edu.jas.ring
Class SolvableReductionSeq<C extends RingElem<C>>

java.lang.Object
  edu.jas.ring.SolvableReductionAbstract<C>
      edu.jas.ring.SolvableReductionSeq<C>

All Implemented Interfaces:

SolvableReduction<C>

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

Solvable polynomial Reduction algorithm. Implements left, right normalform.

Author:

Heinz Kredel

Constructor Summary

SolvableReductionSeq()
Constructor.

Method Summary

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.

Methods inherited from class edu.jas.ring.SolvableReductionAbstract

isLeftReductionNF, leftIrreducibleSet, leftNormalform, leftSPolynomial, leftSPolynomial, 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.

Type parameter:

C coefficient type.

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.

Type parameter:

C coefficient type.

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.

Type parameter:

C coefficient type.

Parameters:

Ap - solvable polynomial.

Pp - solvable polynomial list.

Returns:

right-nf(Ap) with respect to Pp.