edu.jas.application

Class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.ComprehensiveGroebnerBaseSeq<C>

Type Parameters:

C - coefficient type

public class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>
extends java.lang.Object

Comprehensive Groebner Base sequential algorithm. Implements faithful comprehensive Groebner bases via Groebner systems and CGB test.

Constructor Summary

Constructors

Constructor and Description
ComprehensiveGroebnerBaseSeq(CReductionSeq<C> red, RingFactory<C> rf) Constructor.
ComprehensiveGroebnerBaseSeq(RingFactory<C> rf) Constructor.

Method Summary

Modifier and Type	Method and Description
java.util.List<ColoredSystem<C>>	determineAddPairs(ColoredSystem<C> cs, ColorPolynomial<C> A) Determine polynomial relative to a condition of a colored system and add pairs.
java.util.List<GenPolynomial<GenPolynomial<C>>>	GB(java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive Groebner base via Groebner system.
GroebnerSystem<C>	GBsys(java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive Groebner base system using pairlist class.
boolean	isCGB(GroebnerSystem<C> F) Comprehensive-Groebner base test.
boolean	isGB(GroebnerSystem<C> F) Comprehensive-Groebner system and base test.
boolean	isGB(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test.
boolean	isGB(java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test.
boolean	isGBcol(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using colored systems.
boolean	isGBcol(java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using colored systems.
boolean	isGBsubst(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using substitution.
boolean	isGBsubst(java.util.List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using substitution.
boolean	isGBsys(GroebnerSystem<C> F) Comprehensive-Groebner system test.
boolean	isGBsys(int modv, java.util.List<ColoredSystem<C>> CS) Comprehensive-Groebner system test.
boolean	isGBsys(java.util.List<ColoredSystem<C>> CS) Comprehensive-Groebner system test.
ColoredSystem<C>	minimalGB(ColoredSystem<C> cs) Minimal ordered Groebner basis.

Methods inherited from class java.lang.Object

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

Constructor Detail

ComprehensiveGroebnerBaseSeq

public ComprehensiveGroebnerBaseSeq(RingFactory<C> rf)

Constructor.

Parameters:

rf - base coefficient ring factory.

ComprehensiveGroebnerBaseSeq

public ComprehensiveGroebnerBaseSeq(CReductionSeq<C> red,
                                    RingFactory<C> rf)

Constructor.

Parameters:

red - C-pseudo-Reduction engine

rf - base coefficient ring factory.

Method Detail

isGB

public boolean isGB(java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive-Groebner base test.

Parameters:

F - polynomial list.

Returns:

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

isGB

public boolean isGB(int modv,
                    java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive-Groebner base test.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

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

isGBcol

public boolean isGBcol(java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive-Groebner base test using colored systems.

Parameters:

F - polynomial list.

Returns:

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

isGBcol

public boolean isGBcol(int modv,
                       java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive-Groebner base test using colored systems.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

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

isGBsys

public boolean isGBsys(java.util.List<ColoredSystem<C>> CS)

Comprehensive-Groebner system test.

Parameters:

CS - list of colored systems.

Returns:

true, if CS is a Comprehensive-Groebner system, else false.

isGBsys

public boolean isGBsys(int modv,
                       java.util.List<ColoredSystem<C>> CS)

Comprehensive-Groebner system test.

Parameters:

modv - module variable number.

CS - list of colored systems.

Returns:

true, if CS is a Comprehensive-Groebner system, else false.

isGBsubst

public boolean isGBsubst(java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive-Groebner base test using substitution.

Parameters:

F - polynomial list.

Returns:

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

isGBsubst

public boolean isGBsubst(int modv,
                         java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive-Groebner base test using substitution.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

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

isGBsys

public boolean isGBsys(GroebnerSystem<C> F)

Comprehensive-Groebner system test.

Parameters:

F - Groebner system.

Returns:

true, if F is a Comprehensive-Groebner system, else false.

isCGB

public boolean isCGB(GroebnerSystem<C> F)

Comprehensive-Groebner base test.

Parameters:

F - Groebner system.

Returns:

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

isGB

public boolean isGB(GroebnerSystem<C> F)

Comprehensive-Groebner system and base test.

Parameters:

F - Groebner system.

Returns:

true, if F is a Comprehensive-Groebner system and base, else false.

GBsys

public GroebnerSystem<C> GBsys(java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive Groebner base system using pairlist class.

Parameters:

F - polynomial list.

Returns:

GBsys(F) a Comprehensive Groebner system of F.

determineAddPairs

public java.util.List<ColoredSystem<C>> determineAddPairs(ColoredSystem<C> cs,
                                                          ColorPolynomial<C> A)

Determine polynomial relative to a condition of a colored system and add pairs.

Parameters:

cs - a colored system.

A - color polynomial.

Returns:

list of colored systems, the conditions extending the condition of cs.

GB

public java.util.List<GenPolynomial<GenPolynomial<C>>> GB(java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Comprehensive Groebner base via Groebner system.

Parameters:

F - polynomial list.

Returns:

GB(F) a Comprehensive Groebner base of F.

minimalGB

public ColoredSystem<C> minimalGB(ColoredSystem<C> cs)

Minimal ordered Groebner basis.

Parameters:

cs - colored system.

Returns:

a reduced Groebner base of Gp.