• Macaulay2

  • Referenced in 1692 articles [sw00537]
  • rings of graded or multi-graded polynomial rings with a monomial ordering. The core algorithms...
  • SINGULAR

  • Referenced in 1408 articles [sw00866]
  • variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields ... transcendental extensions), or localizations thereof, or quotient rings with respect to an ideal. SINGULAR features ... Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy...
  • Plural

  • Referenced in 83 articles [sw00719]
  • kernel) extension of Singular to noncommutative polynomial rings having PBW bases and their quotients (called...
  • PolyBoRi

  • Referenced in 45 articles [sw00723]
  • Gröbner-basis computations with Boolean polynomials. Boolean polynomials can be modelled in a rather simple ... Boolean polynomials is, however, not a polynomial ring, but rather the quotient ring ... polynomial ring over the field with two elements modulo the field equations ... polynomials. For example, a new useless-pair criterion for Gröbner-basis computations in Boolean rings...
  • Fermat

  • Referenced in 40 articles [sw00277]
  • multivariate polynomials, symbolic calculations, matrices over polynomial rings, graphics, and other numerical calculations ... care most about is oriented toward polynomial and matrix algebra over the rationals...
  • Groebner

  • Referenced in 17 articles [sw06688]
  • related operations for ideals in (commutative) polynomial rings. The Groebner package is actually much more ... handle polynomials in skew polynomial rings (see Groebner/details) and modules over (commutative or skew) polynomial...
  • QuillenSuslin

  • Referenced in 13 articles [sw08611]
  • free module over a polynomial ring. In terms of matrices, this algorithm completes a unimodular ... invertible matrix over the given polynomial ring with rational or integer coefficients. The package ... deal with unimodular rows over Laurent polynomial rings and with heuristic methods for localizations ... polynomial rings...
  • NTRU

  • Referenced in 160 articles [sw11761]
  • NTRU: A ring-based public key cryptosystem. We describe NTRU, a new public key cryptosystem ... decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based...
  • FLINT

  • Referenced in 50 articles [sw00297]
  • optimised routines for polynomial arithmetic and linear algebra in exact rings...
  • BGG

  • Referenced in 12 articles [sw27518]
  • finitely generated modules over a polynomial ring and the derived category of bounded complexes...
  • StronglyStableIdeals

  • Referenced in 8 articles [sw27084]
  • computational applications. In the case of polynomial rings with coefficients in a field of characteristic ... strongly stable ideals in a given polynomial ring with a given Hilbert polynomial...
  • FourTiTwo

  • Referenced in 8 articles [sw07615]
  • chains of lattice ideals in polynomial rings that are invariant under a symmetric group action ... polynomial rings are increasing in Krull dimension. Underlying many computations is the fact that...
  • StatePolytope

  • Referenced in 7 articles [sw07236]
  • stability of an ideal in a polynomial ring with respect to action of the maximal ... ideal must be in a polynomial ring over QQ or ZZ/p with...
  • FoCaLiZe

  • Referenced in 10 articles [sw12384]
  • mathematical algebraic structures up to multivariate polynomial rings, a library of security policies and various...
  • symmChainGens

  • Referenced in 8 articles [sw06689]
  • ambient rings for these ideals are polynomial rings which are increasing in (Krull) dimension. Thus...
  • ffmodstd

  • Referenced in 5 articles [sw27228]
  • ffmodstd.lib: Groebner bases of ideals in polynomial rings over rational function fields. A library ... basis of an ideal in a polynomial ring over an algebraic function field ... these points, we obtain a set of polynomials G by applying the sparse multivariate rational...
  • Givaro

  • Referenced in 7 articles [sw00354]
  • fields, Extensions Fields, Finite Fields, Finite Rings, Polynomials, Algebraic numbers, Arbitrary precision integers and rationals...
  • NLControl

  • Referenced in 7 articles [sw15154]
  • theory of the skew polynomial rings. The functions on the website address both discrete...
  • OreTools

  • Referenced in 6 articles [sw17956]
  • computer algebra library for univariate ore polynomial rings. This document presents the OreTools package which...
  • NFLlib

  • Referenced in 4 articles [sw14675]
  • lattice cryptography in the widely-spread polynomial ring ... number theory libraries NTL and flint implementing polynomial arithmetic, and the optimized library for lattice ... restricting the library to the aforementioned polynomial ring allows to gain several orders of magnitude...