edu.jas.gb

Interface SolvableGroebnerBase<C extends RingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

SolvableGroebnerBaseAbstract, SolvableGroebnerBaseParallel, SolvableGroebnerBaseSeq, SolvableGroebnerBaseSeqPairParallel

public interface SolvableGroebnerBase<C extends RingElem<C>>
extends java.io.Serializable

Solvable Groebner Bases interface. Defines methods for left, right and twosided Groebner bases and left, right and twosided GB tests.

Method Summary

Modifier and Type	Method and Description
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.
boolean	isLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base test.
boolean	isLeftGB(java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base test.
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	isLeftReductionMatrix(SolvableExtendedGB<C> exgb) Test if left reduction matrix.
boolean	isRightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Right Groebner base test.
boolean	isRightGB(java.util.List<GenSolvablePolynomial<C>> F) Right Groebner base test.
boolean	isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base test.
boolean	isTwosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base test.
java.util.List<GenSolvablePolynomial<C>>	leftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) 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>>	rightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Right Groebner base using opposite ring left GB.
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>>	twosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	twosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.

Method Detail

isLeftGB

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

Left Groebner base test.

Parameters:

F - solvable polynomial list.

Returns:

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

isLeftGB

boolean isLeftGB(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.

isTwosidedGB

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

Twosided Groebner base test.

Parameters:

Fp - solvable polynomial list.

Returns:

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

isTwosidedGB

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

Twosided Groebner base test.

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

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

isRightGB

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

Right Groebner base test.

Parameters:

F - solvable polynomial list.

Returns:

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

isRightGB

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

Right Groebner base test.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

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

leftGB

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

Left Groebner base using pairlist class.

Parameters:

F - solvable polynomial list.

Returns:

leftGB(F) a left Groebner base of F.

leftGB

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

Left Groebner base using pairlist class.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

leftGB(F) a left Groebner base of F.

extLeftGB

SolvableExtendedGB<C> extLeftGB(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 left Groebner base of F.

extLeftGB

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

Solvable Extended Groebner base using critical pair class.

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

a container for an extended left Groebner base of F.

leftMinimalGB

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

Left minimal ordered groebner basis.

Parameters:

Gp - a left Groebner base.

Returns:

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

twosidedGB

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

Twosided Groebner base using pairlist class.

Parameters:

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

twosidedGB

java.util.List<GenSolvablePolynomial<C>> twosidedGB(int modv,
                                                    java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base using pairlist class.

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

rightGB

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

Right Groebner base using opposite ring left GB.

Parameters:

F - solvable polynomial list.

Returns:

rightGB(F) a right Groebner base of F.

rightGB

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

Right Groebner base using opposite ring left GB.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

rightGB(F) a right Groebner base of F.

isLeftReductionMatrix

boolean isLeftReductionMatrix(SolvableExtendedGB<C> exgb)

Test if left reduction matrix.

Parameters:

exgb - an SolvableExtendedGB container.

Returns:

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

isLeftReductionMatrix

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.

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.