrdSupp(scfmon stc, int Nstc, varset var, int Nvar)
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
ideal idInit(int idsize, int rank)
initialise an ideal / module
#define id_TestTail(A, lR, tR)
static void hProject(scmon pure, varset sel)
static BOOLEAN hCheck1(indset sm, scmon pure)
void hElimR(scfmon rad, int *e1, int a2, int e2, varset var, int Nvar)
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
const CanonicalForm int s
#define pLmCmp(p, q)
returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
ideal id_Copy(ideal h1, const ring r)
copy an ideal
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
void scPrintDegree(int co, int mu)
#define omFreeBin(addr, bin)
void hLexR(scfmon rad, int Nrad, varset var, int Nvar)
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.
int scMult0Int(ideal S, ideal Q, const ring tailRing)
void hLexS(scfmon stc, int Nstc, varset var, int Nvar)
static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
static void hIndep(scmon pure)