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

Singular:Singular

System Name Singular
Package Name Singular
Link http://www.singular.uni-kl.de/
Modified by Viktor Levandovskyy
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) 2147483629
Extension Fields simple algebraic extensions
algebraic extensions
transcendental extensions
Other Fields GF(p^n), p a prime, n <= 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 orderings

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
slim Groebner bases

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 all the Groebner basics (intersection of submodules, quotient and saturation, kernel of a module homomorphism, kernel of a ring homomorphism, Hilbert function, Betti numbers)

Other functionality
numerical solving of complex zero-dimensional systems, polynomial factorization, homological algebra

Highlights
primary decomposition of ideals and modules, Noether normalization, resolution of singularities