Your location: List of Systems ⁄ Macaulay2 ⁄ Commutative Packages:Macaulay2

Macaulay2:Macaulay2

System Name	Macaulay2
Package Name	Macaulay2
Link	http://www.math.uiuc.edu/Macaulay2/
Modified by	Dan Grayson
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)	2^15
Extension Fields	simple algebraic extensions algebraic extensions transcendental extensions
Other Fields	GF(q), q<2^15

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 mixed local-global

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 intersection, quotient, saturation, kernel, cokernel, image, subquotient, homology, kernel and coimage of ring homomorphisms, hilbert functions, betti functions, betti tables

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 intersection, quotient, saturation, kernel, cokernel, image, subquotient, homology, kernel and coimage of ring homomorphisms, hilbert functions, betti functions, betti tables

Other functionality

polynomial factorization, homological algebra, varieties, coherent sheaves, sheaf cohomology, chain complexes, maps of chain complexes

Highlights

primary decomposition, noether normalization, D-modules, Fourier-Motzkin, depth, generic initial ideal, integral closure, regularity, schur rings, intersection rings