simpleideals.h File Reference

#include "polys/monomials/ring.h"
#include "polys/matpol.h"

Go to the source code of this file.

Data Structures
struct	const_ideal
	The following sip_sideal structure has many different uses throughout Singular. Basic use-cases for it are: More...
struct	const_map
struct	ideal_list

Macros
#define	IDELEMS(i)
#define	id_Init(s, r, R)
#define	id_Elem(F, R)
#define	id_Test(A, lR)
#define	id_LmTest(A, lR)
#define	id_Print(id, lR, tR)

Functions
ideal	idInit (int size, int rank=1)
	creates an ideal / module
void	id_Delete (ideal *h, ring r)
	deletes an ideal/module/matrix
void	id_Delete0 (ideal *h, ring r)
void	id_ShallowDelete (ideal *h, ring r)
	Shallowdeletes an ideal/matrix.
void	idSkipZeroes (ideal ide)
	gives an ideal/module the minimal possible size
int	idSkipZeroes0 (ideal ide)
static int	idElem (const ideal F)
	number of non-zero polys in F
void	id_Normalize (ideal id, const ring r)
	normialize all polys in id
int	id_MinDegW (ideal M, intvec *w, const ring r)
void	id_DBTest (ideal h1, int level, const char *f, const int l, const ring lR, const ring tR)
	Internal verification for ideals/modules and dense matrices!
void	id_DBLmTest (ideal h1, int level, const char *f, const int l, const ring r)
	Internal verification for ideals/modules and dense matrices!
ideal	id_Copy (ideal h1, const ring r)
	copy an ideal
ideal	id_SimpleAdd (ideal h1, ideal h2, const ring r)
	concat the lists h1 and h2 without zeros
ideal	id_SimpleMove (ideal h1, ideal h2, const ring R)
	concat the lists h1 and h2 without zeros, destroys h1,h2
ideal	id_Add (ideal h1, ideal h2, const ring r)
	h1 + h2
ideal	id_Power (ideal given, int exp, const ring r)
BOOLEAN	idIs0 (ideal h)
	returns true if h is the zero ideal
BOOLEAN	idIsMonomial (ideal h)
	returns true if h is generated by monomials
BOOLEAN	idIsSimpleGB (ideal F, ideal Q)
	returns true if F in R/Q has a "simple" GB
BOOLEAN	id_IsModule (ideal A, const ring src)
long	id_RankFreeModule (ideal m, ring lmRing, ring tailRing)
	return the maximal component number found in any polynomial in s
static long	id_RankFreeModule (ideal m, ring r)
ideal	id_FreeModule (int i, const ring r)
	the free module of rank i
int	id_PosConstant (ideal id, const ring r)
	index of generator with leading term in ground ring (if any); otherwise -1
ideal	id_Head (ideal h, const ring r)
	returns the ideals of initial terms
ideal	id_MaxIdeal (const ring r)
	initialise the maximal ideal (at 0)
ideal	id_MaxIdeal (int deg, 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 (Note that the copied entries may be zero.)
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_Norm (ideal id, const ring r)
	ideal id = (id[i]), result is leadcoeff(id[i]) = 1
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
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.
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*LT(j)
BOOLEAN	id_IsConstant (ideal id, const ring r)
	test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant
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
ideal	id_Transp (ideal a, const ring rRing)
	transpose a module
void	id_Compactify (ideal id, 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 columns at all)
ideal	id_Homogen (ideal h, int varnum, const ring r)
ideal	id_HomogenDP (ideal h, int varnum, const ring r)
BOOLEAN	id_HomIdeal (ideal id, ideal Q, const ring r)
BOOLEAN	id_HomIdealDP (ideal id, ideal Q, const ring r)
BOOLEAN	id_HomIdealW (ideal id, ideal Q, const intvec *w, const ring r)
BOOLEAN	id_HomModuleW (ideal id, ideal Q, const intvec *w, const intvec *module_w, const ring r)
BOOLEAN	id_HomModule (ideal m, ideal Q, intvec **w, const ring R)
BOOLEAN	id_IsZeroDim (ideal I, const ring r)
ideal	id_Jet (const ideal i, int d, const ring R)
ideal	id_Jet0 (const ideal i, const ring R)
ideal	id_JetW (const ideal i, int d, intvec *iv, const ring R)
ideal	id_Subst (ideal id, int n, poly e, const ring r)
matrix	id_Module2Matrix (ideal mod, const ring R)
matrix	id_Module2formatedMatrix (ideal mod, int rows, int cols, const ring R)
ideal	id_ResizeModule (ideal mod, int rows, int cols, const ring R)
ideal	id_Matrix2Module (matrix mat, const ring R)
	converts mat to module, destroys mat
ideal	id_Vec2Ideal (poly vec, const ring R)
int	binom (int n, int r)
void	idInitChoise (int r, int beg, int end, BOOLEAN *endch, int *choise)
void	idGetNextChoise (int r, int end, BOOLEAN *endch, int *choise)
int	idGetNumberOfChoise (int t, int d, int begin, int end, int *choise)
void	idShow (const ideal id, const ring lmRing, const ring tailRing, const int debugPrint=0)
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:
intvec *	id_QHomWeight (ideal id, const ring r)
ideal	id_ChineseRemainder (ideal *xx, number *q, int rl, const ring r)
void	id_Shift (ideal M, int s, const ring r)
ideal	id_Delete_Pos (const ideal I, const int pos, const ring r)
poly	id_Array2Vector (poly *m, unsigned n, const ring R)
	for julia: convert an array of poly to vector
ideal	id_PermIdeal (ideal I, int R, int C, const int *perm, const ring src, const ring dst, nMapFunc nMap, const int *par_perm, int P, BOOLEAN use_mult)
	mapping ideals/matrices to other rings

Variables
EXTERN_VAR omBin	sip_sideal_bin

---

Data Structure Documentation

sip_sideal

struct sip_sideal

The following sip_sideal structure has many different uses throughout Singular. Basic use-cases for it are:

• ideal/module: nrows = 1, ncols >=0 and rank:1 for ideals, rank>=0 for modules
• matrix: nrows, ncols >=0, rank == nrows! see mp_* procedures NOTE: the m member point to memory chunk of size (ncols*nrows*sizeof(poly)) or is NULL

Definition at line 17 of file simpleideals.h.

Data Fields
poly *	m
int	ncols
int	nrows
long	rank

sip_smap

struct sip_smap

Definition at line 32 of file simpleideals.h.

Data Fields
poly *	m
int	ncols
int	nrows
char *	preimage

sideal_list

struct sideal_list

Definition at line 45 of file simpleideals.h.

Data Fields
ideal	d
ideal_list	next
int	nr

Macro Definition Documentation

id_Elem

#define id_Elem	(		F,
			R )

Value:

idElem(F)

Definition at line 79 of file simpleideals.h.

id_Init

#define id_Init	(		s,
			r,
			R )

Value:

idInit(s,r)

Definition at line 58 of file simpleideals.h.

id_LmTest

#define id_LmTest	(		A,
			lR )

Value:

id_DBLmTest(A, PDEBUG, __FILE__,__LINE__, lR)

Definition at line 90 of file simpleideals.h.

id_Print

#define id_Print	(		id,
			lR,
			tR )

Value:

idShow(id, lR, tR)

Definition at line 165 of file simpleideals.h.

id_Test

#define id_Test	(		A,
			lR )

Value:

id_DBTest(A, PDEBUG, __FILE__,__LINE__, lR, lR)

Definition at line 89 of file simpleideals.h.

IDELEMS

#define IDELEMS

(

i

)

Value:

((i)->ncols)

Definition at line 23 of file simpleideals.h.

Function Documentation

binom()

int binom	(	int	n,
		int	r )

Definition at line 1293 of file simpleideals.cc.

{
  int i;
  int64 result;
 
  if (r==0) return 1;
  if (n-r<r) return binom(n,n-r);
  result = n-r+1;
  for (i=2;i<=r;i++)
  {
    result *= n-r+i;
    result /= i;
  }
  if (result>MAX_INT_VAL)
  {
    WarnS("overflow in binomials");
    result=0;
  }
  return (int)result;
}

id_Add()

ideal id_Add	(	ideal	h1,
		ideal	h2,
		const ring	r )

h1 + h2

Definition at line 954 of file simpleideals.cc.

{
  id_Test(h1, r);
  id_Test(h2, r);
 
  ideal result = id_SimpleAdd(h1,h2,r);
  id_Compactify(result,r);
  return result;
}

id_Array2Vector()

poly id_Array2Vector	(	poly *	m,
		unsigned	n,
		const ring	R )

for julia: convert an array of poly to vector

Definition at line 1618 of file simpleideals.cc.

{
  poly h;
  int l;
  sBucket_pt bucket = sBucketCreate(R);
 
  for(unsigned j=0;j<n ;j++)
  {
    h = m[j];
    if (h!=NULL)
    {
      h=p_Copy(h, R);
      l=pLength(h);
      p_SetCompP(h,j+1, R);
      sBucket_Merge_p(bucket, h, l);
    }
  }
  sBucketClearMerge(bucket, &h, &l);
  sBucketDestroy(&bucket);
  return h;
}

id_ChineseRemainder()

ideal id_ChineseRemainder	(	ideal *	xx,
		number *	q,
		int	rl,
		const ring	r )

Definition at line 2228 of file simpleideals.cc.

{
  int cnt=0;int rw=0; int cl=0;
  int i,j;
  // find max. size of xx[.]:
  for(j=rl-1;j>=0;j--)
  {
    i=IDELEMS(xx[j])*xx[j]->nrows;
    if (i>cnt) cnt=i;
    if (xx[j]->nrows >rw) rw=xx[j]->nrows; // for lifting matrices
    if (xx[j]->ncols >cl) cl=xx[j]->ncols; // for lifting matrices
  }
  if (rw*cl !=cnt)
  {
    WerrorS("format mismatch in CRT");
    return NULL;
  }
  ideal result=idInit(cnt,xx[0]->rank);
  result->nrows=rw; // for lifting matrices
  result->ncols=cl; // for lifting matrices
  number *x=(number *)omAlloc(rl*sizeof(number));
  poly *p=(poly *)omAlloc(rl*sizeof(poly));
  CFArray inv_cache(rl);
  EXTERN_VAR int n_SwitchChinRem; //TEST
  int save_n_SwitchChinRem=n_SwitchChinRem;
  n_SwitchChinRem=1;
  for(i=cnt-1;i>=0;i--)
  {
    for(j=rl-1;j>=0;j--)
    {
      if(i>=IDELEMS(xx[j])*xx[j]->nrows) // out of range of this ideal
        p[j]=NULL;
      else
        p[j]=xx[j]->m[i];
    }
    result->m[i]=p_ChineseRemainder(p,x,q,rl,inv_cache,r);
    for(j=rl-1;j>=0;j--)
    {
      if(i<IDELEMS(xx[j])*xx[j]->nrows) xx[j]->m[i]=p[j];
    }
  }
  n_SwitchChinRem=save_n_SwitchChinRem;
  omFreeSize(p,rl*sizeof(poly));
  omFreeSize(x,rl*sizeof(number));
  for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]),r);
  omFreeSize(xx,rl*sizeof(ideal));
  return result;
}

id_Compactify()

void id_Compactify	(	ideal	id,
		const ring	r )

Definition at line 1540 of file simpleideals.cc.

{
  int i;
  BOOLEAN b=FALSE;
 
  i = IDELEMS(id)-1;
  while ((! b) && (i>=0))
  {
    b=p_IsUnit(id->m[i],r);
    i--;
  }
  if (b)
  {
    for(i=IDELEMS(id)-1;i>=0;i--) p_Delete(&id->m[i],r);
    id->m[0]=p_One(r);
  }
  else
  {
    id_DelMultiples(id,r);
  }
  idSkipZeroes(id);
}

id_Copy()

ideal id_Copy	(	ideal	h1,
		const ring	r )

copy an ideal

Definition at line 542 of file simpleideals.cc.

{
  id_Test(h1, r);
 
  ideal h2 = idInit(IDELEMS(h1), h1->rank);
  for (int i=IDELEMS(h1)-1; i>=0; i--)
    h2->m[i] = p_Copy(h1->m[i],r);
  return h2;
}

id_CopyFirstK()

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 (Note that the copied entries may be zero.)

Definition at line 266 of file simpleideals.cc.

{
  id_Test(ide, r);
 
  assume( ide != NULL );
  assume( k <= IDELEMS(ide) );
 
  ideal newI = idInit(k, ide->rank);
 
  for (int i = 0; i < k; i++)
    newI->m[i] = p_Copy(ide->m[i],r);
 
  return newI;
}

id_DBLmTest()

void id_DBLmTest	(	ideal	h1,
		int	level,
		const char *	f,
		const int	l,
		const ring	r )

Internal verification for ideals/modules and dense matrices!

Definition at line 605 of file simpleideals.cc.

{
  if (h1 != NULL)
  {
    // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix
    omCheckAddrSize(h1,sizeof(*h1));
 
    assume( h1->ncols >= 0 );
    assume( h1->nrows >= 0 ); // matrix case!
 
    assume( h1->rank >= 0 );
 
    const long n = ((long)h1->ncols * (long)h1->nrows);
 
    assume( !( n > 0 && h1->m == NULL) );
 
    if( h1->m != NULL && n > 0 )
      omdebugAddrSize(h1->m, n * sizeof(poly));
 
    long new_rk = 0; // inlining id_RankFreeModule(h1, r, tailRing);
 
    /* to be able to test matrices: */
    for (long i=n - 1; i >= 0; i--)
    {
      if (h1->m[i]!=NULL)
      {
        _p_LmTest(h1->m[i], r, level);
        const long k = p_GetComp(h1->m[i], r);
        if (k > new_rk) new_rk = k;
      }
    }
 
    // dense matrices only contain polynomials:
    // h1->nrows == h1->rank > 1 && new_rk == 0!
    assume( !( h1->nrows == h1->rank && h1->nrows > 1 && new_rk > 0 ) ); //
 
    if(new_rk > h1->rank)
    {
      dReportError("wrong rank %d (should be %d) in %s:%d\n",
                   h1->rank, new_rk, f,l);
      omPrintAddrInfo(stderr, h1, " for ideal");
      h1->rank = new_rk;
    }
  }
  else
  {
    Print("error: ideal==NULL in %s:%d\n",f,l);
    assume( h1 != NULL );
  }
}

id_DBTest()

void id_DBTest	(	ideal	h1,
		int	level,
		const char *	f,
		const int	l,
		const ring	lR,
		const ring	tR )

Internal verification for ideals/modules and dense matrices!

Definition at line 554 of file simpleideals.cc.

{
  if (h1 != NULL)
  {
    // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix
    omCheckAddrSize(h1,sizeof(*h1));
 
    assume( h1->ncols >= 0 );
    assume( h1->nrows >= 0 ); // matrix case!
 
    assume( h1->rank >= 0 );
 
    const long n = ((long)h1->ncols * (long)h1->nrows);
 
    assume( !( n > 0 && h1->m == NULL) );
 
    if( h1->m != NULL && n > 0 )
      omdebugAddrSize(h1->m, n * sizeof(poly));
 
    long new_rk = 0; // inlining id_RankFreeModule(h1, r, tailRing);
 
    /* to be able to test matrices: */
    for (long i=n - 1; i >= 0; i--)
    {
      _pp_Test(h1->m[i], r, tailRing, level);
      const long k = p_MaxComp(h1->m[i], r, tailRing);
      if (k > new_rk) new_rk = k;
    }
 
    // dense matrices only contain polynomials:
    // h1->nrows == h1->rank > 1 && new_rk == 0!
    assume( !( h1->nrows == h1->rank && h1->nrows > 1 && new_rk > 0 ) ); //
 
    if(new_rk > h1->rank)
    {
      dReportError("wrong rank %d (should be %d) in %s:%d\n",
                   h1->rank, new_rk, f,l);
      omPrintAddrInfo(stderr, h1, " for ideal");
      h1->rank = new_rk;
    }
  }
  else
  {
    Print("error: ideal==NULL in %s:%d\n",f,l);
    assume( h1 != NULL );
  }
}

id_DelDiv()

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*LT(j)

Definition at line 463 of file simpleideals.cc.

{
  id_Test(id, r);
 
  int i, j;
  int k = IDELEMS(id)-1;
#ifdef HAVE_RINGS
  if (rField_is_Ring(r))
  {
    for (i=k-1; i>=0; i--)
    {
      if (id->m[i] != NULL)
      {
        for (j=k; j>i; j--)
        {
          if (id->m[j]!=NULL)
          {
            if (p_DivisibleByRingCase(id->m[i], id->m[j],r))
            {
              p_Delete(&id->m[j],r);
            }
            else if (p_DivisibleByRingCase(id->m[j], id->m[i],r))
            {
              p_Delete(&id->m[i],r);
              break;
            }
          }
        }
      }
    }
  }
  else
#endif
  {
    /* the case of a coefficient field: */
    if (k>9)
    {
      id_DelDiv_SEV(id,k,r);
      return;
    }
    for (i=k-1; i>=0; i--)
    {
      if (id->m[i] != NULL)
      {
        for (j=k; j>i; j--)
        {
          if (id->m[j]!=NULL)
          {
            if (p_LmDivisibleBy(id->m[i], id->m[j],r))
            {
              p_Delete(&id->m[j],r);
            }
            else if (p_LmDivisibleBy(id->m[j], id->m[i],r))
            {
              p_Delete(&id->m[i],r);
              break;
            }
          }
        }
      }
    }
  }
}

id_DelEquals()

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

Definition at line 331 of file simpleideals.cc.

{
  id_Test(id, r);
 
  int i, j;
  int k = IDELEMS(id)-1;
  for (i=k; i>=0; i--)
  {
    if (id->m[i]!=NULL)
    {
      for (j=k; j>i; j--)
      {
        if ((id->m[j]!=NULL)
        && (p_EqualPolys(id->m[i], id->m[j],r)))
        {
          p_Delete(&id->m[j],r);
        }
      }
    }
  }
}

id_Delete()

void id_Delete	(	ideal *	h,
		ring	r )

deletes an ideal/module/matrix

Definition at line 123 of file simpleideals.cc.

{
  if (*h == NULL)
    return;
 
  id_Test(*h, r);
 
  const long elems = (long)(*h)->nrows * (long)(*h)->ncols;
 
  if ( elems > 0 )
  {
    assume( (*h)->m != NULL );
 
    if (r!=NULL)
    {
      long j = elems;
      do
      {
        j--;
        poly pp=((*h)->m[j]);
        if (pp!=NULL) p_Delete(&pp, r);
      }
      while (j>0);
    }
 
    omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems);
  }
 
  omFreeBin((ADDRESS)*h, sip_sideal_bin);
  *h=NULL;
}

id_Delete0()

void id_Delete0	(	ideal *	h,
		ring	r )

Definition at line 155 of file simpleideals.cc.

{
  long j = IDELEMS(*h);
 
  if(j>0)
  {
    do
    {
      j--;
      poly pp=((*h)->m[j]);
      if (pp!=NULL) p_Delete(&pp, r);
    }
    while (j>0);
    omFree((ADDRESS)((*h)->m));
  }
 
  omFreeBin((ADDRESS)*h, sip_sideal_bin);
  *h=NULL;
}

id_Delete_Pos()

ideal id_Delete_Pos	(	const ideal	I,
		const int	pos,
		const ring	r )

Definition at line 2291 of file simpleideals.cc.

{
  if ((p<0)||(p>=IDELEMS(I))) return NULL;
  ideal ret=idInit(IDELEMS(I)-1,I->rank);
  for(int i=0;i<p;i++) ret->m[i]=p_Copy(I->m[i],r);
  for(int i=p+1;i<IDELEMS(I);i++) ret->m[i-1]=p_Copy(I->m[i],r);
  return ret;
}

id_DelLmEquals()

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.

Definition at line 354 of file simpleideals.cc.

{
  id_Test(id, r);
 
  int i, j;
  int k = IDELEMS(id)-1;
  for (i=k; i>=0; i--)
  {
    if (id->m[i] != NULL)
    {
      for (j=k; j>i; j--)
      {
        if ((id->m[j] != NULL)
        && p_LmEqual(id->m[i], id->m[j],r)
#ifdef HAVE_RINGS
        && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf)
#endif
        )
        {
          p_Delete(&id->m[j],r);
        }
      }
    }
  }
}

id_DelMultiples()

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

Definition at line 296 of file simpleideals.cc.

{
  id_Test(id, r);
 
  int i, j;
  int k = IDELEMS(id)-1;
  for (i=k; i>=0; i--)
  {
    if (id->m[i]!=NULL)
    {
      for (j=k; j>i; j--)
      {
        if (id->m[j]!=NULL)
        {
          if (rField_is_Ring(r))
          {
            /* if id[j] = c*id[i] then delete id[j].
               In the below cases of a ground field, we
               check whether id[i] = c*id[j] and, if so,
               delete id[j] for historical reasons (so
               that previous output does not change) */
            if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r);
          }
          else
          {
            if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r);
          }
        }
      }
    }
  }
}

id_FreeModule()

ideal id_FreeModule	(	int	i,
		const ring	r )

the free module of rank i

Definition at line 1316 of file simpleideals.cc.

{
  assume(i >= 0);
  if (r->isLPring)
  {
    PrintS("In order to address bimodules, the command freeAlgebra should be used.");
  }
  ideal h = idInit(i, i);
 
  for (int j=0; j<i; j++)
  {
    h->m[j] = p_One(r);
    p_SetComp(h->m[j],j+1,r);
    p_SetmComp(h->m[j],r);
  }
 
  return h;
}

id_Head()

ideal id_Head	(	ideal	h,
		const ring	r )

returns the ideals of initial terms

Definition at line 1564 of file simpleideals.cc.

{
  ideal m = idInit(IDELEMS(h),h->rank);
 
  if (r->cf->has_simple_Alloc)
  {
    for (int i=IDELEMS(h)-1;i>=0; i--)
      if (h->m[i]!=NULL)
        m->m[i]=p_CopyPowerProduct0(h->m[i],pGetCoeff(h->m[i]),r);
  }
  else
  {
    for (int i=IDELEMS(h)-1;i>=0; i--)
      if (h->m[i]!=NULL)
        m->m[i]=p_Head(h->m[i],r);
  }
 
  return m;
}

id_HomIdeal()

BOOLEAN id_HomIdeal	(	ideal	id,
		ideal	Q,
		const ring	r )

Definition at line 1114 of file simpleideals.cc.

{
  int i;
  BOOLEAN b;
  i = 0;
  b = TRUE;
  while ((i < IDELEMS(id)) && b)
  {
    b = p_IsHomogeneous(id->m[i],r);
    i++;
  }
  if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
  {
    i=0;
    while ((i < IDELEMS(Q)) && b)
    {
      b = p_IsHomogeneous(Q->m[i],r);
      i++;
    }
  }
  return b;
}

id_HomIdealDP()

BOOLEAN id_HomIdealDP	(	ideal	id,
		ideal	Q,
		const ring	r )

Definition at line 1140 of file simpleideals.cc.

{
  int i;
  BOOLEAN b;
  i = 0;
  b = TRUE;
  while ((i < IDELEMS(id)) && b)
  {
    b = p_IsHomogeneousDP(id->m[i],r);
    i++;
  }
  if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
  {
    i=0;
    while ((i < IDELEMS(Q)) && b)
    {
      b = p_IsHomogeneousDP(Q->m[i],r);
      i++;
    }
  }
  return b;
}

id_HomIdealW()

BOOLEAN id_HomIdealW	(	ideal	id,
		ideal	Q,
		const intvec *	w,
		const ring	r )

Definition at line 1163 of file simpleideals.cc.

{
  int i;
  BOOLEAN b;
  i = 0;
  b = TRUE;
  while ((i < IDELEMS(id)) && b)
  {
    b = p_IsHomogeneousW(id->m[i],w,r);
    i++;
  }
  if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
  {
    i=0;
    while ((i < IDELEMS(Q)) && b)
    {
      b = p_IsHomogeneousW(Q->m[i],w,r);
      i++;
    }
  }
  return b;
}

id_HomModule()

BOOLEAN id_HomModule	(	ideal	m,
		ideal	Q,
		intvec **	w,
		const ring	R )

Definition at line 1805 of file simpleideals.cc.

{
  if (w!=NULL) *w=NULL;
  if ((Q!=NULL) && (!id_HomIdeal(Q,NULL,R))) return FALSE;
  if (idIs0(m))
  {
    if (w!=NULL) (*w)=new intvec(m->rank);
    return TRUE;
  }
 
  long cmax=1,order=0,ord,* diff,diffmin=32000;
  int *iscom;
  int i;
  poly p=NULL;
  pFDegProc d;
  if (R->pLexOrder && (R->order[0]==ringorder_lp))
     d=p_Totaldegree;
  else
     d=R->pFDeg;
  int length=IDELEMS(m);
  poly* P=m->m;
  poly* F=(poly*)omAlloc(length*sizeof(poly));
  for (i=length-1;i>=0;i--)
  {
    p=F[i]=P[i];
    cmax=si_max(cmax,p_MaxComp(p,R));
  }
  cmax++;
  diff = (long *)omAlloc0(cmax*sizeof(long));
  if (w!=NULL) *w=new intvec(cmax-1);
  iscom = (int *)omAlloc0(cmax*sizeof(int));
  i=0;
  while (i<=length)
  {
    if (i<length)
    {
      p=F[i];
      while ((p!=NULL) && (iscom[__p_GetComp(p,R)]==0)) pIter(p);
    }
    if ((p==NULL) && (i<length))
    {
      i++;
    }
    else
    {
      if (p==NULL) /* && (i==length) */
      {
        i=0;
        while ((i<length) && (F[i]==NULL)) i++;
        if (i>=length) break;
        p = F[i];
      }
      //if (pLexOrder && (currRing->order[0]==ringorder_lp))
      //  order=pTotaldegree(p);
      //else
      //  order = p->order;
      //  order = pFDeg(p,currRing);
      order = d(p,R) +diff[__p_GetComp(p,R)];
      //order += diff[pGetComp(p)];
      p = F[i];
//Print("Actual p=F[%d]: ",i);pWrite(p);
      F[i] = NULL;
      i=0;
    }
    while (p!=NULL)
    {
      if (R->pLexOrder && (R->order[0]==ringorder_lp))
        ord=p_Totaldegree(p,R);
      else
      //  ord = p->order;
        ord = R->pFDeg(p,R);
      if (iscom[__p_GetComp(p,R)]==0)
      {
        diff[__p_GetComp(p,R)] = order-ord;
        iscom[__p_GetComp(p,R)] = 1;
/*
*PrintS("new diff: ");
*for (j=0;j<cmax;j++) Print("%d ",diff[j]);
*PrintLn();
*PrintS("new iscom: ");
*for (j=0;j<cmax;j++) Print("%d ",iscom[j]);
*PrintLn();
*Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]);
*/
      }
      else
      {
/*
*PrintS("new diff: ");
*for (j=0;j<cmax;j++) Print("%d ",diff[j]);
*PrintLn();
*Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]);
*/
        if (order != (ord+diff[__p_GetComp(p,R)]))
        {
          omFreeSize((ADDRESS) iscom,cmax*sizeof(int));
          omFreeSize((ADDRESS) diff,cmax*sizeof(long));
          omFreeSize((ADDRESS) F,length*sizeof(poly));
          delete *w;*w=NULL;
          return FALSE;
        }
      }
      pIter(p);
    }
  }
  omFreeSize((ADDRESS) iscom,cmax*sizeof(int));
  omFreeSize((ADDRESS) F,length*sizeof(poly));
  for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]);
  for (i=1;i<cmax;i++)
  {
    if (diff[i]<diffmin) diffmin=diff[i];
  }
  if (w!=NULL)
  {
    for (i=1;i<cmax;i++)
    {
      (**w)[i-1]=(int)(diff[i]-diffmin);
    }
  }
  omFreeSize((ADDRESS) diff,cmax*sizeof(long));
  return TRUE;
}

id_HomModuleW()

BOOLEAN id_HomModuleW	(	ideal	id,
		ideal	Q,
		const intvec *	w,
		const intvec *	module_w,
		const ring	r )

Definition at line 1186 of file simpleideals.cc.

{
  int i;
  BOOLEAN b;
  i = 0;
  b = TRUE;
  while ((i < IDELEMS(id)) && b)
  {
    b = p_IsHomogeneousW(id->m[i],w,module_w,r);
    i++;
  }
  if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
  {
    i=0;
    while ((i < IDELEMS(Q)) && b)
    {
      b = p_IsHomogeneousW(Q->m[i],w,r);
      i++;
    }
  }
  return b;
}

id_Homogen()

ideal id_Homogen	(	ideal	h,
		int	varnum,
		const ring	r )

Definition at line 1584 of file simpleideals.cc.

{
  ideal m = idInit(IDELEMS(h),h->rank);
  int i;
 
  for (i=IDELEMS(h)-1;i>=0; i--)
  {
    m->m[i]=p_Homogen(h->m[i],varnum,r);
  }
  return m;
}

id_HomogenDP()

ideal id_HomogenDP	(	ideal	h,
		int	varnum,
		const ring	r )

Definition at line 1596 of file simpleideals.cc.

{
  ideal m = idInit(IDELEMS(h),h->rank);
  int i;
 
  for (i=IDELEMS(h)-1;i>=0; i--)
  {
    m->m[i]=p_HomogenDP(h->m[i],varnum,r);
  }
  return m;
}

id_InsertPolyWithTests()

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:

• if zeroOk is true, then h2 will also be inserted when it is zero
• if duplicateOk is true, then h2 will also be inserted when it is already present in h1 return TRUE iff h2 was indeed inserted

Definition at line 926 of file simpleideals.cc.

{
  id_Test(h1, r);
  p_Test(h2, r);
 
  if ((!zeroOk) && (h2 == NULL)) return FALSE;
  if (!duplicateOk)
  {
    bool h2FoundInH1 = false;
    int i = 0;
    while ((i < validEntries) && (!h2FoundInH1))
    {
      h2FoundInH1 = p_EqualPolys(h1->m[i], h2,r);
      i++;
    }
    if (h2FoundInH1) return FALSE;
  }
  if (validEntries == IDELEMS(h1))
  {
    pEnlargeSet(&(h1->m), IDELEMS(h1), 16);
    IDELEMS(h1) += 16;
  }
  h1->m[validEntries] = h2;
  return TRUE;
}

id_IsConstant()

BOOLEAN id_IsConstant	(	ideal	id,
		const ring	r )

test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant

Definition at line 529 of file simpleideals.cc.

{
  id_Test(id, r);
 
  for (int k = IDELEMS(id)-1; k>=0; k--)
  {
    if (!p_IsConstantPoly(id->m[k],r))
      return FALSE;
  }
  return TRUE;
}

id_IsModule()

BOOLEAN id_IsModule	(	ideal	A,
		const ring	src )

Definition at line 1092 of file simpleideals.cc.

{
  if ((src->VarOffset[0]== -1)
  || (src->pCompIndex<0))
    return FALSE; // ring without components
  for (int i=IDELEMS(A)-1;i>=0;i--)
  {
    if (A->m[i]!=NULL)
    {
      if (p_GetComp(A->m[i],src)>0)
        return TRUE;
      else
        return FALSE;
    }
  }
  return A->rank>1;
}

id_IsZeroDim()

BOOLEAN id_IsZeroDim	(	ideal	I,
		const ring	r )

Definition at line 2045 of file simpleideals.cc.

{
  BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(rVar(r)*sizeof(BOOLEAN));
  int i,n;
  poly po;
  BOOLEAN res=TRUE;
  for(i=IDELEMS(I)-1;i>=0;i--)
  {
    po=I->m[i];
    if ((po!=NULL) &&((n=p_IsPurePower(po,r))!=0)) UsedAxis[n-1]=TRUE;
  }
  for(i=rVar(r)-1;i>=0;i--)
  {
    if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim.
  }
  omFreeSize(UsedAxis,rVar(r)*sizeof(BOOLEAN));
  return res;
}

id_Jet()

ideal id_Jet	(	const ideal	i,
		int	d,
		const ring	R )

Definition at line 1928 of file simpleideals.cc.

{
  ideal r=idInit((i->nrows)*(i->ncols),i->rank);
  r->nrows = i-> nrows;
  r->ncols = i-> ncols;
  //r->rank = i-> rank;
 
  for(long k=((long)(i->nrows))*((long)(i->ncols))-1;k>=0; k--)
    r->m[k]=pp_Jet(i->m[k],d,R);
 
  return r;
}

id_Jet0()

ideal id_Jet0	(	const ideal	i,
		const ring	R )

Definition at line 1941 of file simpleideals.cc.

{
  ideal r=idInit((i->nrows)*(i->ncols),i->rank);
  r->nrows = i-> nrows;
  r->ncols = i-> ncols;
  //r->rank = i-> rank;
 
  for(long k=((long)(i->nrows))*((long)(i->ncols))-1;k>=0; k--)
    r->m[k]=pp_Jet0(i->m[k],R);
 
  return r;
}

id_JetW()

ideal id_JetW	(	const ideal	i,
		int	d,
		intvec *	iv,
		const ring	R )

Definition at line 1954 of file simpleideals.cc.

{
  ideal r=idInit(IDELEMS(i),i->rank);
  if (ecartWeights!=NULL)
  {
    WerrorS("cannot compute weighted jets now");
  }
  else
  {
    int *w=iv2array(iv,R);
    int k;
    for(k=0; k<IDELEMS(i); k++)
    {
      r->m[k]=pp_JetW(i->m[k],d,w,R);
    }
    omFreeSize((ADDRESS)w,(rVar(R)+1)*sizeof(int));
  }
  return r;
}

id_Matrix2Module()

ideal id_Matrix2Module	(	matrix	mat,
		const ring	R )

converts mat to module, destroys mat

Definition at line 1641 of file simpleideals.cc.

{
  int mc=MATCOLS(mat);
  int mr=MATROWS(mat);
  ideal result = idInit(mc,mr);
  int i,j,l;
  poly h;
  sBucket_pt bucket = sBucketCreate(R);
 
  for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */
  {
    for (i=0;i<mr /*MATROWS(mat)*/;i++)
    {
      h = MATELEM0(mat,i,j);
      if (h!=NULL)
      {
        l=pLength(h);
        MATELEM0(mat,i,j)=NULL;
        p_SetCompP(h,i+1, R);
        sBucket_Merge_p(bucket, h, l);
      }
    }
    sBucketClearMerge(bucket, &(result->m[j]), &l);
  }
  sBucketDestroy(&bucket);
 
  // obachman: need to clean this up
  id_Delete((ideal*) &mat,R);
  return result;
}

id_MaxIdeal() [1/2]

ideal id_MaxIdeal

(

const ring

r

)

initialise the maximal ideal (at 0)

Definition at line 98 of file simpleideals.cc.

{
  int nvars;
#ifdef HAVE_SHIFTBBA
  if (r->isLPring)
  {
    nvars = r->isLPring;
  }
  else
#endif
  {
    nvars = rVar(r);
  }
  ideal hh = idInit(nvars, 1);
  for (int l=nvars-1; l>=0; l--)
  {
    hh->m[l] = p_One(r);
    p_SetExp(hh->m[l],l+1,1,r);
    p_Setm(hh->m[l],r);
  }
  id_Test(hh, r);
  return hh;
}

id_MaxIdeal() [2/2]

ideal id_MaxIdeal	(	int	deg,
		const ring	r )

Definition at line 1433 of file simpleideals.cc.

{
  if (deg < 1)
  {
    ideal I=idInit(1,1);
    I->m[0]=p_One(r);
    return I;
  }
  if (deg == 1
#ifdef HAVE_SHIFTBBA
      && !r->isLPring
#endif
     )
  {
    return id_MaxIdeal(r);
  }
 
  int vars, i;
#ifdef HAVE_SHIFTBBA
  if (r->isLPring)
  {
    vars = r->isLPring - r->LPncGenCount;
    i = 1;
    // i = vars^deg
    for (int j = 0; j < deg; j++)
    {
      i *= vars;
    }
  }
  else
#endif
  {
    vars = rVar(r);
    i = binom(vars+deg-1,deg);
  }
  if (i<=0) return idInit(1,1);
  ideal id=idInit(i,1);
  idpower = id->m;
  idpowerpoint = 0;
#ifdef HAVE_SHIFTBBA
  if (r->isLPring)
  {
    lpmakemonoms(vars, deg, r);
  }
  else
#endif
  {
    makemonoms(vars,1,deg,0,r);
  }
  idpower = NULL;
  idpowerpoint = 0;
  return id;
}

id_MinDegW()

int id_MinDegW	(	ideal	M,
		intvec *	w,
		const ring	r )

Definition at line 2075 of file simpleideals.cc.

{
  int d=-1;
  for(int i=0;i<IDELEMS(M);i++)
  {
    if (M->m[i]!=NULL)
    {
      int d0=p_MinDeg(M->m[i],w,r);
      if(-1<d0&&((d0<d)||(d==-1)))
        d=d0;
    }
  }
  return d;
}

id_Module2formatedMatrix()

matrix id_Module2formatedMatrix	(	ideal	mod,
		int	rows,
		int	cols,
		const ring	R )

Definition at line 1721 of file simpleideals.cc.

{
  matrix result = mpNew(rows,cols);
  int i,cp,r=id_RankFreeModule(mod,R),c=IDELEMS(mod);
  poly p,h;
 
  if (r>rows) r = rows;
  if (c>cols) c = cols;
  for(i=0;i<c;i++)
  {
    p=pReverse(mod->m[i]);
    mod->m[i]=NULL;
    while (p!=NULL)
    {
      h=p;
      pIter(p);
      pNext(h)=NULL;
      cp = p_GetComp(h,R);
      if (cp<=r)
      {
        p_SetComp(h,0,R);
        p_SetmComp(h,R);
        MATELEM0(result,cp-1,i) = p_Add_q(MATELEM0(result,cp-1,i),h,R);
      }
      else
        p_Delete(&h,R);
    }
  }
  id_Delete(&mod,R);
  return result;
}

id_Module2Matrix()

matrix id_Module2Matrix	(	ideal	mod,
		const ring	R )

Definition at line 1675 of file simpleideals.cc.

{
  matrix result = mpNew(mod->rank,IDELEMS(mod));
  long i; long cp;
  poly p,h;
 
  for(i=0;i<IDELEMS(mod);i++)
  {
    p=pReverse(mod->m[i]);
    mod->m[i]=NULL;
    while (p!=NULL)
    {
      h=p;
      pIter(p);
      pNext(h)=NULL;
      cp = si_max(1L,p_GetComp(h, R));     // if used for ideals too
      //cp = p_GetComp(h,R);
      p_SetComp(h,0,R);
      p_SetmComp(h,R);
#ifdef TEST
      if (cp>mod->rank)
      {
        Print("## inv. rank %ld -> %ld\n",mod->rank,cp);
        int k,l,o=mod->rank;
        mod->rank=cp;
        matrix d=mpNew(mod->rank,IDELEMS(mod));
        for (l=0; l<o; l++)
        {
          for (k=0; k<IDELEMS(mod); k++)
          {
            MATELEM0(d,l,k)=MATELEM0(result,l,k);
            MATELEM0(result,l,k)=NULL;
          }
        }
        id_Delete((ideal *)&result,R);
        result=d;
      }
#endif
      MATELEM0(result,cp-1,i) = p_Add_q(MATELEM0(result,cp-1,i),h,R);
    }
  }
  // obachman 10/99: added the following line, otherwise memory leak!
  id_Delete(&mod,R);
  return result;
}

id_Mult()

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 columns at all)

Definition at line 967 of file simpleideals.cc.

{
  id_Test(h1, R);
  id_Test(h2, R);
 
  int j = IDELEMS(h1);
  while ((j > 0) && (h1->m[j-1] == NULL)) j--;
 
  int i = IDELEMS(h2);
  while ((i > 0) && (h2->m[i-1] == NULL)) i--;
 
  j *= i;
  int r = si_max( h2->rank, h1->rank );
  if (j==0)
  {
    if ((IDELEMS(h1)>0) && (IDELEMS(h2)>0)) j=1;
    return idInit(j, r);
  }
  ideal  hh = idInit(j, r);
 
  int k = 0;
  for (i=0; i<IDELEMS(h1); i++)
  {
    if (h1->m[i] != NULL)
    {
      for (j=0; j<IDELEMS(h2); j++)
      {
        if (h2->m[j] != NULL)
        {
          hh->m[k] = pp_Mult_qq(h1->m[i],h2->m[j],R);
          k++;
        }
      }
    }
  }
 
  id_Compactify(hh,R);
  return hh;
}

id_Norm()

void id_Norm	(	ideal	id,
		const ring	r )

ideal id = (id[i]), result is leadcoeff(id[i]) = 1

Definition at line 282 of file simpleideals.cc.

{
  id_Test(id, r);
  for (int i=IDELEMS(id)-1; i>=0; i--)
  {
    if (id->m[i] != NULL)
    {
      p_Norm(id->m[i],r);
    }
  }
}

id_Normalize()

void id_Normalize	(	ideal	id,
		const ring	r )

normialize all polys in id

Definition at line 2064 of file simpleideals.cc.

{
  if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */
  int i;
  for(i=I->nrows*I->ncols-1;i>=0;i--)
  {
    poly p=I->m[i];
    if (p!=NULL) p_Normalize(p,r);
  }
}

id_PermIdeal()

ideal id_PermIdeal	(	ideal	I,
		int	R,
		int	C,
		const int *	perm,
		const ring	src,
		const ring	dst,
		nMapFunc	nMap,
		const int *	par_perm,
		int	P,
		BOOLEAN	use_mult )

mapping ideals/matrices to other rings

Definition at line 2300 of file simpleideals.cc.

{
  ideal II=(ideal)mpNew(R,C);
  II->rank=I->rank;
  for(int i=R*C-1; i>=0; i--)
  {
    II->m[i]=p_PermPoly(I->m[i],perm,src,dst,nMap,par_perm,P,use_mult);
  }
  return II;
}

id_PosConstant()

int id_PosConstant	(	ideal	id,
		const ring	r )

index of generator with leading term in ground ring (if any); otherwise -1

Definition at line 80 of file simpleideals.cc.

{
  id_Test(id, r);
  const int N = IDELEMS(id) - 1;
  const poly * m = id->m + N;
 
  for (int k = N; k >= 0; --k, --m)
  {
    const poly p = *m;
    if (p!=NULL)
       if (p_LmIsConstantComp(p, r) == TRUE)
         return k;
  }
 
  return -1;
}

id_Power()

ideal id_Power	(	ideal	given,
		int	exp,
		const ring	r )

Definition at line 1514 of file simpleideals.cc.

{
  ideal result,temp;
  poly p1;
  int i;
 
  if (idIs0(given)) return idInit(1,1);
  temp = id_Copy(given,r);
  idSkipZeroes(temp);
  i = binom(IDELEMS(temp)+exp-1,exp);
  result = idInit(i,1);
  result->nrows = 0;
//Print("ideal contains %d elements\n",i);
  p1=p_One(r);
  id_NextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1,r);
  p_Delete(&p1,r);
  id_Delete(&temp,r);
  result->nrows = 1;
  id_DelEquals(result,r);
  idSkipZeroes(result);
  return result;
}

id_QHomWeight()

intvec * id_QHomWeight	(	ideal	id,
		const ring	r )

Definition at line 1998 of file simpleideals.cc.

{
  poly head, tail;
  int k;
  int in=IDELEMS(id)-1, ready=0, all=0,
      coldim=rVar(r), rowmax=2*coldim;
  if (in<0) return NULL;
  intvec *imat=new intvec(rowmax+1,coldim,0);
 
  do
  {
    head = id->m[in--];
    if (head!=NULL)
    {
      tail = pNext(head);
      while (tail!=NULL)
      {
        all++;
        for (k=1;k<=coldim;k++)
          IMATELEM(*imat,all,k) = p_GetExpDiff(head,tail,k,r);
        if (all==rowmax)
        {
          ivTriangIntern(imat, ready, all);
          if (ready==coldim)
          {
            delete imat;
            return NULL;
          }
        }
        pIter(tail);
      }
    }
  } while (in>=0);
  if (all>ready)
  {
    ivTriangIntern(imat, ready, all);
    if (ready==coldim)
    {
      delete imat;
      return NULL;
    }
  }
  intvec *result = ivSolveKern(imat, ready);
  delete imat;
  return result;
}

id_RankFreeModule() [1/2]

long id_RankFreeModule	(	ideal	m,
		ring	lmRing,
		ring	tailRing )

return the maximal component number found in any polynomial in s

Definition at line 1073 of file simpleideals.cc.

{
  long j = 0;
 
  if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing))
  {
    poly *p=s->m;
    for (unsigned int l=IDELEMS(s); l > 0; --l, ++p)
      if (*p != NULL)
      {
        pp_Test(*p, lmRing, tailRing);
        const long k = p_MaxComp(*p, lmRing, tailRing);
        if (k>j) j = k;
      }
  }
 
  return j; //  return -1;
}

id_RankFreeModule() [2/2]

long id_RankFreeModule ( ideal m, ring r )

inlinestatic

Definition at line 112 of file simpleideals.h.

{return id_RankFreeModule(m, r, r);}

id_ResizeModule()

ideal id_ResizeModule	(	ideal	mod,
		int	rows,
		int	cols,
		const ring	R )

Definition at line 1753 of file simpleideals.cc.

{
  // columns?
  if (cols!=IDELEMS(mod))
  {
    for(int i=IDELEMS(mod)-1;i>=cols;i--) p_Delete(&mod->m[i],R);
    pEnlargeSet(&(mod->m),IDELEMS(mod),cols-IDELEMS(mod));
    IDELEMS(mod)=cols;
  }
  // rows?
  if (rows<mod->rank)
  {
    for(int i=IDELEMS(mod)-1;i>=0;i--)
    {
      if (mod->m[i]!=NULL)
      {
        while((mod->m[i]!=NULL) && (p_GetComp(mod->m[i],R)>rows))
          mod->m[i]=p_LmDeleteAndNext(mod->m[i],R);
        poly p=mod->m[i];
        while(pNext(p)!=NULL)
        {
          if (p_GetComp(pNext(p),R)>rows)
            pNext(p)=p_LmDeleteAndNext(pNext(p),R);
          else
            pIter(p);
        }
      }
    }
  }
  mod->rank=rows;
  return mod;
}

id_ShallowDelete()

void id_ShallowDelete	(	ideal *	h,
		ring	r )

Shallowdeletes an ideal/matrix.

Definition at line 177 of file simpleideals.cc.

{
  id_Test(*h, r);
 
  if (*h == NULL)
    return;
 
  int j,elems;
  elems=j=(*h)->nrows*(*h)->ncols;
  if (j>0)
  {
    assume( (*h)->m != NULL );
    do
    {
      p_ShallowDelete(&((*h)->m[--j]), r);
    }
    while (j>0);
    omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems);
  }
  omFreeBin((ADDRESS)*h, sip_sideal_bin);
  *h=NULL;
}

id_Shift()

void id_Shift	(	ideal	M,
		int	s,
		const ring	r )

Definition at line 2277 of file simpleideals.cc.

{
//  id_Test( M, r );
 
//  assume( s >= 0 ); // negative is also possible // TODO: verify input ideal in such a case!?
 
  for(int i=IDELEMS(M)-1; i>=0;i--)
    p_Shift(&(M->m[i]),s,r);
 
  M->rank += s;
 
//  id_Test( M, r );
}

id_SimpleAdd()

ideal id_SimpleAdd	(	ideal	h1,
		ideal	h2,
		const ring	r )

concat the lists h1 and h2 without zeros

Definition at line 790 of file simpleideals.cc.

{
  id_Test(h1, R);
  id_Test(h2, R);
 
  if ( idIs0(h1) )
  {
    ideal res=id_Copy(h2,R);
    if (res->rank<h1->rank) res->rank=h1->rank;
    return res;
  }
  if ( idIs0(h2) )
  {
    ideal res=id_Copy(h1,R);
    if (res->rank<h2->rank) res->rank=h2->rank;
    return res;
  }
 
  int j = IDELEMS(h1)-1;
  while ((j >= 0) && (h1->m[j] == NULL)) j--;
 
  int i = IDELEMS(h2)-1;
  while ((i >= 0) && (h2->m[i] == NULL)) i--;
 
  const int r = si_max(h1->rank, h2->rank);
 
  ideal result = idInit(i+j+2,r);
 
  int l;
 
  for (l=j; l>=0; l--)
    result->m[l] = p_Copy(h1->m[l],R);
 
  j = i+j+1;
  for (l=i; l>=0; l--, j--)
    result->m[j] = p_Copy(h2->m[l],R);
 
  return result;
}

id_SimpleMove()

ideal id_SimpleMove	(	ideal	h1,
		ideal	h2,
		const ring	R )

concat the lists h1 and h2 without zeros, destroys h1,h2

Definition at line 831 of file simpleideals.cc.

{
  if ( idIs0(h1) )
  {
    ideal res=h2;
    if (res->rank<h1->rank) res->rank=h1->rank;
    id_Delete(&h1,R);
    return res;
  }
  if ( idIs0(h2) )
  {
    ideal res=h1;
    if (res->rank<h2->rank) res->rank=h2->rank;
    id_Delete(&h2,R);
    return res;
  }
 
  int j = IDELEMS(h1)-1;
  while ((j >= 0) && (h1->m[j] == NULL)) j--;
 
  int i = IDELEMS(h2)-1;
  while ((i >= 0) && (h2->m[i] == NULL)) i--;
 
  const int r = si_max(h1->rank, h2->rank);
 
  ideal result = idInit(i+j+2,r);
 
  int l;
 
  for (l=j; l>=0; l--)
  {
    result->m[l] = h1->m[l];
    h1->m[l] = NULL;
  }
 
  j = i+j+1;
  for (l=i; l>=0; l--, j--)
  {
    result->m[j] = h2->m[l];
    h2->m[l] = NULL;
  }
 
  id_Delete(&h1,R);
  id_Delete(&h2,R);
  return result;
}

id_Sort()

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

Definition at line 695 of file simpleideals.cc.

{
  id_Test(id, r);
 
  intvec * result = new intvec(IDELEMS(id));
  int i, j, actpos=0, newpos;
  int diff, olddiff, lastcomp, newcomp;
  BOOLEAN notFound;
 
  for (i=0;i<IDELEMS(id);i++)
  {
    if (id->m[i]!=NULL)
    {
      notFound = TRUE;
      newpos = actpos / 2;
      diff = (actpos+1) / 2;
      diff = (diff+1) / 2;
      lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r);
      if (lastcomp<0)
      {
        newpos -= diff;
      }
      else if (lastcomp>0)
      {
        newpos += diff;
      }
      else
      {
        notFound = FALSE;
      }
      //while ((newpos>=0) && (newpos<actpos) && (notFound))
      while (notFound && (newpos>=0) && (newpos<actpos))
      {
        newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r);
        olddiff = diff;
        if (diff>1)
        {
          diff = (diff+1) / 2;
          if ((newcomp==1)
          && (actpos-newpos>1)
          && (diff>1)
          && (newpos+diff>=actpos))
          {
            diff = actpos-newpos-1;
          }
          else if ((newcomp==-1)
          && (diff>1)
          && (newpos<diff))
          {
            diff = newpos;
          }
        }
        if (newcomp<0)
        {
          if ((olddiff==1) && (lastcomp>0))
            notFound = FALSE;
          else
            newpos -= diff;
        }
        else if (newcomp>0)
        {
          if ((olddiff==1) && (lastcomp<0))
          {
            notFound = FALSE;
            newpos++;
          }
          else
          {
            newpos += diff;
          }
        }
        else
        {
          notFound = FALSE;
        }
        lastcomp = newcomp;
        if (diff==0) notFound=FALSE; /*hs*/
      }
      if (newpos<0) newpos = 0;
      if (newpos>actpos) newpos = actpos;
      while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0))
        newpos++;
      for (j=actpos;j>newpos;j--)
      {
        (*result)[j] = (*result)[j-1];
      }
      (*result)[newpos] = i;
      actpos++;
    }
  }
  for (j=0;j<actpos;j++) (*result)[j]++;
  return result;
}

id_Subst()

ideal id_Subst	(	ideal	id,
		int	n,
		poly	e,
		const ring	r )

Definition at line 1790 of file simpleideals.cc.

{
  int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
  ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));
 
  res->rank = id->rank;
  for(k--;k>=0;k--)
  {
    res->m[k]=p_Subst(id->m[k],n,e,r);
    id->m[k]=NULL;
  }
  id_Delete(&id,r);
  return res;
}

id_Transp()

ideal id_Transp	(	ideal	a,
		const ring	rRing )

transpose a module

Definition at line 2095 of file simpleideals.cc.

{
  int r = a->rank, c = IDELEMS(a);
  ideal b =  idInit(r,c);
 
  int i;
  for (i=c; i>0; i--)
  {
    poly p=a->m[i-1];
    while(p!=NULL)
    {
      poly h=p_Head(p, rRing);
      int co=__p_GetComp(h, rRing)-1;
      p_SetComp(h, i, rRing);
      p_Setm(h, rRing);
      h->next=b->m[co];
      b->m[co]=h;
      pIter(p);
    }
  }
  for (i=IDELEMS(b)-1; i>=0; i--)
  {
    poly p=b->m[i];
    if(p!=NULL)
    {
      b->m[i]=p_SortMerge(p,rRing,TRUE);
    }
  }
  return b;
}

id_Vec2Ideal()

ideal id_Vec2Ideal	(	poly	vec,
		const ring	R )

Definition at line 1609 of file simpleideals.cc.

{
   ideal result=idInit(1,1);
   omFreeBinAddr((ADDRESS)result->m);
   p_Vec2Polys(vec, &(result->m), &(IDELEMS(result)),R);
   return result;
}

idElem()

int idElem ( const ideal F )

inlinestatic

number of non-zero polys in F

Definition at line 69 of file simpleideals.h.

{
  int i=0;
  for(int j=IDELEMS(F)-1;j>=0;j--)
  {
    if ((F->m)[j]!=NULL) i++;
  }
  return i;
}

idGetNextChoise()

void idGetNextChoise	(	int	r,
		int	end,
		BOOLEAN *	endch,
		int *	choise )

Definition at line 1235 of file simpleideals.cc.

{
  int i = r-1,j;
  while ((i >= 0) && (choise[i] == end))
  {
    i--;
    end--;
  }
  if (i == -1)
    *endch = TRUE;
  else
  {
    choise[i]++;
    for (j=i+1; j<r; j++)
    {
      choise[j] = choise[i]+j-i;
    }
    *endch = FALSE;
  }
}

idGetNumberOfChoise()

int idGetNumberOfChoise	(	int	t,
		int	d,
		int	begin,
		int	end,
		int *	choise )

Definition at line 1261 of file simpleideals.cc.

{
  int * localchoise,i,result=0;
  BOOLEAN b=FALSE;
 
  if (d<=1) return 1;
  localchoise=(int*)omAlloc((d-1)*sizeof(int));
  idInitChoise(d-1,begin,end,&b,localchoise);
  while (!b)
  {
    result++;
    i = 0;
    while ((i<t) && (localchoise[i]==choise[i])) i++;
    if (i>=t)
    {
      i = t+1;
      while ((i<d) && (localchoise[i-1]==choise[i])) i++;
      if (i>=d)
      {
        omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int));
        return result;
      }
    }
    idGetNextChoise(d-1,end,&b,localchoise);
  }
  omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int));
  return 0;
}

idInit()

ideal idInit	(	int	idsize,
		int	rank )

creates an ideal / module

creates an ideal / module

Definition at line 35 of file simpleideals.cc.

{
  assume( idsize >= 0 && rank >= 0 );
 
  ideal hh = (ideal)omAllocBin(sip_sideal_bin);
 
  IDELEMS(hh) = idsize; // ncols
  hh->nrows = 1; // ideal/module!
 
  hh->rank = rank; // ideal: 1, module: >= 0!
 
  if (idsize>0)
    hh->m = (poly *)omAlloc0(idsize*sizeof(poly));
  else
    hh->m = NULL;
 
  return hh;
}

idInitChoise()

void idInitChoise	(	int	r,
		int	beg,
		int	end,
		BOOLEAN *	endch,
		int *	choise )

Definition at line 1213 of file simpleideals.cc.

{
  /*returns the first choise of r numbers between beg and end*/
  int i;
  for (i=0; i<r; i++)
  {
    choise[i] = 0;
  }
  if (r <= end-beg+1)
    for (i=0; i<r; i++)
    {
      choise[i] = beg+i;
    }
  if (r > end-beg+1)
    *endch = TRUE;
  else
    *endch = FALSE;
}

idIs0()

BOOLEAN idIs0

(

ideal

h

)

returns true if h is the zero ideal

Definition at line 1008 of file simpleideals.cc.

{
  if ((h!=NULL) && (h->m!=NULL))
  {
    for( int i = IDELEMS(h)-1; i >= 0; i-- )
      if(h->m[i] != NULL)
        return FALSE;
  }
  return TRUE;
}

idIsMonomial()

BOOLEAN idIsMonomial

(

ideal

h

)

returns true if h is generated by monomials

Definition at line 1020 of file simpleideals.cc.

{
  assume (h != NULL);
 
  BOOLEAN found_mon=FALSE;
  if (h->m!=NULL)
  {
    for( int i = IDELEMS(h)-1; i >= 0; i-- )
    {
      if(h->m[i] != NULL)
      {
        if(pNext(h->m[i])!=NULL) return FALSE;
        found_mon=TRUE;
      }
    }
  }
  return found_mon;
}

idIsSimpleGB()

BOOLEAN idIsSimpleGB	(	ideal	F,
		ideal	Q )

returns true if F in R/Q has a "simple" GB

Definition at line 1040 of file simpleideals.cc.

{
  assume (F != NULL);
  int non_zero=0;
  int triple=0;
 
  if (LIKELY(F->m!=NULL))
  {
    for( int i = IDELEMS(F)-1; i >= 0; i-- )
    {
      poly p;
      if((p=F->m[i]) != NULL)
      {
        non_zero++;
        if (Q!=NULL) return FALSE;
        if(pNext(p)!=NULL)
        {
          if(pNext(pNext(p))!=NULL)
          {
            triple++;
            if (non_zero>1) return FALSE;
          }
        }
      }
    }
  }
  if (non_zero<=1) return TRUE; // no zerodivisors
  if (triple>1) return FALSE;
  if ((triple==1)&&(non_zero>1)) return FALSE;
  return TRUE;
}

idShow()

void idShow	(	const ideal	id,
		const ring	lmRing,
		const ring	tailRing,
		const int	debugPrint = 0 )

Definition at line 57 of file simpleideals.cc.

{
  assume( debugPrint >= 0 );
 
  if( id == NULL )
    PrintS("(NULL)");
  else
  {
    Print("Module of rank %ld,real rank %ld and %d generators.\n",
          id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id));
 
    int j = (id->ncols*id->nrows) - 1;
    while ((j > 0) && (id->m[j]==NULL)) j--;
    for (int i = 0; i <= j; i++)
    {
      Print("generator %d: ",i); p_wrp(id->m[i], lmRing, tailRing);PrintLn();
    }
  }
}

idSkipZeroes()

void idSkipZeroes

(

ideal

ide

)

gives an ideal/module the minimal possible size

Definition at line 201 of file simpleideals.cc.

{
  if(ide!=NULL)
  {
    int k;
    int j = -1;
    int idelems=IDELEMS(ide);
    BOOLEAN change=FALSE;
 
    for (k=0; k<idelems; k++)
    {
      if (ide->m[k] != NULL)
      {
        j++;
        if (change)
        {
          ide->m[j] = ide->m[k];
          ide->m[k] = NULL;
        }
      }
      else
      {
        change=TRUE;
      }
    }
    if (change)
    {
      if (j == -1)
        j = 0;
      j++;
      pEnlargeSet(&(ide->m),idelems,j-idelems);
      IDELEMS(ide) = j;
    }
  }
}

idSkipZeroes0()

int idSkipZeroes0

(

ideal

ide

)

Definition at line 237 of file simpleideals.cc.

{
  assume (ide != NULL);
 
  int k;
  int j = -1;
  int idelems=IDELEMS(ide);
 
  k=0;
  while((k<idelems)&&(ide->m[k] != NULL)) k++;
  if (k==idelems) return idelems;
  // now: k: pos of first NULL entry
  j=k; k=k+1;
  for (; k<idelems; k++)
  {
    if (ide->m[k] != NULL)
    {
      ide->m[j] = ide->m[k];
      ide->m[k] = NULL;
      j++;
    }
  }
  if (j<=1) return 1;
  return j;
}

Variable Documentation

sip_sideal_bin

EXTERN_VAR omBin sip_sideal_bin

Definition at line 54 of file simpleideals.h.