
Macaulay2
 Referenced in 1692 articles
[sw00537]
 rings of graded or multigraded 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]
 Gröbnerbasis 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 uselesspair criterion for Gröbnerbasis 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 ringbased 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 widelyspread 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...