• Magma

  • Referenced in 2185 articles [sw00540]
  • algebra, number theory, algebraic geometry and algebraic combinatorics. It provides a mathematically rigorous environment ... with structures such as groups, rings, fields, modules, algebras, schemes, curves, graphs, designs, codes...
  • GAP

  • Referenced in 2273 articles [sw00320]
  • well as large data libraries of algebraic objects. See also the overview and the description ... studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system...
  • Macaulay2

  • Referenced in 1243 articles [sw00537]
  • supporting research in algebraic geometry and commutative algebra, whose creation has been funded ... graded free resolutions of modules over quotient rings of graded or multi-graded polynomial rings ... ideals, integral closure of rings, and more. Computer algebra system...
  • SINGULAR

  • Referenced in 1129 articles [sw00866]
  • polynomial computations in commutative algebra, algebraic geometry, and singularity theory. SINGULAR’s main computational objects ... variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields ... rationals, floats, algebraic extensions, transcendental extensions), or localizations thereof, or quotient rings with respect...
  • FLINT

  • Referenced in 29 articles [sw00297]
  • polynomial arithmetic and linear algebra in exact rings...
  • homalg

  • Referenced in 26 articles [sw00411]
  • homalg: a meta-package for homological algebra. The central notion of this work is that ... finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically ... mathematical object in a computer algebra system. Once this is achieved, one can compose ... extend any computer algebra software implementing the arithmetics of a computable ring R, as soon...
  • NTRU

  • Referenced in 135 articles [sw11761]
  • NTRU: A ring-based public key cryptosystem. We describe NTRU, a new public key cryptosystem ... mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability...
  • Kan

  • Referenced in 41 articles [sw04929]
  • system for computing in the ring of differential operators D (and difference operators ... computer package for symbolic computations in Weyl algebras...
  • Plural

  • Referenced in 64 articles [sw00719]
  • Singular is a computer algebra system (CAS) developed for efficient computations with polynomials. We describe ... extension of Singular to noncommutative polynomial rings (G-/GR-algebras): to which structures does it apply...
  • Felix

  • Referenced in 17 articles [sw01048]
  • computer algebra system (CAS) for the computation in commutative and non-commutative rings and modules ... generalizations to non-commutative rings, in particular to free k-algebras and algebras of solvable...
  • Fermat

  • Referenced in 30 articles [sw00277]
  • Fermat is a computer algebra system (CAS) for Macintosh, Windows, Linux, and Unix ... multivariate polynomials, symbolic calculations, matrices over polynomial rings, graphics, and other numerical calculations ... about is oriented toward polynomial and matrix algebra over the rationals Q and finite fields...
  • Givaro

  • Referenced in 4 articles [sw00354]
  • library for arithmetic and algebraic computations. Its main features are implementations of the basic arithmetic ... fields, Extensions Fields, Finite Fields, Finite Rings, Polynomials, Algebraic numbers, Arbitrary precision integers and rationals...
  • SONATA

  • Referenced in 18 articles [sw04904]
  • deal with very large near-rings, in some cases up to 10^50 elements ... very useful major achievement. Computer algebra system...
  • Mod-p group cohomology

  • Referenced in 7 articles [sw08638]
  • Sage computer algebra system. It computes modular cohomology rings of finite groups. It yields minimal...
  • OOLACA

  • Referenced in 3 articles [sw09956]
  • work with abstract algebraic structures, such as: groups, rings, fields, etc., define new algebraic structures...
  • PolyBoRi

  • Referenced in 40 articles [sw00723]
  • criterion for Gröbner-basis computations in Boolean rings is introduced. One of the motivations ... arithmetic components. We are convinced that algebraic methods are more suited and we believe that...
  • JanetOre

  • Referenced in 5 articles [sw09587]
  • algebras and more generally for submodules of free left modules over those non-commutative rings ... basis technique over some classes of Ore algebras. JanetOre computes Janet bases and Janet-like ... bases. The coefficient domain for the Ore algebra may be any field existing in Maple ... chosen to be the ring of rational integers. Among the monomial orderings which are available...
  • MAS

  • Referenced in 5 articles [sw08442]
  • implemented Groebner basis algorithms for nearly all algebraic structures where such methods exist. MAS further ... counting, and for computing in (noncommutative) polynomial rings...
  • OreTools

  • Referenced in 4 articles [sw17956]
  • OreTools: a computer algebra library for univariate ore polynomial rings. This document presents the OreTools ... tools for performing basic arithmetic in Ore algebra. These tools can be used...
  • Rings

  • Referenced in 1 article [sw22196]
  • multivariate polynomial arithmetic over arbitrary coefficient rings. Basic algebra, GCDs and factorization of polynomials ... modern asymptotically fast algorithms. Rings provides a clean API for algebra and a fully typed ... expressive code for applications. Performance achieved in Rings is similar to such well known specialized...