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DoCon:Groebner basis

System Name DoCon
Package Name Groebner basis
Link http://www.haskell.org/docon/
Modified by Sergei Mechveliani
Email
incomplete information or not officially approved by the authors

Coefficient Domains
Rings as Coefficients Z
Z[x]
Other Rings any Euclidean ring
Floating Point Numbers (up to precision, if limited)
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 any field

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

Functionality Criteria

Ideals
Submodules of free modules

Gröbner Basis
Standard Basis

FGLM
Gröbner Walk/Fractal Walk

Hilbert-driven Gröbner Basis
Factorizing Gröbner Basis

Faugère F4
Faugère F5

Heuristic Command based on "BestChoice"

Other variants of the algorithm, computing Gröbner Bases
Over a field: the algorithm by the first Buchberger's paper about GB.
Over an Euclidean ring: the algorithm from the paper by Michel Moeller, with repeated solving of linear equation defined by the corresponding leading coefficients.

Product Criterion

Chain Criterion

Gebauer-Möller Criterion

Other

Elements of Gröbner Basics

Syzygies and resolutions

Lift (Transformation matrix between two bases)

Elimination

(Krull) dimension

Other none

Other functionality
none

Highlights
none