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Mathematica:Mathematica

System Name Mathematica
Package Name Mathematica
Link http://www.wolfram.com/products/mathematica/index.html
Modified by Daniel Lichtblau
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)
Extension Fields simple algebraic extensions
algebraic extensions
transcendental extensions
Other Fields (1) rational functions
(2) handles algebraic extensions if provided via polynomial defining relations

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
Has some special case code to recognize and speed computation of toric ideals

Product Criterion

Chain Criterion

Gebauer-Möller Criterion

Other
Uses a variant loosely related to Gebauer-Möller Criterion

Elements of Gröbner Basics

Syzygies and resolutions

Lift (Transformation matrix between two bases)

Elimination

(Krull) dimension

Other Code to compute Krull dimension (about 35 lines) may be found at:
http://forums.wolfram.com/mathgroup/archive/1999/Jul/msg00150.html

Other functionality
none

Highlights
none