Rings v2.5 Release Notes

Release Date: 2018-07-24 // about 4 years ago
  • ๐Ÿ‘ This version introduces rigorous support of algebraic number fields and general field extensions (#43):

    • โœ… Implementation of algebraic number fields (AlgebraicNumberField) via simple (SimpleFieldExtension) and multiple (MultipleFieldExtension) field extensions
    • ๐Ÿ‘ Fully support polynomial GCD, resultants and factorization over algebraic number fields
    • Methods for constructing splitting fields (SplittingField(poly))

    Various methods from theory of resultants:

    • โœ… Implementation of different univariate polynomial remainder sequences, subresultant sequences, resultants and discriminants over arbitrary fields (UnivariateResultants)
    • โœ… Efficient multivariate resultants and discriminants over arbitrary fields by adapting Brown's and Zippel's algorithms for GCD (MultivariateResultants)

    โœ… Methods related to Groebner bases (GroebnerMethods):

    • Special elimination methods GroebnerMethods.eliminate(polys, variable)
    • โœ… Methods for testing algebraic dependence of polynomials and computing algebraic relations (annihilators) GroebnerMethods.algebraicRelations(polys)
    • Computation of Nullstellensatz certificates GroebnerMethods.NullstellensatzCertificate(polys)
    • Leinart's partial fraction decomposition of multivariate fractions (GroebnerMethods.LeinartDecomposition(fraction))