Package edu.jas.gbufd
Class SolvablePseudoReductionSeq<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.gb.SolvableReductionAbstract<C>
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- edu.jas.gbufd.SolvablePseudoReductionSeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
SolvableReduction<C>
,SolvablePseudoReduction<C>
,java.io.Serializable
public class SolvablePseudoReductionSeq<C extends GcdRingElem<C>> extends SolvableReductionAbstract<C> implements SolvablePseudoReduction<C>
Polynomial pseudo reduction sequential use algorithm. Coefficients of polynomials must not be from a field, i.e. the fraction free reduction is implemented. Implements normalform.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Constructor Summary
Constructors Constructor Description SolvablePseudoReductionSeq()
Constructor.
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Method Summary
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Methods inherited from class edu.jas.gb.SolvableReductionAbstract
isLeftReductionNF, isNormalform, isReducible, isRightReductionNF, isTopReducible, leftIrreducibleSet, leftNormalform, leftNormalform, leftNormalform, leftSPolynomial, leftSPolynomial, normalform, rightSPolynomial, rightSPolynomial
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface edu.jas.gb.SolvableReduction
isLeftReductionNF, isNormalform, isReducible, isRightReductionNF, isTopReducible, leftIrreducibleSet, leftNormalform, leftSPolynomial, leftSPolynomial, normalform, rightSPolynomial
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Constructor Detail
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SolvablePseudoReductionSeq
public SolvablePseudoReductionSeq()
Constructor.
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Method Detail
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leftNormalform
public GenSolvablePolynomial<C> leftNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)
Left normalform.- Specified by:
leftNormalform
in interfaceSolvableReduction<C extends GcdRingElem<C>>
- Parameters:
Ap
- polynomial.Pp
- polynomial list.- Returns:
- nf(Ap) with respect to Pp.
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leftNormalformRecursive
public GenSolvablePolynomial<GenPolynomial<C>> leftNormalformRecursive(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Pp, GenSolvablePolynomial<GenPolynomial<C>> Ap)
Left normalform recursive.- Specified by:
leftNormalformRecursive
in interfaceSolvablePseudoReduction<C extends GcdRingElem<C>>
- Parameters:
Ap
- recursive polynomial.Pp
- recursive polynomial list.- Returns:
- nf(Ap) with respect to Pp.
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leftNormalform
public GenSolvablePolynomial<C> leftNormalform(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)
Left normalform with recording. Note: Only meaningful if all divisions are exact. Compute first the multiplication factormf
with(nf,mf) = normalformfactor(Pp,Ap)
, then call this method withnormalform(row,Pp,mf*Ap)
.- Specified by:
leftNormalform
in interfaceSolvableReduction<C extends GcdRingElem<C>>
- Parameters:
row
- recording matrix, is modified.Pp
- a polynomial list for reduction.Ap
- a polynomial.- Returns:
- nf(Pp,Ap), the normal form of Ap wrt. Pp.
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leftNormalformFactor
public PseudoReductionEntry<C> leftNormalformFactor(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)
Left normalform with factor.- Specified by:
leftNormalformFactor
in interfaceSolvablePseudoReduction<C extends GcdRingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- ( nf(Ap), mf ) with respect to Pp and mf as multiplication factor for Ap.
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rightNormalform
public GenSolvablePolynomial<C> rightNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)
Right normalform.- Specified by:
rightNormalform
in interfaceSolvableReduction<C extends GcdRingElem<C>>
- Parameters:
Ap
- polynomial.Pp
- polynomial list.- Returns:
- nf(Ap) with respect to Pp.
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rightNormalformRecursive
public GenSolvablePolynomial<GenPolynomial<C>> rightNormalformRecursive(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Pp, GenSolvablePolynomial<GenPolynomial<C>> Ap)
Right normalform recursive.- Specified by:
rightNormalformRecursive
in interfaceSolvablePseudoReduction<C extends GcdRingElem<C>>
- Parameters:
Ap
- recursive polynomial.Pp
- recursive polynomial list.- Returns:
- nf(Ap) with respect to Pp.
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rightNormalform
public GenSolvablePolynomial<C> rightNormalform(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)
Right normalform with recording. Note: Only meaningful if all divisions are exact. Compute first the multiplication factormf
with(nf, mf) = normalformfactor(Pp,Ap)
, then call this method withnormalform(row,Pp,mf*Ap)
.- Specified by:
rightNormalform
in interfaceSolvableReduction<C extends GcdRingElem<C>>
- Parameters:
row
- recording matrix, is modified.Pp
- a polynomial list for reduction.Ap
- a polynomial.- Returns:
- nf(Pp,Ap), the normal form of Ap wrt. Pp.
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rightNormalformFactor
public PseudoReductionEntry<C> rightNormalformFactor(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)
Right normalform with multiplication factor.- Specified by:
rightNormalformFactor
in interfaceSolvablePseudoReduction<C extends GcdRingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- ( nf(Ap), mf ) with respect to Pp and mf as multiplication factor for Ap.
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