
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 multigraded 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 ... /GRalgebras, also known as solvable polynomial algebras and PBWalgebras). All fields available in Singular...

homalg
 Referenced in 28 articles
[sw00411]
 homalg: a metapackage for homological algebra. The central notion of this work is that ... finitely presented modules over socalled 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 ringbased 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 noncommutative rings and modules ... generalizations to noncommutative rings, in particular to free kalgebras 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 nearrings, 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...

Modp 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 Gröbnerbasis 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...