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Bergman:Bergman, non-commutative (graded) mode

System Name Bergman
Package Name Bergman, non-commutative (graded) mode
Link http://servus.math.su.se/bergman/
Modified by Jörgen Backelin
Email
incomplete information or not officially approved by the authors

Coefficient Domain
Rings as Coefficients Z
Z[x]
Other Rings
Basic Exact Fields Q
Z/pZ
Maximal value for prime p (if limited) Unlimited
Extension Fields simple algebraic extensions
algebraic extensions
transcendental extensions
Other Fields

Monomial Orderings
classical well-orderings (Lex, DegLex, DegRevLex)
weighted well-orderings (WDegLex, WDegRevLex)
product (block) orderings
matrix-defined orderings
extra weight (elimination) orderings
local orderings
Other Ordering (weighted) LeftLex; some elimination orderings

Available Algebras
path algebras
free algebras
algebras of solvable type/ PBW algebras/ G-algebras
Weyl algebras (relations are like d*x = x*d + 1)
shift algebras (relations are like s*x = x*s + s)
exterior algebras x_j*x_i = -x_i*x_j for all 1<=i,j<=N
universal enveloping algebras of fin.dim. Lie algebras
localized PBW algebras
localization by an ideal of commutative variables
Ore algebras
Other Localizations

Functionality Criteria

Ideals
Submodules of free modules

left Gröbner basis
right Gröbner basis
two-sided Groebner basis

non-commutative Faugère F4
non-commutative Faugère F5

Other variants of the algorithm, computing Gröbner Bases

Product Criterion

Chain Criterion

Gebauer-Möller Criterion

Other

Elements of Gröbner Basics

one-sided syzygy
two-sided syzygy

projective or free resolutions

elimination

Poincare or Hilbert series, polynomials

(Gel'fand-Kirillov) dimension

Other

Other functionality
Hilbert-driven Gröbner basis, Anick resolution, Betti numbers,Hochschild homology.

Highlights