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35 ideal
idInit(
int idsize,
int rank)
37 assume( idsize >= 0 && rank >= 0 );
47 hh->m = (poly *)
omAlloc0(idsize*
sizeof(poly));
57 void idShow(
const ideal
id,
const ring lmRing,
const ring tailRing,
const int debugPrint)
65 Print(
"Module of rank %ld,real rank %ld and %d generators.\n",
68 int j = (
id->ncols*
id->nrows) - 1;
69 while ((
j > 0) && (
id->m[
j]==
NULL))
j--;
70 for (
int i = 0;
i <=
j;
i++)
84 const poly *
m =
id->m +
N;
86 for (
int k =
N;
k >= 0; --
k, --
m)
111 ideal hh =
idInit(nvars, 1);
112 for (
int l=nvars-1;
l>=0;
l--)
130 const int elems = (*h)->nrows * (*h)->ncols;
142 poly
pp=((*h)->m[
j]);
165 elems=
j=(*h)->nrows*(*h)->ncols;
191 if (ide->m[
k] !=
NULL)
196 ide->m[
j] = ide->m[
k];
242 ideal newI =
idInit(
k, ide->rank);
244 for (
int i = 0;
i <
k;
i++)
251 void id_Norm(ideal
id,
const ring r)
256 if (id->m[
i] !=
NULL)
331 if (id->m[
i] !=
NULL)
335 if ((id->m[
j] !=
NULL)
359 if (id->m[
i] !=
NULL)
413 ideal
id_Copy(ideal h1,
const ring r)
425 void id_DBTest(ideal h1,
int level,
const char *
f,
const int l,
const ring r,
const ring tailRing)
437 const int n = (h1->ncols * h1->nrows);
441 if( h1->m !=
NULL && n > 0 )
447 for (
int i=n - 1;
i >= 0;
i--)
451 if (
k > new_rk) new_rk =
k;
456 assume( !( h1->nrows == h1->rank && h1->nrows > 1 && new_rk > 0 ) );
458 if(new_rk > h1->rank)
461 h1->rank, new_rk,
f,
l);
468 Print(
"error: ideal==NULL in %s:%d\n",
f,
l);
477 if (
b==
NULL)
return 1;
478 if (a==
NULL)
return -1;
517 int i,
j, actpos=0, newpos;
518 int diff, olddiff, lastcomp, newcomp;
527 diff = (actpos+1) / 2;
543 while (notFound && (newpos>=0) && (newpos<actpos))
553 && (newpos+
diff>=actpos))
555 diff = actpos-newpos-1;
557 else if ((newcomp==-1)
566 if ((olddiff==1) && (lastcomp>0))
573 if ((olddiff==1) && (lastcomp<0))
590 if (newpos<0) newpos = 0;
591 if (newpos>actpos) newpos = actpos;
594 for (
j=actpos;
j>newpos;
j--)
596 (*result)[
j] = (*result)[
j-1];
598 (*result)[newpos] =
i;
615 if (
res->rank<h1->rank)
res->rank=h1->rank;
621 if (
res->rank<h2->rank)
res->rank=h2->rank;
626 while ((
j >= 0) && (h1->m[
j] ==
NULL))
j--;
629 while ((
i >= 0) && (h2->m[
i] ==
NULL))
i--;
631 const int r =
si_max(h1->rank, h2->rank);
641 for (
l=
i;
l>=0;
l--,
j--)
656 while ((
j >= 0) && (h1->m[
j] ==
NULL))
j--;
675 while ((
j >= 0) && (I->m[
j] ==
NULL))
j--;
696 const poly h2,
const bool zeroOk,
const bool duplicateOk,
const ring r)
701 if ((!zeroOk) && (h2 ==
NULL))
return FALSE;
704 bool h2FoundInH1 =
false;
706 while ((
i < validEntries) && (!h2FoundInH1))
711 if (h2FoundInH1)
return FALSE;
713 if (validEntries ==
IDELEMS(h1))
718 h1->m[validEntries] = h2;
723 ideal
id_Add (ideal h1,ideal h2,
const ring r)
736 ideal
id_Mult (ideal h1,ideal h2,
const ring
R)
742 while ((
j > 0) && (h1->m[
j-1] ==
NULL))
j--;
745 while ((
i > 0) && (h2->m[
i-1] ==
NULL))
i--;
748 int r =
si_max( h2->rank, h1->rank );
759 if (h1->m[
i] !=
NULL)
763 if (h2->m[
j] !=
NULL)
867 while ((
i >= 0) && (choise[
i] == end))
877 for (
j=
i+1;
j<r;
j++)
879 choise[
j] = choise[
i]+
j-
i;
896 localchoise=(
int*)
omAlloc((d-1)*
sizeof(int));
902 while ((
i<t) && (localchoise[
i]==choise[
i]))
i++;
906 while ((
i<d) && (localchoise[
i-1]==choise[
i]))
i++;
922 int binom (
int n,
int r)
927 if (n-r<r)
return binom(n,n-r);
934 WarnS(
"overflow in binomials");
949 for (
int j=0;
j<
i;
j++)
971 static void makemonoms(
int vars,
int actvar,
int deg,
int monomdeg,
const ring r)
1011 #ifdef HAVE_SHIFTBBA
1019 static void lpmakemonoms(
int vars,
int deg,
const ring r)
1021 assume(deg <= r->
N/r->isLPring);
1033 for (
int j = 2;
j <= vars;
j++)
1035 for (
int i = 0;
i <
size;
i++)
1041 for (
int j = 1;
j <= vars;
j++)
1043 for (
int i = 0;
i <
size;
i++)
1071 #ifdef HAVE_SHIFTBBA
1077 for (
int j = 0;
j < deg;
j++)
1086 i =
binom(vars+deg-1,deg);
1092 #ifdef HAVE_SHIFTBBA
1108 int begin,
int end,
int deg,
int restdeg, poly
ap,
const ring r)
1123 if (begin == end)
return;
1124 for (
i=restdeg-1;
i>0;
i--)
1166 while ((!
b) && (
i>=0))
1184 ideal
id_Head(ideal
h,
const ring r)
1195 ideal
id_Homogen(ideal
h,
int varnum,
const ring r)
1223 for(
unsigned j=0;
j<n ;
j++)
1296 Print(
"## inv. rank %ld -> %ld\n",
mod->rank,cp);
1297 int k,
l,o=
mod->rank;
1326 if (r>rows) r = rows;
1327 if (c>cols) c = cols;
1389 ideal
id_Subst(ideal
id,
int n, poly e,
const ring r)
1394 res->rank =
id->rank;
1414 long cmax=1,order=0,ord,*
diff,diffmin=32000;
1434 iscom = (
int *)
omAlloc0(cmax*
sizeof(
int));
1474 ord =
R->pFDeg(
p,
R);
1511 for (
i=1;
i<cmax;
i++) (**
w)[
i-1]=(int)(
diff[
i]);
1512 for (
i=1;
i<cmax;
i++)
1518 for (
i=1;
i<cmax;
i++)
1520 (**w)[
i-1]=(int)(
diff[
i]-diffmin);
1527 ideal
id_Jet(
const ideal
i,
int d,
const ring
R)
1529 ideal r=
idInit((
i->nrows)*(
i->ncols),
i->rank);
1534 for(
int k=(
i->nrows)*(
i->ncols)-1;
k>=0;
k--)
1545 WerrorS(
"cannot compute weighted jets now");
1566 if (
idIs0(arg))
return -1;
1567 int i=0,
j, generator=-1;
1568 int rk_arg=arg->rank;
1569 int * componentIsUsed =(
int *)
omAlloc((rk_arg+1)*
sizeof(int));
1572 while ((generator<0) && (
i<
IDELEMS(arg)))
1574 memset(componentIsUsed,0,(rk_arg+1)*
sizeof(
int));
1579 if (componentIsUsed[
j]==0)
1585 componentIsUsed[
j] = 1;
1589 componentIsUsed[
j] = -1;
1592 else if (componentIsUsed[
j]>0)
1594 (componentIsUsed[
j])++;
1602 for (
j=0;
j<=rk_arg;
j++)
1604 if (componentIsUsed[
j]>0)
1606 if ((*
comp==-1) || (componentIsUsed[
j]<
i))
1609 i= componentIsUsed[
j];
1618 static void idDeleteComp(ideal arg,
int red_comp)
1645 int in=
IDELEMS(
id)-1, ready=0, all=0,
1646 coldim=
rVar(r), rowmax=2*coldim;
1647 if (in<0)
return NULL;
1659 for (
k=1;
k<=coldim;
k++)
1711 for(
i=I->nrows*I->ncols-1;
i>=0;
i--)
1725 if(-1<d0&&((d0<d)||(d==-1)))
1737 ideal
id_Transp(ideal a,
const ring rRing)
1739 int r = a->rank, c =
IDELEMS(a);
1798 const int n = rRing->N;
1806 for(
int i = 0;
i <
k;
i++ )
1808 poly pTempSum =
NULL;
1833 if( cc == 0) cc =
m;
1834 int vv = 1 + (gen - cc) /
m;
1846 assume( (cc + (vv-1)*
m) == gen );
1853 pTempSum =
p_Add_q(pTempSum,
h, rRing);
1858 idTemp->m[
i] = pTempSum;
1863 ideal idResult =
id_Transp(idTemp, rRing);
1872 int cnt=0;
int rw=0;
int cl=0;
1875 for(
j=rl-1;
j>=0;
j--)
1879 if (xx[
j]->
nrows >rw) rw=xx[
j]->nrows;
1884 WerrorS(
"format mismatch in CRT");
1890 number *
x=(number *)
omAlloc(rl*
sizeof(number));
1891 poly *
p=(poly *)
omAlloc(rl*
sizeof(poly));
1896 for(
i=cnt-1;
i>=0;
i--)
1898 for(
j=rl-1;
j>=0;
j--)
1906 for(
j=rl-1;
j>=0;
j--)
#define omdebugAddrSize(addr, size)
STATIC_VAR poly * idpower
ideal id_FreeModule(int i, const ring r)
the free module of rank i
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R)
int dReportError(const char *fmt,...)
ideal id_Homogen(ideal h, int varnum, const ring r)
#define omCheckAddrSize(addr, size)
void sBucketClearMerge(sBucket_pt bucket, poly *p, int *length)
int idElem(const ideal F)
count non-zero elements
static poly p_LmDeleteAndNext(poly p, const ring r)
poly p_Subst(poly p, int n, poly e, const ring r)
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
#define pGetComp(p)
Component.
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
void p_Normalize(poly p, const ring r)
static void lpmakemonoms(int vars, int deg, 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.
ideal id_Matrix2Module(matrix mat, const ring R)
converts mat to module, destroys mat
#define omGetSpecBin(size)
BOOLEAN idInsertPolyOnPos(ideal I, poly p, int pos)
insert p into I on position pos
void id_Norm(ideal id, const ring r)
ideal id = (id[i]), result is leadcoeff(id[i]) = 1
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
void pEnlargeSet(poly **p, int l, int increment)
long(* pFDegProc)(poly p, ring r)
static poly p_Head(poly p, const ring r)
copy the i(leading) term of p
ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing)
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
#define omPrintAddrInfo(A, B, C)
int id_PosConstant(ideal id, const ring r)
index of generator with leading term in ground ring (if any); otherwise -1
static void p_SetCompP(poly p, int i, ring r)
BOOLEAN idIs0(ideal h)
returns true if h is the zero 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 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:
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_MaxIdeal(const ring r)
initialise the maximal ideal (at 0)
poly p_Homogen(poly p, int varnum, 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
intvec * id_QHomWeight(ideal id, const ring r)
short * iv2array(intvec *iv, const ring R)
static BOOLEAN length(leftv result, leftv arg)
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
#define __p_GetComp(p, r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
void p_wrp(poly p, ring lmRing, ring tailRing)
ideal id_Copy(ideal h1, const ring r)
copy an ideal
const CanonicalForm CFMap CFMap & N
void id_Shift(ideal M, int s, const ring r)
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
void id_ShallowDelete(ideal *h, ring r)
Shallowdeletes an ideal/matrix.
BOOLEAN p_IsHomogeneous(poly p, const ring r)
BOOLEAN id_HomIdeal(ideal id, ideal Q, const ring r)
#define p_LmEqual(p1, p2, r)
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!
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 pLength(poly a)
static poly p_Copy(poly p, const ring r)
returns a copy of p
poly p_Power(poly p, int i, const ring r)
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
static short rVar(const ring r)
#define rVar(r) (r->N)
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint)
void PrintS(const char *s)
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.
#define omFreeSize(addr, size)
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!
poly id_Array2Vector(poly *m, unsigned n, const ring R)
for julia: convert an array of poly to vector
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
static BOOLEAN rField_is_Ring(const ring r)
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
matrix id_Module2Matrix(ideal mod, const ring R)
sBucket_pt sBucketCreate(const ring r)
static void makemonoms(int vars, int actvar, int deg, int monomdeg, 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 ivTriangIntern(intvec *imat, int &ready, int &all)
static poly pp_Mult_qq(poly p, poly q, const ring r)
static int p_LtCmp(poly p, poly q, const ring r)
ideal id_Jet(const ideal i, int d, const ring R)
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
int p_MinDeg(poly p, intvec *w, const ring R)
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
static BOOLEAN p_IsUnit(const poly p, const ring r)
ideal id_Power(ideal given, int exp, const ring r)
void p_ShallowDelete(poly *p, const ring r)
matrix mpNew(int r, int c)
create a r x c zero-matrix
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
poly pp_JetW(poly p, int m, short *w, const ring R)
ideal id_ResizeModule(ideal mod, int rows, int cols, const ring R)
gmp_float exp(const gmp_float &a)
static FORCE_INLINE number n_Sub(number a, number b, const coeffs r)
return the difference of 'a' and 'b', i.e., a-b
poly pp_Jet(poly p, int m, const ring R)
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
#define IMATELEM(M, I, J)
static void p_Delete(poly *p, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
ideal id_Delete_Pos(const ideal I, const int p, const ring r)
The following sip_sideal structure has many different uses thoughout Singular. Basic use-cases for it...
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
static int si_max(const int a, const int b)
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
#define rRing_has_Comp(r)
ideal id_JetW(const ideal i, int d, intvec *iv, const ring R)
ideal id_Vec2Ideal(poly vec, const ring R)
ideal idInit(int idsize, int rank)
initialise an ideal / module
#define pp_Test(p, lmRing, tailRing)
void p_Vec2Polys(poly v, poly **p, int *len, const 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),...
#define id_TestTail(A, lR, tR)
void WerrorS(const char *s)
static long p_GetExpDiff(poly p1, poly p2, int i, ring r)
static BOOLEAN rField_has_simple_inverse(const ring r)
#define MATELEM0(mat, i, j)
0-based access to matrix
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
int id_ReadOutPivot(ideal arg, int *comp, const ring r)
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_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...
static void p_Setm(poly p, const ring r)
static void id_NextPotence(ideal given, ideal result, int begin, int end, int deg, int restdeg, poly ap, const ring r)
static long p_IncrExp(poly p, int v, ring r)
int id_MinDegW(ideal M, intvec *w, const ring r)
static long p_Totaldegree(poly p, const ring r)
static BOOLEAN p_IsConstantPoly(const poly p, const ring r)
const CanonicalForm int s
STATIC_VAR int idpowerpoint
void p_Norm(poly p1, const ring r)
matrix id_Module2formatedMatrix(ideal mod, int rows, int cols, const ring R)
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
static poly p_Mult_q(poly p, poly q, const ring r)
void id_Compactify(ideal id, const ring r)
ideal id_Add(ideal h1, ideal h2, const ring r)
h1 + h2
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
intvec * ivSolveKern(intvec *imat, int dimtr)
ideal id_Transp(ideal a, const ring rRing)
transpose a module
BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level)
void sBucketDestroy(sBucket_pt *bucket)
EXTERN_VAR short * ecartWeights
#define omFreeBin(addr, bin)
STATIC_VAR gmp_float * diff
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
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),...
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 poly pReverse(poly p)
static poly p_SortMerge(poly p, const ring r, BOOLEAN revert=FALSE)
ideal id_Subst(ideal id, int n, poly e, const ring r)
void id_Normalize(ideal I, const ring r)
normialize all polys in id
BOOLEAN id_IsZeroDim(ideal I, const ring r)
int idGetNumberOfChoise(int t, int d, int begin, int end, int *choise)