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Maple:Groebner

System Name Maple
Package Name Groebner
Link http://www.maplesoft.com
Modified by Jürgen Gerhard
Email
incomplete information or not officially approved by the authors

Coefficient Domains
Rings as Coefficients Z
Z[x]
Other Rings
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

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
none

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
- Hilbert invariants
- maximal independent set
- rational univariate representation
- PolynomialIdeals package with data structures and algorithms for ideals (primary and prime decompositions, equidimensional decomposition, radical computation, zero-dimensional decomposition)
- RegularChains package for triangular decompositions and computations with triangular sets
- Rif package for involutive bases
- RootFinding package for real roots, based on Gröbner methods

Highlights
- uses FGb for computing total degree Gröbner bases over Q and Z/pZ
- library implementation of F4
- rational univariate representation