Package edu.jas.gb

Class SolvableReductionSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.SolvableReductionAbstract<C>

edu.jas.gb.SolvableReductionSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableReduction<C>, java.io.Serializable

public class SolvableReductionSeq<C extends RingElem<C>>
extends SolvableReductionAbstract<C>

Solvable polynomial Reduction algorithm. Implements left, right normalform.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
SolvableReductionSeq()	Constructor.

Method Summary

Modifier and Type	Method	Description
GenSolvablePolynomial<C>	leftNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Left Normalform.
GenSolvablePolynomial<C>	leftNormalform(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	LeftNormalform with recording.
GenSolvablePolynomial<C>	rightNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Right Normalform.
GenSolvablePolynomial<C>	rightNormalform(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	RightNormalform with recording.

Methods inherited from class edu.jas.gb.SolvableReductionAbstract

isLeftReductionNF, isNormalform, isReducible, isRightReductionNF, isTopReducible, leftIrreducibleSet, leftNormalform, leftNormalform, leftNormalform, leftSPolynomial, leftSPolynomial, normalform, rightSPolynomial, rightSPolynomial

Methods inherited from class java.lang.Object

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

Constructor Detail

SolvableReductionSeq

public SolvableReductionSeq()

Constructor.

Method Detail

leftNormalform

public GenSolvablePolynomial<C> leftNormalform(java.util.List<GenSolvablePolynomial<C>> Pp,
                                               GenSolvablePolynomial<C> Ap)

Left Normalform.

Parameters:

Ap - solvable polynomial.

Pp - solvable polynomial list.

Returns:

left-nf(Ap) with respect to Pp.

leftNormalform

public GenSolvablePolynomial<C> leftNormalform(java.util.List<GenSolvablePolynomial<C>> row,
                                               java.util.List<GenSolvablePolynomial<C>> Pp,
                                               GenSolvablePolynomial<C> Ap)

LeftNormalform with recording.

Parameters:

row - recording matrix, is modified.

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

nf(Pp,Ap), the left normal form of Ap wrt. Pp.

rightNormalform

public GenSolvablePolynomial<C> rightNormalform(java.util.List<GenSolvablePolynomial<C>> Pp,
                                                GenSolvablePolynomial<C> Ap)

Right Normalform.

Parameters:

Ap - solvable polynomial.

Pp - solvable polynomial list.

Returns:

right-nf(Ap) with respect to Pp.

rightNormalform

public GenSolvablePolynomial<C> rightNormalform(java.util.List<GenSolvablePolynomial<C>> row,
                                                java.util.List<GenSolvablePolynomial<C>> Pp,
                                                GenSolvablePolynomial<C> Ap)

RightNormalform with recording.

Parameters:

row - recording matrix, is modified.

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

nf(Pp,Ap), the right normal form of Ap wrt. Pp.