Computing syzygies after Schreyer. More...

#include <syzextra.h>

Public Member Functions
	SchreyerSyzygyComputation (const ideal idLeads, const ideal idTails, const SchreyerSyzygyComputationFlags setting)
	Construct a global object for given input data (separated into leads & tails) More...

	SchreyerSyzygyComputation (const ideal idLeads, const ideal idTails, const ideal syzLeads, const SchreyerSyzygyComputationFlags setting)
	Construct a global object for given input data (separated into leads & tails) More...

	~SchreyerSyzygyComputation ()
	Destructor should not destruct the resulting m_syzLeads, m_syzTails. More...

void	SetUpTailTerms ()
	Convert the given ideal of tails into the internal representation (with reducers!) Preprocess m_idTails as well...? More...

void	PrintStats () const
	print statistics about the used heuristics More...

void	ReadOffResult (ideal &syzL, ideal &syzT)
	Read off the results while detaching them from this object NOTE: no copy! More...

void	ComputeSyzygy ()
	The main driver function: computes. More...

void	ComputeLeadingSyzygyTerms (bool bComputeSecondTerms=true)
	Computes Syz(leads) or only LEAD of it. The result is stored into m_syzLeads. More...

poly	SchreyerSyzygyNF (const poly syz_lead, poly syz_2=NULL) const
	Main HybridNF == 1: poly reduce + LOT + LCM? More...

poly	TraverseNF (const poly syz_lead, const poly syz_2=NULL) const

poly	TraverseTail (poly multiplier, const int tail) const
	High level caching function!!! More...

poly	TraverseTail (poly multiplier, poly tail) const
	called only from above and from outside (for testing) More...

poly	ReduceTerm (poly multiplier, poly term4reduction, poly syztermCheck) const
	TODO: save shortcut (syz: \|-.->) LM(m) * "t" -> ? ??? More...

poly	ComputeImage (poly multiplier, const int tail) const
	low level computation... More...

poly	_FindReducer (const poly product, const poly syzterm) const
	just for testing via the wrapper below More...

Public Member Functions inherited from SchreyerSyzygyComputationFlags
	SchreyerSyzygyComputationFlags (idhdl rootRingHdl)

	SchreyerSyzygyComputationFlags (const SchreyerSyzygyComputationFlags &attr)

void	nextSyzygyLayer () const

Protected Member Functions
ideal	Compute1LeadingSyzygyTerms ()
	just leading terms More...

ideal	Compute2LeadingSyzygyTerms ()
	leading + second terms More...

Private Member Functions
void	CleanUp ()

Private Attributes
const ideal	m_idLeads
	input leading terms More...

const ideal	m_idTails
	input tails More...

ideal	m_syzLeads
	output (syzygy) leading terms (+2nd terms?) More...

ideal	m_syzTails
	output (syzygy) tails More...

ideal	m_LS
	leading syzygy terms used for reducing syzygy tails More...

const CLCM	m_lcm
	Bitmask for variables occuring in leading terms. More...

const CReducerFinder	m_div
	Divisor finder. More...

CReducerFinder	m_checker
	for checking tail-terms and makeing them irreducible (wrt m_LS!) More...

TCache	m_cache

SBucketFactory	m_sum_bucket_factory
	used for simple summing up More...

kBucket_pt	m_spoly_bucket
	for S-Polynomial reductions More...

unsigned long	m_stat [9]
	Statistics: 0..3: as in SetUpTailTerms()::PreProcessTerm() // TODO!!?? 4: number of terms discarded due to LOT heuristics 5: number of terms discarded due to LCM heuristics 6, 7: lookups without & with rescale, 8: stores. More...

Friends
class	CLCM

class	CReducerFinder

Additional Inherited Members
Data Fields inherited from SchreyerSyzygyComputationFlags
const int	OPT__DEBUG
	output all the intermediate states More...

const int	OPT__LEAD2SYZ
	? More...

const int	OPT__TAILREDSYZ
	Reduce syzygy tails wrt the leading syzygy terms. More...

const int	OPT__HYBRIDNF
	Use the usual NF's S-poly reduction while dropping lower order terms 2 means - smart selection! More...

const int	OPT__IGNORETAILS
	ignore tails and compute the pure Schreyer frame More...

int	OPT__SYZNUMBER
	Syzygy level (within a resolution) More...

const int	OPT__TREEOUTPUT
	output lifting tree More...

const int	OPT__SYZCHECK
	CheckSyzygyProperty: TODO. More...

const bool	OPT__PROT
	TEST_OPT_PROT. More...

const int	OPT__NOCACHING
	no caching/stores/lookups More...

const ring	m_rBaseRing
	global base ring More...

Detailed Description

Computing syzygies after Schreyer.

Storing/accumulating data during the computation requires some global object, like this class. Ideally the above global functions should not be used in favour of this class.

See also: Schreyer Syzygy Computation Paper & Talk & Python prototype

Definition at line 328 of file syzextra.h.

Constructor & Destructor Documentation

◆ SchreyerSyzygyComputation() [1/2]

SchreyerSyzygyComputation::SchreyerSyzygyComputation	(	const ideal	idLeads,
		const ideal	idTails,
		const SchreyerSyzygyComputationFlags	setting
	)

inline

Construct a global object for given input data (separated into leads & tails)

Definition at line 335 of file syzextra.h.

                                                                                                                     :
        SchreyerSyzygyComputationFlags(setting),
        m_idLeads(idLeads), m_idTails(id_Copy(idTails, setting.m_rBaseRing)),
        m_syzLeads(NULL), m_syzTails(NULL),
        m_LS(NULL), m_lcm(m_idLeads, setting),
        m_div(m_idLeads, setting), m_checker(NULL, setting), m_cache(),
        m_sum_bucket_factory(setting.m_rBaseRing),
        m_spoly_bucket(NULL)
    {
      if( UNLIKELY(OPT__PROT) ) memset( &m_stat, 0, sizeof(m_stat) );
    }

◆ SchreyerSyzygyComputation() [2/2]

SchreyerSyzygyComputation::SchreyerSyzygyComputation	(	const ideal	idLeads,
		const ideal	idTails,
		const ideal	syzLeads,
		const SchreyerSyzygyComputationFlags	setting
	)

inline

Construct a global object for given input data (separated into leads & tails)

Definition at line 348 of file syzextra.h.

                                                                                                                                           :
        SchreyerSyzygyComputationFlags(setting),
        m_idLeads(idLeads), m_idTails(id_Copy(idTails, setting.m_rBaseRing)),
        m_syzLeads(syzLeads), m_syzTails(NULL),
        m_LS(syzLeads), m_lcm(m_idLeads, setting),
        m_div(m_idLeads, setting), m_checker(NULL, setting), m_cache(),
        m_sum_bucket_factory(setting.m_rBaseRing),
        m_spoly_bucket(NULL)
    {
      if( UNLIKELY(OPT__PROT) ) memset( &m_stat, 0, sizeof(m_stat) );
 
      if( LIKELY(OPT__TAILREDSYZ && !OPT__IGNORETAILS) )
      {
        if (syzLeads != NULL)
          m_checker.Initialize(syzLeads);
//        if( idTails != NULL )
//          SetUpTailTerms();
      }
    }

◆ ~SchreyerSyzygyComputation()

SchreyerSyzygyComputation::~SchreyerSyzygyComputation ( )

inline

Destructor should not destruct the resulting m_syzLeads, m_syzTails.

Definition at line 369 of file syzextra.h.

369{ CleanUp(); }

SchreyerSyzygyComputation::CleanUp

void CleanUp()

Member Function Documentation

◆ _FindReducer()

poly SchreyerSyzygyComputation::_FindReducer	(	const poly	product,
		const poly	syzterm
	)		const

inline

just for testing via the wrapper below

Definition at line 422 of file syzextra.h.

423 { return m_div.FindReducer(product, syzterm, m_checker); }

CReducerFinder::FindReducer

poly FindReducer(const poly multiplier, const poly monom, const poly syzterm, const CReducerFinder &checker) const

◆ CleanUp()

void SchreyerSyzygyComputation::CleanUp ( )

private

◆ Compute1LeadingSyzygyTerms()

ideal SchreyerSyzygyComputation::Compute1LeadingSyzygyTerms ( )

protected

just leading terms

◆ Compute2LeadingSyzygyTerms()

ideal SchreyerSyzygyComputation::Compute2LeadingSyzygyTerms ( )

protected

leading + second terms

◆ ComputeImage()

poly SchreyerSyzygyComputation::ComputeImage	(	poly	multiplier,
		const int	tail
	)		const

low level computation...

◆ ComputeLeadingSyzygyTerms()

void SchreyerSyzygyComputation::ComputeLeadingSyzygyTerms ( bool bComputeSecondTerms = true )

Computes Syz(leads) or only LEAD of it. The result is stored into m_syzLeads.

◆ ComputeSyzygy()

void SchreyerSyzygyComputation::ComputeSyzygy ( )

The main driver function: computes.

◆ PrintStats()

void SchreyerSyzygyComputation::PrintStats ( ) const

print statistics about the used heuristics

◆ ReadOffResult()

void SchreyerSyzygyComputation::ReadOffResult	(	ideal &	syzL,
		ideal &	syzT
	)

inline

Read off the results while detaching them from this object NOTE: no copy!

Definition at line 380 of file syzextra.h.

    {
      syzL = m_syzLeads; syzT = m_syzTails;
 
      m_syzLeads = m_syzTails = NULL; // m_LS ?
 
      if ( UNLIKELY(OPT__PROT) )
        PrintStats();
    }

◆ ReduceTerm()

poly SchreyerSyzygyComputation::ReduceTerm	(	poly	multiplier,
		poly	term4reduction,
		poly	syztermCheck
	)		const

TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? ???

◆ SchreyerSyzygyNF()

poly SchreyerSyzygyComputation::SchreyerSyzygyNF	(	const poly	syz_lead,
		poly	syz_2 = `NULL`
	)		const

Main HybridNF == 1: poly reduce + LOT + LCM?

◆ SetUpTailTerms()

void SchreyerSyzygyComputation::SetUpTailTerms ( )

Convert the given ideal of tails into the internal representation (with reducers!) Preprocess m_idTails as well...?

◆ TraverseNF()

poly SchreyerSyzygyComputation::TraverseNF	(	const poly	syz_lead,
		const poly	syz_2 = `NULL`
	)		const

◆ TraverseTail() [1/2]

poly SchreyerSyzygyComputation::TraverseTail	(	poly	multiplier,
		const int	tail
	)		const

High level caching function!!!

◆ TraverseTail() [2/2]

poly SchreyerSyzygyComputation::TraverseTail	(	poly	multiplier,
		poly	tail
	)		const

called only from above and from outside (for testing)

Friends And Related Function Documentation

◆ CLCM

friend class CLCM

friend

Definition at line 330 of file syzextra.h.

◆ CReducerFinder

friend class CReducerFinder

friend

Definition at line 331 of file syzextra.h.

Field Documentation

◆ m_cache

TCache SchreyerSyzygyComputation::m_cache

mutableprivate

Definition at line 462 of file syzextra.h.

◆ m_checker

CReducerFinder SchreyerSyzygyComputation::m_checker

private

for checking tail-terms and makeing them irreducible (wrt m_LS!)

Definition at line 460 of file syzextra.h.

◆ m_div

const CReducerFinder SchreyerSyzygyComputation::m_div

private

Divisor finder.

Definition at line 457 of file syzextra.h.

◆ m_idLeads

const ideal SchreyerSyzygyComputation::m_idLeads

private

input leading terms

Definition at line 439 of file syzextra.h.

◆ m_idTails

const ideal SchreyerSyzygyComputation::m_idTails

private

input tails

Definition at line 442 of file syzextra.h.

◆ m_lcm

const CLCM SchreyerSyzygyComputation::m_lcm

private

Bitmask for variables occuring in leading terms.

Definition at line 454 of file syzextra.h.

◆ m_LS

ideal SchreyerSyzygyComputation::m_LS

private

leading syzygy terms used for reducing syzygy tails

Definition at line 450 of file syzextra.h.

◆ m_spoly_bucket

kBucket_pt SchreyerSyzygyComputation::m_spoly_bucket

mutableprivate

for S-Polynomial reductions

Definition at line 468 of file syzextra.h.

◆ m_stat

unsigned long SchreyerSyzygyComputation::m_stat[9]

mutableprivate

Statistics: 0..3: as in SetUpTailTerms()::PreProcessTerm() // TODO!!?? 4: number of terms discarded due to LOT heuristics 5: number of terms discarded due to LCM heuristics 6, 7: lookups without & with rescale, 8: stores.

Definition at line 476 of file syzextra.h.

◆ m_sum_bucket_factory

SBucketFactory SchreyerSyzygyComputation::m_sum_bucket_factory

mutableprivate

used for simple summing up

Definition at line 465 of file syzextra.h.

◆ m_syzLeads

ideal SchreyerSyzygyComputation::m_syzLeads

private

output (syzygy) leading terms (+2nd terms?)

Definition at line 445 of file syzextra.h.

◆ m_syzTails

ideal SchreyerSyzygyComputation::m_syzTails

private

output (syzygy) tails

Definition at line 448 of file syzextra.h.

The documentation for this class was generated from the following file:

Singular/dyn_modules/syzextra/syzextra.h

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SchreyerSyzygyComputation() [1/2]

◆ SchreyerSyzygyComputation() [2/2]

◆ ~SchreyerSyzygyComputation()

Member Function Documentation

◆ _FindReducer()

◆ CleanUp()

◆ Compute1LeadingSyzygyTerms()

◆ Compute2LeadingSyzygyTerms()

◆ ComputeImage()

◆ ComputeLeadingSyzygyTerms()

◆ ComputeSyzygy()

◆ PrintStats()

◆ ReadOffResult()

◆ ReduceTerm()

◆ SchreyerSyzygyNF()

◆ SetUpTailTerms()

◆ TraverseNF()

◆ TraverseTail() [1/2]

◆ TraverseTail() [2/2]

Friends And Related Function Documentation

◆ CLCM

◆ CReducerFinder

Field Documentation

◆ m_cache

◆ m_checker

◆ m_div

◆ m_idLeads

◆ m_idTails

◆ m_lcm

◆ m_LS

◆ m_spoly_bucket

◆ m_stat

◆ m_sum_bucket_factory

◆ m_syzLeads

◆ m_syzTails