Package edu.jas.gbufd
Interface SolvableSyzygy<C extends RingElem<C>>
- Type Parameters:
C
- coefficient type
- All Superinterfaces:
Serializable
- All Known Implementing Classes:
SolvableSyzygyAbstract
,SolvableSyzygySeq
Syzygy interface for solvable polynomials. Defines syzygy computations and
tests.
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Method Summary
Modifier and TypeMethodDescriptionboolean
isLeftOreCond
(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc) Test left Ore condition.boolean
isLeftZeroRelation
(ModuleList<C> Z, ModuleList<C> F) Test if left sysygy of modulesboolean
Test if left syzygy.boolean
isRightOreCond
(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc) Test right Ore condition.boolean
isRightZeroRelation
(ModuleList<C> Z, ModuleList<C> F) Test if right sysygy of modulesboolean
Test if right syzygy.Left Ore condition.leftZeroRelations
(int modv, List<GenSolvablePolynomial<C>> F) Left syzygy for left Groebner base.Left syzygy for left module Groebner base.Left syzygy for left Groebner base.leftZeroRelationsArbitrary
(int modv, List<GenSolvablePolynomial<C>> F) Left syzygy module from arbitrary base.Left syzygy for arbitrary left module base.Left syzygy module from arbitrary base.List
<SolvResPart<C>> resolution
(ModuleList<C> M) Resolution of a module.Resolution of a polynomial list.List
<SolvResPart<C>> Resolution of a module.Resolution of a polynomial list.Right Ore condition.rightZeroRelationsArbitrary
(int modv, List<GenSolvablePolynomial<C>> F) Right syzygy module from arbitrary base.Right syzygy module from arbitrary base.
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Method Details
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leftZeroRelations
Left syzygy for left Groebner base.- Parameters:
F
- a Groebner base.- Returns:
- leftSyz(F), a basis for the left module of syzygies for F.
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leftZeroRelations
Left syzygy for left Groebner base.- Parameters:
modv
- number of module variables.F
- a Groebner base.- Returns:
- leftSyz(F), a basis for the left module of syzygies for F.
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leftZeroRelations
Left syzygy for left module Groebner base.- Parameters:
M
- a Groebner base.- Returns:
- leftSyz(M), a basis for the left module of syzygies for M.
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isLeftZeroRelation
boolean isLeftZeroRelation(List<List<GenSolvablePolynomial<C>>> Z, List<GenSolvablePolynomial<C>> F) Test if left syzygy.- Parameters:
Z
- list of sysygies.F
- a polynomial list.- Returns:
- true, if Z is a list of left syzygies for F, else false.
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isRightZeroRelation
boolean isRightZeroRelation(List<List<GenSolvablePolynomial<C>>> Z, List<GenSolvablePolynomial<C>> F) Test if right syzygy.- Parameters:
Z
- list of sysygies.F
- a polynomial list.- Returns:
- true, if Z is a list of right syzygies for F, else false.
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isLeftZeroRelation
Test if left sysygy of modules- Parameters:
Z
- list of sysygies.F
- a module list.- Returns:
- true, if Z is a list of left syzygies for F, else false.
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isRightZeroRelation
Test if right sysygy of modules- Parameters:
Z
- list of sysygies.F
- a module list.- Returns:
- true, if Z is a list of right syzygies for F, else false.
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resolution
Resolution of a module. Only with direct GBs.- Parameters:
M
- a module list of a Groebner basis.- Returns:
- a resolution of M.
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resolution
Resolution of a polynomial list. Only with direct GBs.- Parameters:
F
- a polynomial list of a Groebner basis.- Returns:
- a resolution of F.
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resolutionArbitrary
Resolution of a module.- Parameters:
M
- a module list of an arbitrary basis.- Returns:
- a resolution of M.
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resolutionArbitrary
Resolution of a polynomial list.- Parameters:
F
- a polynomial list of an arbitrary basis.- Returns:
- a resolution of F.
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leftZeroRelationsArbitrary
Left syzygy module from arbitrary base.- Parameters:
F
- a solvable polynomial list.- Returns:
- syz(F), a basis for the module of left syzygies for F.
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leftZeroRelationsArbitrary
List<List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(int modv, List<GenSolvablePolynomial<C>> F) Left syzygy module from arbitrary base.- Parameters:
modv
- number of module variables.F
- a solvable polynomial list.- Returns:
- syz(F), a basis for the module of left syzygies for F.
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leftZeroRelationsArbitrary
Left syzygy for arbitrary left module base.- Parameters:
M
- an arbitrary base.- Returns:
- leftSyz(M), a basis for the left module of syzygies for M.
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rightZeroRelationsArbitrary
Right syzygy module from arbitrary base.- Parameters:
F
- a solvable polynomial list.- Returns:
- syz(F), a basis for the module of right syzygies for F.
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rightZeroRelationsArbitrary
List<List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary(int modv, List<GenSolvablePolynomial<C>> F) Right syzygy module from arbitrary base.- Parameters:
modv
- number of module variables.F
- a solvable polynomial list.- Returns:
- syz(F), a basis for the module of right syzygies for F.
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isLeftOreCond
boolean isLeftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc) Test left Ore condition.- Parameters:
a
- solvable polynomialb
- solvable polynomialoc
- = [p,q] two solvable polynomials- Returns:
- true if p*a = q*b, else false
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isRightOreCond
boolean isRightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc) Test right Ore condition.- Parameters:
a
- solvable polynomialb
- solvable polynomialoc
- = [p,q] two solvable polynomials- Returns:
- true if a*p = b*q, else false
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leftOreCond
Left Ore condition. Generators for the left Ore condition of two solvable polynomials.- Parameters:
a
- solvable polynomialb
- solvable polynomial- Returns:
- [p,q] with p*a = q*b
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rightOreCond
Right Ore condition. Generators for the right Ore condition of two solvable polynomials.- Parameters:
a
- solvable polynomialb
- solvable polynomial- Returns:
- [p,q] with a*p = b*q
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