Package edu.jas.gb

Class SolvableGroebnerBaseAbstract<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.SolvableGroebnerBaseAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableGroebnerBase<C>, java.io.Serializable

Direct Known Subclasses:

SGBProxy, SolvableGroebnerBaseParallel, SolvableGroebnerBasePseudoRecSeq, SolvableGroebnerBasePseudoSeq, SolvableGroebnerBaseSeq, SolvableGroebnerBaseSeqPairParallel

public abstract class SolvableGroebnerBaseAbstract<C extends RingElem<C>>
extends java.lang.Object
implements SolvableGroebnerBase<C>

Solvable Groebner Bases abstract class. Implements common left, right and twosided Groebner bases and left, right and twosided GB tests.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected BasicLinAlg<GenPolynomial<C>>	blas	Linear algebra engine.
GroebnerBaseAbstract<C>	cbb	Commutative Groebner bases engine.
Reduction<C>	red	Reduction engine.
SolvableReduction<C>	sred	Solvable reduction engine.
PairList<C>	strategy	Strategy for pair selection.

Constructor Summary

Constructors

Constructor	Description
SolvableGroebnerBaseAbstract()	Constructor.
SolvableGroebnerBaseAbstract(PairList<C> pl)	Constructor.
SolvableGroebnerBaseAbstract(SolvableReduction<C> sred)	Constructor.
SolvableGroebnerBaseAbstract(SolvableReduction<C> sred, PairList<C> pl)	Constructor.

Method Summary

Modifier and Type	Method	Description
int	cancel()	Cancel ThreadPool.
int	commonZeroTest(java.util.List<GenSolvablePolynomial<C>> A)	Ideal common zero test.
GenSolvablePolynomial<C>	constructUnivariate(int i, java.util.List<GenSolvablePolynomial<C>> G)	Construct univariate solvable polynomial of minimal degree in variable i of a zero dimensional ideal(G).
java.util.List<GenSolvablePolynomial<C>>	constructUnivariate(java.util.List<GenSolvablePolynomial<C>> G)	Construct univariate solvable polynomials of minimal degree in all variables in zero dimensional left ideal(G).
SolvableExtendedGB<C>	extLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Solvable Extended Groebner base using critical pair class.
SolvableExtendedGB<C>	extLeftGB(java.util.List<GenSolvablePolynomial<C>> F)	Solvable Extended Groebner base using critical pair class.
SolvableExtendedGB<C>	extRightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Solvable Extended Groebner base using critical pair class.
SolvableExtendedGB<C>	extRightGB(java.util.List<GenSolvablePolynomial<C>> F)	Solvable Extended Groebner base using critical pair class.
boolean	isLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Left Groebner base test.
boolean	isLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F, boolean b)	Left Groebner base test.
boolean	isLeftGB(ModuleList<C> M)	Module left Groebner base test.
boolean	isLeftGB(ModuleList<C> M, boolean top)	Module left Groebner base test.
boolean	isLeftGB(java.util.List<GenSolvablePolynomial<C>> F)	Left Groebner base test.
boolean	isLeftGB(java.util.List<GenSolvablePolynomial<C>> F, boolean b)	Left Groebner base test.
boolean	isLeftGBidem(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Left Groebner base idempotence test.
boolean	isLeftGBsimple(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Left Groebner base test.
boolean	isLeftReductionMatrix(SolvableExtendedGB<C> exgb)	Test if left reduction matrix.
boolean	isLeftReductionMatrix(java.util.List<GenSolvablePolynomial<C>> F, java.util.List<GenSolvablePolynomial<C>> G, java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mf, java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mg)	Test if left reduction matrix.
boolean	isRightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Right Groebner base test.
boolean	isRightGB(ModuleList<C> M)	Module right Groebner base test.
boolean	isRightGB(ModuleList<C> M, boolean top)	Module right Groebner base test.
boolean	isRightGB(java.util.List<GenSolvablePolynomial<C>> F)	Right Groebner base test.
boolean	isRightGBidem(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Right Groebner base idempotence test.
boolean	isRightGBidem(java.util.List<GenSolvablePolynomial<C>> F)	Right Groebner base idempotence test.
boolean	isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp)	Twosided Groebner base test.
boolean	isTwosidedGB(ModuleList<C> M)	Module twosided Groebner base test.
boolean	isTwosidedGB(ModuleList<C> M, boolean top)	Module twosided Groebner base test.
boolean	isTwosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)	Twosided Groebner base test.
boolean	isTwosidedGBidem(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Twosided Groebner base idempotence test.
boolean	isTwosidedGBidem(java.util.List<GenSolvablePolynomial<C>> F)	Twosided Groebner base idempotence test.
ModuleList<C>	leftGB(ModuleList<C> M)	Left Groebner base using pairlist class.
ModuleList<C>	leftGB(ModuleList<C> M, boolean top)	Left Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	leftGB(java.util.List<GenSolvablePolynomial<C>> F)	Left Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)	Left minimal ordered groebner basis.
java.util.List<GenSolvablePolynomial<C>>	normalizeZerosOnes(java.util.List<GenSolvablePolynomial<C>> A)	Normalize polynomial list.
java.util.List<GenSolvablePolynomial<C>>	rightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Right Groebner base using opposite ring left GB.
ModuleList<C>	rightGB(ModuleList<C> M)	Right Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	rightGB(java.util.List<GenSolvablePolynomial<C>> F)	Right Groebner base using opposite ring left GB.
java.util.List<GenSolvablePolynomial<C>>	rightMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)	Right minimal ordered groebner basis.
void	terminate()	Cleanup and terminate ThreadPool.
ModuleList<C>	twosidedGB(ModuleList<C> M)	Twosided Groebner base using pairlist class.
ModuleList<C>	twosidedGB(ModuleList<C> M, boolean top)	Twosided Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	twosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)	Twosided Groebner base using pairlist class.
java.util.List<java.lang.Long>	univariateDegrees(java.util.List<GenSolvablePolynomial<C>> A)	Univariate head term degrees.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface edu.jas.gb.SolvableGroebnerBase

leftGB, twosidedGB

Field Detail

sred

public SolvableReduction<C extends RingElem<C>> sred

Solvable reduction engine.

red

public final Reduction<C extends RingElem<C>> red

Reduction engine.

strategy

public final PairList<C extends RingElem<C>> strategy

Strategy for pair selection.

blas

protected final BasicLinAlg<GenPolynomial<C extends RingElem<C>>> blas

Linear algebra engine.

cbb

public final GroebnerBaseAbstract<C extends RingElem<C>> cbb

Commutative Groebner bases engine.

Constructor Detail

SolvableGroebnerBaseAbstract

public SolvableGroebnerBaseAbstract()

Constructor.

SolvableGroebnerBaseAbstract

public SolvableGroebnerBaseAbstract(SolvableReduction<C> sred)

Constructor.

Parameters:

sred - Solvable reduction engine

SolvableGroebnerBaseAbstract

public SolvableGroebnerBaseAbstract(PairList<C> pl)

Constructor.

Parameters:

pl - pair selection strategy

SolvableGroebnerBaseAbstract

public SolvableGroebnerBaseAbstract(SolvableReduction<C> sred,
                                    PairList<C> pl)

Constructor.

Parameters:

sred - Solvable reduction engine

pl - pair selection strategy

Method Detail

normalizeZerosOnes

public java.util.List<GenSolvablePolynomial<C>> normalizeZerosOnes(java.util.List<GenSolvablePolynomial<C>> A)

Normalize polynomial list.

Parameters:

A - list of polynomials.

Returns:

list of polynomials with zeros removed and ones/units reduced.

isLeftGB

public boolean isLeftGB(java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base test.

Specified by:

isLeftGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

F - solvable polynomial list.

Returns:

true, if F is a left Groebner base, else false.

isLeftGB

public boolean isLeftGB(java.util.List<GenSolvablePolynomial<C>> F,
                        boolean b)

Left Groebner base test.

Parameters:

F - solvable polynomial list.

b - true for simple test, false for GB test.

Returns:

true, if F is a Groebner base, else false.

isLeftGB

public boolean isLeftGB(int modv,
                        java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base test.

Specified by:

isLeftGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

true, if F is a Groebner base, else false.

isLeftGB

public boolean isLeftGB(int modv,
                        java.util.List<GenSolvablePolynomial<C>> F,
                        boolean b)

Left Groebner base test.

Parameters:

modv - module variable number.

F - solvable polynomial list.

b - true for simple test, false for GB test.

Returns:

true, if F is a Groebner base, else false.

isLeftGBsimple

public boolean isLeftGBsimple(int modv,
                              java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base test.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

true, if F is a left Groebner base, else false.

isLeftGBidem

public boolean isLeftGBidem(int modv,
                            java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base idempotence test.

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

true, if F is equal to GB(F), else false.

isTwosidedGB

public boolean isTwosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base test.

Specified by:

isTwosidedGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

Fp - solvable polynomial list.

Returns:

true, if Fp is a two-sided Groebner base, else false.

isTwosidedGB

public boolean isTwosidedGB(int modv,
                            java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base test.

Specified by:

isTwosidedGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

true, if Fp is a two-sided Groebner base, else false.

isTwosidedGBidem

public boolean isTwosidedGBidem(java.util.List<GenSolvablePolynomial<C>> F)

Twosided Groebner base idempotence test.

Parameters:

F - solvable polynomial list.

Returns:

true, if F is equal to GB(F), else false.

isTwosidedGBidem

public boolean isTwosidedGBidem(int modv,
                                java.util.List<GenSolvablePolynomial<C>> F)

Twosided Groebner base idempotence test.

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

true, if F is equal to GB(F), else false.

isRightGB

public boolean isRightGB(java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base test.

Specified by:

isRightGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

F - solvable polynomial list.

Returns:

true, if F is a right Groebner base, else false.

isRightGB

public boolean isRightGB(int modv,
                         java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base test.

Specified by:

isRightGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

true, if F is a right Groebner base, else false.

isRightGBidem

public boolean isRightGBidem(java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base idempotence test.

Parameters:

F - solvable polynomial list.

Returns:

true, if F is equal to GB(F), else false.

isRightGBidem

public boolean isRightGBidem(int modv,
                             java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base idempotence test.

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

true, if F is equal to GB(F), else false.

leftGB

public java.util.List<GenSolvablePolynomial<C>> leftGB(java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base using pairlist class.

Specified by:

leftGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

F - solvable polynomial list.

Returns:

leftGB(F) a left Groebner base of F.

extLeftGB

public SolvableExtendedGB<C> extLeftGB(java.util.List<GenSolvablePolynomial<C>> F)

Solvable Extended Groebner base using critical pair class.

Specified by:

extLeftGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

F - solvable polynomial list.

Returns:

a container for an extended left Groebner base of F.

extLeftGB

public SolvableExtendedGB<C> extLeftGB(int modv,
                                       java.util.List<GenSolvablePolynomial<C>> F)

Solvable Extended Groebner base using critical pair class.

Specified by:

extLeftGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

a container for an extended left Groebner base G of F together with back-and-forth transformations.

leftMinimalGB

public java.util.List<GenSolvablePolynomial<C>> leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)

Left minimal ordered groebner basis.

Specified by:

leftMinimalGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

Gp - a left Groebner base.

Returns:

leftGBmi(F) a minimal left Groebner base of Gp.

rightMinimalGB

public java.util.List<GenSolvablePolynomial<C>> rightMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)

Right minimal ordered groebner basis.

Parameters:

Gp - a right Groebner base.

Returns:

rightGBmi(F) a minimal right Groebner base of Gp.

twosidedGB

public java.util.List<GenSolvablePolynomial<C>> twosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base using pairlist class.

Specified by:

twosidedGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

rightGB

public java.util.List<GenSolvablePolynomial<C>> rightGB(java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base using opposite ring left GB.

Specified by:

rightGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

F - solvable polynomial list.

Returns:

rightGB(F) a right Groebner base of F.

rightGB

public java.util.List<GenSolvablePolynomial<C>> rightGB(int modv,
                                                        java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base using opposite ring left GB.

Specified by:

rightGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

rightGB(F) a right Groebner base of F.

extRightGB

public SolvableExtendedGB<C> extRightGB(java.util.List<GenSolvablePolynomial<C>> F)

Solvable Extended Groebner base using critical pair class.

Parameters:

F - solvable polynomial list.

Returns:

a container for an extended right Groebner base of F.

extRightGB

public SolvableExtendedGB<C> extRightGB(int modv,
                                        java.util.List<GenSolvablePolynomial<C>> F)

Solvable Extended Groebner base using critical pair class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

a container for an extended right Groebner base G of F together with back-and-forth transformations.

isLeftGB

public boolean isLeftGB(ModuleList<C> M)

Module left Groebner base test.

Specified by:

isLeftGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

M - a module basis.

Returns:

true, if M is a left Groebner base, else false.

isLeftGB

public boolean isLeftGB(ModuleList<C> M,
                        boolean top)

Module left Groebner base test.

Parameters:

M - a module basis.

top - true for TOP term order, false for POT term order.

Returns:

true, if M is a left Groebner base, else false.

leftGB

public ModuleList<C> leftGB(ModuleList<C> M)

Left Groebner base using pairlist class.

Specified by:

leftGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

M - a module basis.

Returns:

leftGB(M) a left Groebner base for M.

leftGB

public ModuleList<C> leftGB(ModuleList<C> M,
                            boolean top)

Left Groebner base using pairlist class.

Parameters:

M - a module basis.

top - true for TOP term order, false for POT term order.

Returns:

leftGB(M) a left Groebner base for M.

isTwosidedGB

public boolean isTwosidedGB(ModuleList<C> M)

Module twosided Groebner base test.

Specified by:

isTwosidedGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

M - a module basis.

Returns:

true, if M is a twosided Groebner base, else false.

isTwosidedGB

public boolean isTwosidedGB(ModuleList<C> M,
                            boolean top)

Module twosided Groebner base test.

Parameters:

M - a module basis.

top - true for TOP term order, false for POT term order.

Returns:

true, if M is a twosided Groebner base, else false.

twosidedGB

public ModuleList<C> twosidedGB(ModuleList<C> M)

Twosided Groebner base using pairlist class.

Specified by:

twosidedGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

M - a module basis.

Returns:

twosidedGB(M) a twosided Groebner base for M.

twosidedGB

public ModuleList<C> twosidedGB(ModuleList<C> M,
                                boolean top)

Twosided Groebner base using pairlist class.

Parameters:

M - a module basis.

top - true for TOP term order, false for POT term order.

Returns:

tsGB(M) a twosided Groebner base for M.

isRightGB

public boolean isRightGB(ModuleList<C> M)

Module right Groebner base test.

Specified by:

isRightGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

M - a module basis.

Returns:

true, if M is a right Groebner base, else false.

isRightGB

public boolean isRightGB(ModuleList<C> M,
                         boolean top)

Module right Groebner base test.

Parameters:

M - a module basis.

top - true for TOP term order, false for POT term order.

Returns:

true, if M is a right Groebner base, else false.

rightGB

public ModuleList<C> rightGB(ModuleList<C> M)

Right Groebner base using pairlist class.

Specified by:

rightGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

M - a module basis.

Returns:

rightGB(M) a right Groebner base for M.

isLeftReductionMatrix

public boolean isLeftReductionMatrix(SolvableExtendedGB<C> exgb)

Test if left reduction matrix.

Specified by:

isLeftReductionMatrix in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

exgb - an SolvableExtendedGB container.

Returns:

true, if exgb contains a left reduction matrix, else false.

isLeftReductionMatrix

public boolean isLeftReductionMatrix(java.util.List<GenSolvablePolynomial<C>> F,
                                     java.util.List<GenSolvablePolynomial<C>> G,
                                     java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mf,
                                     java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mg)

Test if left reduction matrix.

Specified by:

isLeftReductionMatrix in interface SolvableGroebnerBase<C extends RingElem<C>>

Parameters:

F - a solvable polynomial list.

G - a left Groebner base.

Mf - a possible left reduction matrix.

Mg - a possible left reduction matrix.

Returns:

true, if Mg and Mf are left reduction matrices, else false.

commonZeroTest

public int commonZeroTest(java.util.List<GenSolvablePolynomial<C>> A)

Ideal common zero test.

Returns:

-1, 0 or 1 if dimension(this) &eq; -1, 0 or ≥ 1.

univariateDegrees

public java.util.List<java.lang.Long> univariateDegrees(java.util.List<GenSolvablePolynomial<C>> A)

Univariate head term degrees.

Parameters:

A - list of solvable polynomials.

Returns:

a list of the degrees of univariate head terms.

constructUnivariate

public GenSolvablePolynomial<C> constructUnivariate(int i,
                                                    java.util.List<GenSolvablePolynomial<C>> G)

Construct univariate solvable polynomial of minimal degree in variable i of a zero dimensional ideal(G).

Parameters:

i - variable index.

G - list of solvable polynomials, a monic reduced left Gröbner base of a zero dimensional ideal.

Returns:

univariate solvable polynomial of minimal degree in variable i in ideal_left(G)

constructUnivariate

public java.util.List<GenSolvablePolynomial<C>> constructUnivariate(java.util.List<GenSolvablePolynomial<C>> G)

Construct univariate solvable polynomials of minimal degree in all variables in zero dimensional left ideal(G).

Returns:

list of univariate polynomial of minimal degree in each variable in ideal_left(G)

terminate

public void terminate()

Cleanup and terminate ThreadPool.

cancel

public int cancel()

Cancel ThreadPool.