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Terms and polynomials

This section contains information about the handling of terms and polynomials constructed and used during OAVI and VCA. Many of the functions work relatively similar, simply adjusted to the respective structure of storing the information.

Sets $\mathcal{O}$ and $\mathcal{G}$

ApproximateVanishingIdeals.evaluate_transformation_oavi — Method

Evaluates the transformation corresponding to the polynomials in Gcoefficientvectors.

Arguments

  • 'sets::SetsOandG': instance of SetsOandG, containing transformation

Returns

  • 'totalnumberofzeros::Int64': Sum of all zero entries in coefficientvectors in Gcoefficientvectors.
  • 'totalnumberofentries::Int64': Total number of entries in coefficientvectors in Gcoefficientvectors.
  • 'avgsparsity::Float64': The average sparsity of coefficientvectors in Gcoefficientvectors.
  • 'numberofpolynomials::Int64': Number of polynomials in G.
  • 'numberofterms::Int64': Number of terms in O.
  • 'degree::Float64': Average degree of polynomials in G.
source

Sets $\mathcal{F}$ and $\mathcal{V}$

ApproximateVanishingIdeals.evaluate_transformation_vca — Method

Evaluates the transformation corresponding to the polynomials in V w.r.t. the functions in F and C

Arguments

  • 'sets::SetsVCA': instance of SetsVCA.

Returns

  • 'totalnumberofzeros::Int64': Sum of all zero entries in coefficientvectors in Vcoefficientvectors.
  • 'totalnumberofentries::Int64': Total number of entries in coefficientvectors in Vcoefficientvectors.
  • 'avgsparsity::Float64': The average sparsity of coefficientvectors in Vcoefficientvectors.
  • 'numberofpolynomials::Int64': Number of polynomials in Vcoefficientvectors.
  • 'numberofterms::Int64': Number of non-vanishing terms.
  • 'degree::Float64': Average degree of polynomials in V.
source

Index