Package edu.jas.gbufd

Interface SolvableSyzygy<C extends RingElem<C>>

Type Parameters:
C - coefficient type
All Superinterfaces:
Serializable
All Known Implementing Classes:
SolvableSyzygyAbstract, SolvableSyzygySeq

public interface SolvableSyzygy<C extends RingElem<C>> extends Serializable
Syzygy interface for solvable polynomials. Defines syzygy computations and tests.
  • Method Details

    • 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.
    • leftZeroRelations

      List<List<GenSolvablePolynomial<C>>> leftZeroRelations(int modv, List<GenSolvablePolynomial<C>> F)
      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.
    • leftZeroRelations

      ModuleList<C> leftZeroRelations(ModuleList<C> M)
      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.
    • 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.
    • 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.
    • isLeftZeroRelation

      boolean isLeftZeroRelation(ModuleList<C> Z, ModuleList<C> F)
      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.
    • isRightZeroRelation

      boolean isRightZeroRelation(ModuleList<C> Z, ModuleList<C> F)
      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.
    • resolution

      List<SolvResPart<C>> resolution(ModuleList<C> M)
      Resolution of a module. Only with direct GBs.
      Parameters:
      M - a module list of a Groebner basis.
      Returns:
      a resolution of M.
    • resolution

      List resolution(PolynomialList<C> F)
      Resolution of a polynomial list. Only with direct GBs.
      Parameters:
      F - a polynomial list of a Groebner basis.
      Returns:
      a resolution of F.
    • resolutionArbitrary

      List<SolvResPart<C>> resolutionArbitrary(ModuleList<C> M)
      Resolution of a module.
      Parameters:
      M - a module list of an arbitrary basis.
      Returns:
      a resolution of M.
    • resolutionArbitrary

      List resolutionArbitrary(PolynomialList<C> F)
      Resolution of a polynomial list.
      Parameters:
      F - a polynomial list of an arbitrary basis.
      Returns:
      a resolution of F.
    • leftZeroRelationsArbitrary

      List<List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(List<GenSolvablePolynomial<C>> F)
      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.
    • 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.
    • leftZeroRelationsArbitrary

      ModuleList<C> leftZeroRelationsArbitrary(ModuleList<C> M)
      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.
    • rightZeroRelationsArbitrary

      List<List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary(List<GenSolvablePolynomial<C>> F)
      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.
    • 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.
    • isLeftOreCond

      boolean isLeftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc)
      Test left Ore condition.
      Parameters:
      a - solvable polynomial
      b - solvable polynomial
      oc - = [p,q] two solvable polynomials
      Returns:
      true if p*a = q*b, else false
    • isRightOreCond

      boolean isRightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc)
      Test right Ore condition.
      Parameters:
      a - solvable polynomial
      b - solvable polynomial
      oc - = [p,q] two solvable polynomials
      Returns:
      true if a*p = b*q, else false
    • leftOreCond

      Left Ore condition. Generators for the left Ore condition of two solvable polynomials.
      Parameters:
      a - solvable polynomial
      b - solvable polynomial
      Returns:
      [p,q] with p*a = q*b
    • rightOreCond

      Right Ore condition. Generators for the right Ore condition of two solvable polynomials.
      Parameters:
      a - solvable polynomial
      b - solvable polynomial
      Returns:
      [p,q] with a*p = b*q