syzextra.h File Reference

Computation of Syzygies. More...

#include <vector>
#include <map>
#include <string.h>
#include <stack>
#include "singularxx_defs.h"
#include "kernel/ideals.h"

Go to the source code of this file.

Data Structures
class	SBucketFactory
	sBucket Factory More...
struct	SchreyerSyzygyComputationFlags
	Computation attribute storage. More...
class	CLCM
class	CLeadingTerm
class	CReducerFinder
struct	CCacheCompare
class	SchreyerSyzygyComputation
	Computing syzygies after Schreyer. More...

Macros
#define	NOPRODUCT   1
#define	NODIVISION   1

Typedefs
typedef idrec *	idhdl
typedef kBucket *	kBucket_pt
typedef sBucket *	sBucket_pt
typedef poly	TCacheKey
typedef poly	TCacheValue
typedef std::map< TCacheKey, TCacheValue, CCacheCompare >	TP2PCache
typedef std::map< int, TP2PCache >	TCache

Functions
poly	leadmonom (const poly p, const ring r, const bool bSetZeroComp=true)
poly	p_Tail (const poly p, const ring r)
	return the tail of a given polynomial or vector returns NULL if input is NULL, otherwise the result is a new polynomial/vector in the ring r More...
ideal	id_Tail (const ideal id, const ring r)
	return the tail of a given ideal or module returns NULL if input is NULL, otherwise the result is a new ideal/module in the ring r NOTE: the resulting rank is autocorrected More...
void	Sort_c_ds (const ideal id, const ring r)
	inplace sorting of the module (ideal) id wrt <_(c,ds) More...
bool	my_p_LmCmp (poly, poly, const ring)
static void	ComputeSyzygy (const ideal L, const ideal T, ideal &LL, ideal &TT, const SchreyerSyzygyComputationFlags A)
static ideal	ComputeLeadingSyzygyTerms (const ideal &L, const SchreyerSyzygyComputationFlags A)
static ideal	Compute2LeadingSyzygyTerms (const ideal &L, const SchreyerSyzygyComputationFlags A)
static poly	FindReducer (poly product, poly syzterm, ideal L, ideal LS, const SchreyerSyzygyComputationFlags A)
static poly	TraverseTail (poly multiplier, poly tail, ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A)
static poly	ReduceTerm (poly multiplier, poly term4reduction, poly syztermCheck, ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A)
static poly	SchreyerSyzygyNF (poly syz_lead, poly syz_2, ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A)

Detailed Description

Computation of Syzygies.

ABSTRACT: Computation of Syzygies due to Schreyer

Author

Oleksandr Motsak

Definition in file syzextra.h.

Macro Definition Documentation

NODIVISION

#define NODIVISION   1

Definition at line 39 of file syzextra.h.

NOPRODUCT

#define NOPRODUCT   1

Definition at line 33 of file syzextra.h.

Typedef Documentation

idhdl

typedef idrec* idhdl

Definition at line 28 of file syzextra.h.

kBucket_pt

typedef kBucket* kBucket_pt

Definition at line 30 of file syzextra.h.

sBucket_pt

typedef sBucket* sBucket_pt

Definition at line 60 of file syzextra.h.

TCache

typedef std::map<int, TP2PCache> TCache

Definition at line 328 of file syzextra.h.

TCacheKey

typedef poly TCacheKey

Definition at line 310 of file syzextra.h.

TCacheValue

typedef poly TCacheValue

Definition at line 311 of file syzextra.h.

TP2PCache

typedef std::map<TCacheKey, TCacheValue, CCacheCompare> TP2PCache

Definition at line 327 of file syzextra.h.

Function Documentation

Compute2LeadingSyzygyTerms()

static ideal Compute2LeadingSyzygyTerms ( const ideal &  L, const SchreyerSyzygyComputationFlags  A  )

inlinestatic

Definition at line 510 of file syzextra.h.

{
  SchreyerSyzygyComputation syz(L, NULL, A);
  syz.ComputeLeadingSyzygyTerms(true);
  ideal LL, TT;
  syz.ReadOffResult(LL, TT);
  return LL; // assume TT is NULL!
}

ComputeLeadingSyzygyTerms()

static ideal ComputeLeadingSyzygyTerms ( const ideal &  L, const SchreyerSyzygyComputationFlags  A  )

inlinestatic

Definition at line 501 of file syzextra.h.

{
  SchreyerSyzygyComputation syz(L, NULL, A);
  syz.ComputeLeadingSyzygyTerms(false);
  ideal LL, TT;
  syz.ReadOffResult(LL, TT);
  return LL; // assume TT is NULL!
}

ComputeSyzygy()

static void ComputeSyzygy ( const ideal  L, const ideal  T, ideal &  LL, ideal &  TT, const SchreyerSyzygyComputationFlags  A  )

inlinestatic

Definition at line 494 of file syzextra.h.

{
  SchreyerSyzygyComputation syz(L, T, A);
  syz.ComputeSyzygy();
  syz.ReadOffResult(LL, TT);
}

FindReducer()

static poly FindReducer ( poly  product, poly  syzterm, ideal  L, ideal  LS, const SchreyerSyzygyComputationFlags  A  )

inlinestatic

Definition at line 519 of file syzextra.h.

{
  SchreyerSyzygyComputation syz(L, NULL, LS, A);
  return syz._FindReducer(product, syzterm);
}

id_Tail()

ideal id_Tail	(	const ideal	id,
		const ring	r
	)

return the tail of a given ideal or module returns NULL if input is NULL, otherwise the result is a new ideal/module in the ring r NOTE: the resulting rank is autocorrected

Definition at line 48 of file syzextra.cc.

{
  if( UNLIKELY(id == NULL) )
    return NULL;
 
  const ideal newid = idInit(IDELEMS(id),id->rank);
 
  for (int i=IDELEMS(id) - 1; i >= 0; i--)
    newid->m[i] = p_Tail( id->m[i], r );
 
  newid->rank = id_RankFreeModule(newid, currRing);
 
  return newid;
}

leadmonom()

poly leadmonom	(	const poly	p,
		const ring	r,
		const bool	bSetZeroComp = true
	)

my_p_LmCmp()

bool my_p_LmCmp	(	poly	,
		poly	,
		const	ring
	)

p_Tail()

poly p_Tail	(	const poly	p,
		const ring	r
	)

return the tail of a given polynomial or vector returns NULL if input is NULL, otherwise the result is a new polynomial/vector in the ring r

Definition at line 40 of file syzextra.cc.

{
  if( UNLIKELY(p == NULL) )
    return NULL;
  else
    return p_Copy( pNext(p), r );
}

ReduceTerm()

static poly ReduceTerm ( poly  multiplier, poly  term4reduction, poly  syztermCheck, ideal  L, ideal  T, ideal  LS, const SchreyerSyzygyComputationFlags  A  )

inlinestatic

Definition at line 533 of file syzextra.h.

{
  SchreyerSyzygyComputation syz(L, T, LS, A);
  return syz.ReduceTerm(multiplier, term4reduction, syztermCheck);
}

SchreyerSyzygyNF()

static poly SchreyerSyzygyNF ( poly  syz_lead, poly  syz_2, ideal  L, ideal  T, ideal  LS, const SchreyerSyzygyComputationFlags  A  )

inlinestatic

Definition at line 541 of file syzextra.h.

{
  SchreyerSyzygyComputation syz(L, T, LS, A);
  return syz.SchreyerSyzygyNF(syz_lead, syz_2);
}

Sort_c_ds()

void Sort_c_ds	(	const ideal	id,
		const ring	r
	)

inplace sorting of the module (ideal) id wrt <_(c,ds)

TraverseTail()

static poly TraverseTail ( poly  multiplier, poly  tail, ideal  L, ideal  T, ideal  LS, const SchreyerSyzygyComputationFlags  A  )

inlinestatic

Definition at line 526 of file syzextra.h.

{
  SchreyerSyzygyComputation syz(L, T, LS, A);
  return syz.TraverseTail(multiplier, tail);
}