39 assume( idsize >= 0 && rank >= 0 );
49 hh->m = (poly *)
omAlloc0(idsize*
sizeof(poly));
59 void idShow(
const ideal
id,
const ring lmRing,
const ring tailRing,
const int debugPrint)
67 Print(
"Module of rank %ld,real rank %ld and %d generators.\n",
70 int j = (
id->ncols*
id->nrows) - 1;
71 while ((
j > 0) && (
id->m[
j]==
NULL))
j--;
72 for (
int i = 0;
i <=
j;
i++)
86 const poly *
m =
id->m +
N;
88 for (
int k =
N;
k >= 0; --
k, --
m)
103 for (
int l=
rVar(r)-1;
l>=0;
l--)
121 const int elems = (*h)->nrows * (*h)->ncols;
133 poly
pp=((*h)->m[
j]);
156 elems=
j=(*h)->nrows*(*h)->ncols;
182 if (ide->m[
k] !=
NULL)
187 ide->m[
j] = ide->m[
k];
233 ideal newI =
idInit(
k, ide->rank);
235 for (
int i = 0;
i <
k;
i++)
247 if (id->m[
i] !=
NULL)
322 if (id->m[
i] !=
NULL)
326 if ((id->m[
j] !=
NULL)
350 if (id->m[
i] !=
NULL)
416 void id_DBTest(ideal h1,
int level,
const char *
f,
const int l,
const ring r,
const ring tailRing)
428 const int n = (h1->ncols * h1->nrows);
432 if( h1->m !=
NULL && n > 0 )
438 for (
int i=n - 1;
i >= 0;
i--)
442 if (
k > new_rk) new_rk =
k;
447 assume( !( h1->nrows == h1->rank && h1->nrows > 1 && new_rk > 0 ) );
449 if(new_rk > h1->rank)
452 h1->rank, new_rk,
f,
l);
459 Print(
"error: ideal==NULL in %s:%d\n",
f,
l);
468 if (
b==
NULL)
return 1;
469 if (a==
NULL)
return -1;
508 int i,
j, actpos=0, newpos;
509 int diff, olddiff, lastcomp, newcomp;
518 diff = (actpos+1) / 2;
534 while (notFound && (newpos>=0) && (newpos<actpos))
544 && (newpos+
diff>=actpos))
546 diff = actpos-newpos-1;
548 else if ((newcomp==-1)
557 if ((olddiff==1) && (lastcomp>0))
564 if ((olddiff==1) && (lastcomp<0))
581 if (newpos<0) newpos = 0;
582 if (newpos>actpos) newpos = actpos;
585 for (
j=actpos;
j>newpos;
j--)
587 (*result)[
j] = (*result)[
j-1];
589 (*result)[newpos] =
i;
606 if (
res->rank<h1->rank)
res->rank=h1->rank;
612 if (
res->rank<h2->rank)
res->rank=h2->rank;
617 while ((
j >= 0) && (h1->m[
j] ==
NULL))
j--;
620 while ((
i >= 0) && (h2->m[
i] ==
NULL))
i--;
622 const int r =
si_max(h1->rank, h2->rank);
632 for (
l=
i;
l>=0;
l--,
j--)
647 while ((
j >= 0) && (h1->m[
j] ==
NULL))
j--;
666 while ((
j >= 0) && (I->m[
j] ==
NULL))
j--;
687 const poly h2,
const bool zeroOk,
const bool duplicateOk,
const ring r)
692 if ((!zeroOk) && (h2 ==
NULL))
return FALSE;
695 bool h2FoundInH1 =
false;
697 while ((
i < validEntries) && (!h2FoundInH1))
702 if (h2FoundInH1)
return FALSE;
704 if (validEntries ==
IDELEMS(h1))
709 h1->m[validEntries] = h2;
714 ideal
id_Add (ideal h1,ideal h2,
const ring r)
733 while ((
j > 0) && (h1->m[
j-1] ==
NULL))
j--;
736 while ((
i > 0) && (h2->m[
i-1] ==
NULL))
i--;
739 int r =
si_max( h2->rank, h1->rank );
750 if (h1->m[
i] !=
NULL)
754 if (h2->m[
j] !=
NULL)
858 while ((
i >= 0) && (choise[
i] == end))
868 for (
j=
i+1;
j<r;
j++)
870 choise[
j] = choise[
i]+
j-
i;
887 localchoise=(
int*)
omAlloc((d-1)*
sizeof(int));
893 while ((
i<t) && (localchoise[
i]==choise[
i]))
i++;
897 while ((
i<d) && (localchoise[
i-1]==choise[
i]))
i++;
918 if (n-r<r)
return binom(n,n-r);
925 WarnS(
"overflow in binomials");
940 for (
int j=0;
j<
i;
j++)
962 static void makemonoms(
int vars,
int actvar,
int deg,
int monomdeg,
const ring r)
1009 WarnS(
"maxideal: power must be non-negative");
1023 int i =
binom(vars+deg-1,deg);
1035 int begin,
int end,
int deg,
int restdeg, poly
ap,
const ring r)
1050 if (begin == end)
return;
1051 for (
i=restdeg-1;
i>0;
i--)
1093 while ((!
b) && (
i>=0))
1150 for(
unsigned j=0;
j<n ;
j++)
1178 for (
i=1;
i<=mr ;
i++)
1223 Print(
"## inv. rank %ld -> %ld\n",
mod->rank,cp);
1224 int k,
l,o=
mod->rank;
1227 for (
l=1;
l<=o;
l++)
1253 if (r>rows) r = rows;
1254 if (c>cols) c = cols;
1321 res->rank =
id->rank;
1341 long cmax=1,order=0,ord,*
diff,diffmin=32000;
1361 iscom = (
int *)
omAlloc0(cmax*
sizeof(
int));
1401 ord =
R->pFDeg(
p,
R);
1438 for (
i=1;
i<cmax;
i++) (**
w)[
i-1]=(int)(
diff[
i]);
1439 for (
i=1;
i<cmax;
i++)
1445 for (
i=1;
i<cmax;
i++)
1447 (**w)[
i-1]=(int)(
diff[
i]-diffmin);
1456 ideal r=
idInit((
i->nrows)*(
i->ncols),
i->rank);
1461 for(
int k=(
i->nrows)*(
i->ncols)-1;
k>=0;
k--)
1472 WerrorS(
"cannot compute weighted jets now");
1493 if (
idIs0(arg))
return -1;
1494 int i=0,
j, generator=-1;
1495 int rk_arg=arg->rank;
1496 int * componentIsUsed =(
int *)
omAlloc((rk_arg+1)*
sizeof(int));
1499 while ((generator<0) && (
i<
IDELEMS(arg)))
1501 memset(componentIsUsed,0,(rk_arg+1)*
sizeof(
int));
1506 if (componentIsUsed[
j]==0)
1512 componentIsUsed[
j] = 1;
1516 componentIsUsed[
j] = -1;
1519 else if (componentIsUsed[
j]>0)
1521 (componentIsUsed[
j])++;
1529 for (
j=0;
j<=rk_arg;
j++)
1531 if (componentIsUsed[
j]>0)
1533 if ((*
comp==-1) || (componentIsUsed[
j]<
i))
1536 i= componentIsUsed[
j];
1545 static void idDeleteComp(ideal arg,
int red_comp)
1572 int in=
IDELEMS(
id)-1, ready=0, all=0,
1573 coldim=
rVar(r), rowmax=2*coldim;
1574 if (in<0)
return NULL;
1586 for (
k=1;
k<=coldim;
k++)
1638 for(
i=I->nrows*I->ncols-1;
i>=0;
i--)
1652 if(-1<d0&&((d0<d)||(d==-1)))
1666 int r = a->rank, c =
IDELEMS(a);
1725 const int n = rRing->N;
1733 for(
int i = 0;
i <
k;
i++ )
1735 poly pTempSum =
NULL;
1760 if( cc == 0) cc =
m;
1761 int vv = 1 + (gen - cc) /
m;
1773 assume( (cc + (vv-1)*
m) == gen );
1780 pTempSum =
p_Add_q(pTempSum,
h, rRing);
1785 idTemp->m[
i] = pTempSum;
1790 ideal idResult =
id_Transp(idTemp, rRing);
1799 int cnt=0;
int rw=0;
int cl=0;
1802 for(
j=rl-1;
j>=0;
j--)
1806 if (xx[
j]->
nrows >rw) rw=xx[
j]->nrows;
1811 WerrorS(
"format mismatch in CRT");
1817 number *
x=(number *)
omAlloc(rl*
sizeof(number));
1818 poly *
p=(poly *)
omAlloc(rl*
sizeof(poly));
1823 for(
i=cnt-1;
i>=0;
i--)
1825 for(
j=rl-1;
j>=0;
j--)
1833 for(
j=rl-1;
j>=0;
j--)
static int si_max(const int a, const int b)
const CanonicalForm CFMap CFMap & N
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.
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2),...
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
static FORCE_INLINE number n_Sub(number a, number b, const coeffs r)
return the difference of 'a' and 'b', i.e., a-b
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
const CanonicalForm int s
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
void WerrorS(const char *s)
static BOOLEAN length(leftv result, leftv arg)
void ivTriangIntern(intvec *imat, int &ready, int &all)
intvec * ivSolveKern(intvec *imat, int dimtr)
#define IMATELEM(M, I, J)
matrix mpNew(int r, int c)
create a r x c zero-matrix
#define MATELEM(mat, i, j)
int dReportError(const char *fmt,...)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
#define __p_GetComp(p, r)
#define rRing_has_Comp(r)
gmp_float exp(const gmp_float &a)
#define omFreeSize(addr, size)
#define omdebugAddrSize(addr, size)
#define omCheckAddrSize(addr, size)
#define omFreeBin(addr, bin)
#define omGetSpecBin(size)
void omPrintAddrInfo(FILE *fd, void *addr, const char *s)
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
poly pp_Jet(poly p, int m, const ring R)
BOOLEAN p_ComparePolys(poly p1, poly p2, const ring r)
returns TRUE if p1 is a skalar multiple of p2 assume p1 != NULL and p2 != NULL
BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r)
divisibility check over ground ring (which may contain zero divisors); TRUE iff LT(f) divides LT(g),...
poly p_Homogen(poly p, int varnum, const ring r)
poly p_Subst(poly p, int n, poly e, const ring r)
void p_Vec2Polys(poly v, poly **p, int *len, const ring r)
poly pp_JetW(poly p, int m, short *w, const ring R)
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
poly p_Power(poly p, int i, const ring r)
void p_Normalize(poly p, const ring r)
void p_Norm(poly p1, const ring r)
int p_MinDeg(poly p, intvec *w, const ring R)
void pEnlargeSet(poly **p, int l, int increment)
BOOLEAN p_IsHomogeneous(poly p, const ring r)
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
static long p_GetExpDiff(poly p1, poly p2, int i, ring r)
static poly p_Add_q(poly p, poly q, const ring r)
static poly p_Mult_q(poly p, poly q, const ring r)
static poly p_Head(poly p, const ring r)
#define p_LmEqual(p1, p2, r)
void p_ShallowDelete(poly *p, const ring r)
static void p_SetCompP(poly p, int i, 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
#define pp_Test(p, lmRing, tailRing)
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
static long p_IncrExp(poly p, int v, ring r)
static void p_Setm(poly p, const ring r)
static poly p_SortMerge(poly p, const ring r, BOOLEAN revert=FALSE)
static poly pReverse(poly p)
static int p_LtCmp(poly p, poly q, const ring r)
static BOOLEAN p_LmIsConstantComp(const poly p, 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_DivisibleBy(poly a, poly b, const ring r)
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
static void p_Delete(poly *p, const ring r)
static unsigned pLength(poly a)
static poly pp_Mult_qq(poly p, poly q, const ring r)
static BOOLEAN p_IsUnit(const poly p, const ring r)
static poly p_LmDeleteAndNext(poly p, const ring r)
static poly p_Copy(poly p, const ring r)
returns a copy of p
static long p_Totaldegree(poly p, const ring r)
BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level)
static BOOLEAN p_IsConstantPoly(const poly p, const ring r)
void p_wrp(poly p, ring lmRing, ring tailRing)
#define pGetComp(p)
Component.
void PrintS(const char *s)
static BOOLEAN rField_is_Ring(const ring r)
long(* pFDegProc)(poly p, ring r)
static short rVar(const ring r)
#define rVar(r) (r->N)
static BOOLEAN rField_has_simple_inverse(const ring r)
void sBucketClearMerge(sBucket_pt bucket, poly *p, int *length)
void sBucket_Merge_p(sBucket_pt bucket, poly p, int length)
Merges p into Spoly: assumes Bpoly and p have no common monoms destroys p!
void sBucketDestroy(sBucket_pt *bucket)
sBucket_pt sBucketCreate(const ring r)
ideal id_Add(ideal h1, ideal h2, const ring r)
h1 + h2
ideal id_Vec2Ideal(poly vec, const ring R)
ideal idInit(int idsize, int rank)
initialise an ideal / module
int id_PosConstant(ideal id, const ring r)
index of generator with leading term in ground ring (if any); otherwise -1
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
void id_DBTest(ideal h1, int level, const char *f, const int l, const ring r, const ring tailRing)
Internal verification for ideals/modules and dense matrices!
poly id_Array2Vector(poly *m, unsigned n, const ring R)
for julia: convert an array of poly to vector
static void id_NextPotence(ideal given, ideal result, int begin, int end, int deg, int restdeg, poly ap, const ring r)
void id_Norm(ideal id, const ring r)
ideal id = (id[i]), result is leadcoeff(id[i]) = 1
BOOLEAN id_HomIdeal(ideal id, ideal Q, const ring r)
intvec * id_QHomWeight(ideal id, const ring r)
static void makemonoms(int vars, int actvar, int deg, int monomdeg, const ring r)
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
void id_Normalize(ideal I, const ring r)
normialize all polys in id
ideal id_Transp(ideal a, const ring rRing)
transpose a module
ideal id_FreeModule(int i, const ring r)
the free module of rank i
BOOLEAN id_IsZeroDim(ideal I, const ring r)
ideal id_Homogen(ideal h, int varnum, const ring r)
ideal id_Power(ideal given, int exp, const ring r)
matrix id_Module2Matrix(ideal mod, const ring R)
int idElem(const ideal F)
count non-zero elements
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
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 id_IsConstant(ideal id, const ring r)
test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing)
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
BOOLEAN idInsertPolyOnPos(ideal I, poly p, int pos)
insert p into I on position pos
int id_ReadOutPivot(ideal arg, int *comp, const ring r)
ideal id_MaxIdeal(const ring r)
initialise the maximal ideal (at 0)
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...
int id_MinDegW(ideal M, intvec *w, const ring r)
void id_DelMultiples(ideal id, const ring r)
ideal id = (id[i]), c any unit if id[i] = c*id[j] then id[j] is deleted for j > i
void id_ShallowDelete(ideal *h, ring r)
Shallowdeletes an ideal/matrix.
BOOLEAN id_InsertPolyWithTests(ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk, const ring r)
insert h2 into h1 depending on the two boolean parameters:
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 (...
matrix id_Module2formatedMatrix(ideal mod, int rows, int cols, const ring R)
void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint)
ideal id_Matrix2Module(matrix mat, const ring R)
converts mat to module, destroys mat
ideal id_ResizeModule(ideal mod, int rows, int cols, const ring R)
ideal id_Delete_Pos(const ideal I, const int p, const ring r)
static int p_Comp_RevLex(poly a, poly b, BOOLEAN nolex, const ring R)
for idSort: compare a and b revlex inclusive module comp.
void id_DelEquals(ideal id, const ring r)
ideal id = (id[i]) if id[i] = id[j] then id[j] is deleted for j > i
ideal id_Jet(const ideal i, int d, const ring R)
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
void id_DelLmEquals(ideal id, const ring r)
Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i.
ideal id_JetW(const ideal i, int d, intvec *iv, const ring R)
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
void id_Shift(ideal M, int s, const ring r)
int idGetNumberOfChoise(int t, int d, int begin, int end, int *choise)
intvec * id_Sort(const ideal id, const BOOLEAN nolex, const ring r)
sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
void id_Compactify(ideal id, const ring r)
BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R)
ideal id_Subst(ideal id, int n, poly e, const ring r)
#define id_TestTail(A, lR, tR)
The following sip_sideal structure has many different uses thoughout Singular. Basic use-cases for it...
short * iv2array(intvec *iv, const ring R)