• Magma

  • Referenced in 2917 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 2876 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 1692 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 1408 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 50 articles [sw00297]
  • polynomial arithmetic and linear algebra in exact rings...
  • Plural

  • Referenced in 83 articles [sw00719]
  • Singular is a computer algebra system (CAS) developed for efficient computations with polynomials. Plural ... kernel) extension of Singular to noncommutative polynomial rings having PBW bases and their quotients (called ... /GR-algebras, also known as solvable polynomial algebras and PBW-algebras). All fields available in Singular...
  • homalg

  • Referenced in 28 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 160 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 45 articles [sw04929]
  • system for computing in the ring of differential operators D (and difference operators ... computer package for symbolic computations in Weyl algebras...
  • Felix

  • Referenced in 19 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...
  • Givaro

  • Referenced in 7 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...
  • Fermat

  • Referenced in 40 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...
  • SONATA

  • Referenced in 21 articles [sw04904]
  • deal with very large near-rings, in some cases up to 10^50 elements ... very useful major achievement. Computer algebra system...
  • FoCaLiZe

  • Referenced in 10 articles [sw12384]
  • library of mathematical algebraic structures up to multivariate polynomial rings, a library of security policies ... instance, the complex algorithms of the algebraic library provide runtime performances comparable to the best...
  • Schubert2

  • Referenced in 4 articles [sw16709]
  • Instead, one gives its graded intersection ring of algebraic cycle classes modulo numerical equivalence (tensored ... rational numbers or perhaps with some algebra over the rational numbers), its dimension, a method ... tangent bundle (if known). The intersection ring is represented as a Macaulay2 ring...
  • Mod-p group cohomology

  • Referenced in 8 articles [sw08638]
  • Sage computer algebra system. It computes modular cohomology rings of finite groups. It yields minimal...
  • ffmodstd

  • Referenced in 5 articles [sw27228]
  • ideal in a polynomial ring over an algebraic function field...
  • Rings

  • Referenced in 2 articles [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...
  • OreTools

  • Referenced in 6 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...
  • PolyBoRi

  • Referenced in 45 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...