31 int dn, iv, rad0,
b, c,
x;
44 while(pure[var[iv]]) iv--;
45 hStepR(rad, Nrad, var, iv, &rad0);
53 hDimSolve(pn, Npure + 1, rn, rad0, var, iv);
56 hElimR(rn, &rad0,
b, c, var, iv);
57 hPure(rn,
b, &c, var, iv, pn, &
x);
64 hDimSolve(pure, Npure, rad, Nrad, var, iv);
135 int dn, iv, rad0,
b, c,
x;
172 while(pure[var[iv]]) iv--;
173 hStepR(rad, Nrad, var, iv, &rad0);
182 hIndSolve(pn, Npure + 1, rn, rad0, var, iv);
186 hElimR(rn, &rad0,
b, c, var, iv);
187 hPure(rn,
b, &c, var, iv, pn, &
x);
194 hIndSolve(pure, Npure, rad, Nrad, var, 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--;
365 hStepR(rad, Nrad, var, iv, &rad0);
372 hIndMult(pn, Npure + 1, rn, rad0, var, iv);
376 hElimR(rn, &rad0,
b, c, var, iv);
377 hPure(rn,
b, &c, var, iv, pn, &
x);
380 hIndMult(pn, Npure +
x, rn, rad0, var, iv);
384 hIndMult(pure, Npure, rad, Nrad, var, 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--;
527 hStepR(rad, Nrad, var, iv, &rad0);
538 hElimR(rn, &rad0,
b, c, var, iv);
539 hPure(rn,
b, &c, var, iv, pn, &
x);
554 int iv = Nvar -1, sum, a, a0, a1,
b,
i;
563 for (
i = Nvar;
i;
i--)
570 hStepS(sn, Nstc, var, Nvar, &a, &
x);
572 return pure[var[Nvar]] *
hZeroMult(pn, sn, a, var, iv);
580 hStepS(sn, Nstc, var, Nvar, &a, &
x);
581 hElimS(sn, &
b, a0, a, var, iv);
583 hPure(sn, a0, &a1, var, iv, pn, &
i);
592 sum += (pure[var[Nvar]] - x0) *
hZeroMult(pn, sn,
b, var, iv);
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--;
674 hStepR(rad, Nrad, var, iv, &rad0);
681 hDimMult(pn, Npure + 1, rn, rad0, var, iv);
685 hElimR(rn, &rad0,
b, c, var, iv);
686 hPure(rn,
b, &c, var, iv, pn, &
x);
689 hDimMult(pn, Npure +
x, rn, rad0, var, iv);
693 hDimMult(pure, Npure, rad, Nrad, var, 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--)
967 hStepS(sn, Nstc, var, Nvar, &a, &
x);
984 hStepS(sn, Nstc, var, Nvar, &a, &
x);
985 hElimS(sn, &
b, a0, a, var, iv);
987 hPure(sn, a0, &a1, var, iv, pn, &
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))
void mu(int **points, int sizePoints)
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.
const CanonicalForm int s
const CanonicalForm int const CFList const Variable & y
int scMult0Int(ideal S, ideal Q, const ring tailRing)
static void hHedgeStep(scmon pure, scfmon stc, int Nstc, varset var, int Nvar, poly hEdge)
static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
ideal scKBase(int deg, ideal s, ideal Q, intvec *mv)
void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
intvec * scIndIntvec(ideal S, ideal Q)
static int scMin(int i, scfmon stc, int Nvar)
static indset hCheck2(indset sm, scmon pure)
void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge, ring tailRing)
static BOOLEAN hCheck1(indset sm, scmon pure)
static void hDegree(ideal S, ideal Q)
static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar)
static void hDegree0(ideal S, ideal Q, const ring tailRing)
static void hHedge(poly hEdge)
static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
static int scRestrict(int &Nstc, scfmon stc, int Nvar)
static void scAllKbase(int Nvar, int ideg, int deg)
static void scAll(int Nvar, int deg)
int scMultInt(ideal S, ideal Q)
static void scDegKbase(scfmon stc, int Nstc, int Nvar, int deg)
static void hCheckIndep(scmon pure)
void scPrintDegree(int co, int mu)
static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar)
static int scMax(int i, scfmon stc, int Nvar)
static ideal scIdKbase(poly q, const int rank)
static void hIndep(scmon pure)
static void scInKbase(scfmon stc, int Nstc, int Nvar)
static void hProject(scmon pure, varset sel)
void scDegree(ideal S, intvec *modulweight, ideal Q)
int scDimInt(ideal S, ideal Q)
void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
intvec * hSecondSeries(intvec *hseries1)
intvec * hFirstSeries(ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
void hComp(scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
scfmon hInit(ideal S, ideal Q, int *Nexist, ring tailRing)
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 hLexR(scfmon rad, int Nrad, varset var, int Nvar)
void hStepR(scfmon rad, int Nrad, varset var, int Nvar, int *a)
void hLex2R(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
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 hElimR(scfmon rad, int *e1, int a2, int e2, varset var, int Nvar)
void hOrdSupp(scfmon stc, int Nstc, varset var, int Nvar)
void hRadical(scfmon rad, int *Nrad, int Nvar)
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
#define omFreeSize(addr, size)
#define omFreeBin(addr, bin)
#define omGetSpecBin(size)
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)
static unsigned pLength(poly a)
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Compatiblity layer for legacy polynomial operations (over currRing)
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced
#define pGetExp(p, i)
Exponent.
#define pInit()
allocates a new monomial and initializes everything to 0
#define pLmCmp(p, q)
returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering
static BOOLEAN rField_is_Ring(const ring r)
ideal idInit(int idsize, int rank)
initialise an ideal / module
int idElem(const ideal F)
count non-zero elements
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
#define id_TestTail(A, lR, tR)