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Non-Commutative Packages:D-modules
Macaulay2:D-modules
System Name | Macaulay2 |
Package Name | D-modules |
Link | http://www.ima.umn.edu/~leykin/Dmodules/ |
Modified by | Viktor Levandovskyy |
Coefficient Domain
Rings as Coefficients |
Z Z[x] |
Other Rings |
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
Available Algebras
path algebras free algebras
algebras of solvable type/ PBW algebras/ G-algebras
Weyl algebras (relations are like d*x = x*d + 1) |
shift algebras (relations are like s*x = x*s + s) |
exterior algebras x_j*x_i = -x_i*x_j for all 1<=i,j<=N |
universal enveloping algebras of fin.dim. Lie algebras |
localization by an ideal of commutative variables |
Ore algebras |
Other Localizations |
Functionality | Criteria |
---|---|
Ideals
left Gröbner basis
non-commutative Faugère F4
Other variants of the algorithm, computing Gröbner Bases
|
Product Criterion Chain Criterion Gebauer-Möller Criterion Other Elements of Gröbner Basics
one-sided syzygy projective or free resolutions elimination Poincare or Hilbert series, polynomials (Gel'fand-Kirillov) dimension Other |
Other functionality
annihilator of f^s, f a polynomial, s a symbol; Bernstein-Sato polynomial of f
Highlights
local cohomology, de Rham cohomology