Objects

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  Groebner

  UNDOCUMENTED

  Properties of Groebner

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    BASIS: common::Array<Polynomial<Rational, Int>>
    

    UNDOCUMENTED

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    INITIAL_IDEAL: Ideal
    

    UNDOCUMENTED

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    ORDER: common::String
    

    UNDOCUMENTED

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    ORDER_MATRIX: common::Matrix<Int, NonSymmetric>
    

    UNDOCUMENTED

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  Ideal

  UNDOCUMENTED

  Properties of Ideal

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    DEPTH: common::Int
    

    UNDOCUMENTED

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    DIM: common::Int
    

    UNDOCUMENTED

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    HILBERT_POLYNOMIAL: common::Polynomial<Rational, Int>
    

    UNDOCUMENTED

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    ??

    UNDOCUMENTED

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      GROEBNER: Groebner
      

      Subobject containing properties that depend on the monomial ordering of the ring.

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      HOMOGENEOUS: common::Bool
      

      True if ideal can be generated by homogeneous polynomials.

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      MONOMIAL: common::Bool
      

      Can the ideal be generated by monomials?

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      PRIMARY: common::Bool
      

      Is the ideal a primary ideal? I.e. its radical is prime and in the quotient ring by the ideal every zero divisor is nilpotent.

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      PRIMARY_DECOMPOSITION: Array<Ideal>
      

      An array containing the primary decomposition of the given ideal, i.e. the contained ideals are primary and their intersection is the given ideal.

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      PRIME: common::Bool
      

      Is the ideal a prime ideal?

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      RADICAL: Ideal
      

      The radical of the ideal.

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      RING: common::Ring<Rational, Int>
      

      The ambient (polynomial) ring containing the ideal.

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      ZERO: common::Bool
      

      True if the ideal is the zero ideal.

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    Input Property

    UNDOCUMENTED

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      GENERATORS: common::Array<Polynomial<Rational, Int>>
      

      A set of generators usually given by the user and in no way unique.