C
- coefficient typepublic abstract class SolvableSyzygyAbstract<C extends GcdRingElem<C>> extends java.lang.Object implements SolvableSyzygy<C>
Modifier and Type | Field and Description |
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protected BasicLinAlg<GenPolynomial<C>> |
blas
Linear algebra engine.
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protected Reduction<C> |
red
Reduction engine.
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SolvableReduction<C> |
sred
Solvable reduction engine.
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Constructor and Description |
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SolvableSyzygyAbstract()
Constructor.
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Modifier and Type | Method and Description |
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int |
compare(GenSolvablePolynomial<C> num,
GenSolvablePolynomial<C> den,
GenSolvablePolynomial<C> n,
GenSolvablePolynomial<C> d)
Comparison like SolvableLocal or SolvableQuotient.
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boolean |
isLeftOreCond(GenSolvablePolynomial<C> a,
GenSolvablePolynomial<C> b,
GenSolvablePolynomial<C>[] oc)
Test left Ore condition.
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boolean |
isLeftZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z,
java.util.List<GenSolvablePolynomial<C>> F)
Test if left syzygy.
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boolean |
isLeftZeroRelation(ModuleList<C> Z,
ModuleList<C> F)
Test if left sysygy of modules
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boolean |
isRightOreCond(GenSolvablePolynomial<C> a,
GenSolvablePolynomial<C> b,
GenSolvablePolynomial<C>[] oc)
Test right Ore condition.
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boolean |
isRightZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z,
java.util.List<GenSolvablePolynomial<C>> F)
Test if right syzygy.
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boolean |
isRightZeroRelation(ModuleList<C> Z,
ModuleList<C> F)
Test if right sysygy of modules
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abstract GenSolvablePolynomial<C>[] |
leftSimplifier(GenSolvablePolynomial<C> a,
GenSolvablePolynomial<C> b)
Left simplifier.
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java.util.List<java.util.List<GenSolvablePolynomial<C>>> |
leftZeroRelations(int modv,
java.util.List<GenSolvablePolynomial<C>> F)
Left syzygy for left Groebner base.
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java.util.List<java.util.List<GenSolvablePolynomial<C>>> |
leftZeroRelations(java.util.List<GenSolvablePolynomial<C>> F)
Left syzygy for left Groebner base.
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ModuleList<C> |
leftZeroRelations(ModuleList<C> M)
Left syzygy for left module Groebner base.
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java.util.List<java.util.List<GenSolvablePolynomial<C>>> |
leftZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F)
Left syzygy module from arbitrary base.
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ModuleList<C> |
leftZeroRelationsArbitrary(ModuleList<C> M)
Left syzygy for arbitrary left module base.
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java.util.List<java.util.List<GenSolvablePolynomial<C>>> |
rightZeroRelations(int modv,
java.util.List<GenSolvablePolynomial<C>> F)
Right syzygy module from Groebner base.
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java.util.List<java.util.List<GenSolvablePolynomial<C>>> |
rightZeroRelations(java.util.List<GenSolvablePolynomial<C>> F)
Right syzygy module from Groebner base.
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ModuleList<C> |
rightZeroRelations(ModuleList<C> M)
Right syzygy for right module Groebner base.
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java.util.List<java.util.List<GenSolvablePolynomial<C>>> |
rightZeroRelationsArbitrary(int modv,
java.util.List<GenSolvablePolynomial<C>> F)
Right syzygy module from arbitrary base.
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java.util.List<java.util.List<GenSolvablePolynomial<C>>> |
rightZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F)
Right syzygy module from arbitrary base.
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ModuleList<C> |
rightZeroRelationsArbitrary(ModuleList<C> M)
Right syzygy for arbitrary base.
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
leftOreCond, leftZeroRelationsArbitrary, resolution, resolution, resolutionArbitrary, resolutionArbitrary, rightOreCond
public final SolvableReduction<C extends GcdRingElem<C>> sred
protected Reduction<C extends GcdRingElem<C>> red
protected BasicLinAlg<GenPolynomial<C extends GcdRingElem<C>>> blas
public SolvableSyzygyAbstract()
public java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelations(java.util.List<GenSolvablePolynomial<C>> F)
leftZeroRelations
in interface SolvableSyzygy<C extends GcdRingElem<C>>
F
- a Groebner base.public java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelations(int modv, java.util.List<GenSolvablePolynomial<C>> F)
leftZeroRelations
in interface SolvableSyzygy<C extends GcdRingElem<C>>
modv
- number of module variables.F
- a Groebner base.public ModuleList<C> leftZeroRelations(ModuleList<C> M)
leftZeroRelations
in interface SolvableSyzygy<C extends GcdRingElem<C>>
M
- a Groebner base.public java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelations(java.util.List<GenSolvablePolynomial<C>> F)
F
- a solvable polynomial list, a Groebner base.public java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelations(int modv, java.util.List<GenSolvablePolynomial<C>> F)
modv
- number of module variables.F
- a solvable polynomial list, a Groebner base.public ModuleList<C> rightZeroRelations(ModuleList<C> M)
M
- a Groebner base.public boolean isLeftZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z, java.util.List<GenSolvablePolynomial<C>> F)
isLeftZeroRelation
in interface SolvableSyzygy<C extends GcdRingElem<C>>
Z
- list of sysygies.F
- a polynomial list.public boolean isRightZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z, java.util.List<GenSolvablePolynomial<C>> F)
isRightZeroRelation
in interface SolvableSyzygy<C extends GcdRingElem<C>>
Z
- list of sysygies.F
- a polynomial list.public boolean isLeftZeroRelation(ModuleList<C> Z, ModuleList<C> F)
isLeftZeroRelation
in interface SolvableSyzygy<C extends GcdRingElem<C>>
Z
- list of sysygies.F
- a module list.public boolean isRightZeroRelation(ModuleList<C> Z, ModuleList<C> F)
isRightZeroRelation
in interface SolvableSyzygy<C extends GcdRingElem<C>>
Z
- list of sysygies.F
- a module list.public java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F)
leftZeroRelationsArbitrary
in interface SolvableSyzygy<C extends GcdRingElem<C>>
F
- a solvable polynomial list.public ModuleList<C> leftZeroRelationsArbitrary(ModuleList<C> M)
leftZeroRelationsArbitrary
in interface SolvableSyzygy<C extends GcdRingElem<C>>
M
- an arbitrary base.public java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F)
rightZeroRelationsArbitrary
in interface SolvableSyzygy<C extends GcdRingElem<C>>
F
- a solvable polynomial list.public java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary(int modv, java.util.List<GenSolvablePolynomial<C>> F)
rightZeroRelationsArbitrary
in interface SolvableSyzygy<C extends GcdRingElem<C>>
modv
- number of module variables.F
- a solvable polynomial list.public ModuleList<C> rightZeroRelationsArbitrary(ModuleList<C> M)
M
- an arbitray base.public boolean isLeftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc)
isLeftOreCond
in interface SolvableSyzygy<C extends GcdRingElem<C>>
a
- solvable polynomialb
- solvable polynomialoc
- = [p,q] two solvable polynomialspublic boolean isRightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc)
isRightOreCond
in interface SolvableSyzygy<C extends GcdRingElem<C>>
a
- solvable polynomialb
- solvable polynomialoc
- = [p,q] two solvable polynomialspublic abstract GenSolvablePolynomial<C>[] leftSimplifier(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)
a
- solvable polynomialb
- solvable polynomialpublic int compare(GenSolvablePolynomial<C> num, GenSolvablePolynomial<C> den, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)
num
- SolvablePolynomial.den
- SolvablePolynomial.n
- SolvablePolynomial.d
- SolvablePolynomial.