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Rings v2.5 Release Notes

Release Date: 2018-07-24 // almost 6 years ago

  • 👍 This version introduces rigorous support of algebraic number fields and general field extensions (#43):

    • ✅ Implementation of algebraic number fields (AlgebraicNumberField) via simple (SimpleFieldExtension) and multiple (MultipleFieldExtension) field extensions
    • 👍 Fully support polynomial GCD, resultants and factorization over algebraic number fields
    • Methods for constructing splitting fields (SplittingField(poly))

    Various methods from theory of resultants:

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

    ✅ Methods related to Groebner bases (GroebnerMethods):

    • Special elimination methods GroebnerMethods.eliminate(polys, variable)
    • ✅ 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))