
LiE
 Referenced in 157 articles
[sw01075]
 groups and algebras, and on the structure of their Weyl groups and root systems ... with elements of the Lie groups and algebras themselves; it rather computes with weights, roots ... tensor product decompositions, branching to subgroups, Weyl group orbits, reduced elements in Weyl groups, distinguished ... about currently valid definitions and values. Computer algebra system...

Janet
 Referenced in 36 articles
[sw07776]
 works with left modules over differential algebras defined over differential fields of characteristic zero which ... notation and vice versa. For the Weyl algebra representing ordinary differential operators in characteristic zero ... matrix with entries in this Weyl algebra. Among the orderings for differential monomials which...

Kan
 Referenced in 45 articles
[sw04929]
 computer package for symbolic computations in Weyl algebras...

MuPADCombinat
 Referenced in 25 articles
[sw04933]
 some support for combinatorial Lie algebras, operads, (affine) Weyl groups, crystals, Schubert polynomials, ... The development...

NPspinor
 Referenced in 16 articles
[sw00633]
 With the assistance of the computer algebra system MAPLE’s NPspinor package, two propositions ... principal spinors of the Maxwell and Weyl spinors. The first proposition states that the validity ... algebraically degenerate and its principal spinor is aligned with one of the doubly degenerate Weyl...

coxeter
 Referenced in 22 articles
[sw07772]
 finds in the appendices of Bourbaki. The weyl subpackage provides 12 additional procedures for manipulating ... characters of irreducible representations of semisimple Lie algebras, including functions for computing weight multiplicities, tensor...

LieART
 Referenced in 46 articles
[sw08573]
 algebras. It computes root systems of Lie algebras, weight systems and several other properties ... input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting...

ncfactor.lib
 Referenced in 1 article
[sw23797]
 algebras, all generated by 2*n, n in NN, generators (n’th Weyl ... graded polynomials in n’th qWeyl algebras) over a field K. More detailled description...

xTensor
 Referenced in 30 articles
[sw04984]
 xTensor: Fast abstract tensor computer algebra. xTensor extends Mathematica capabilities in abstract tensor calculus, specially ... associated tensors (Riemann, Ricci, Einstein, Weyl, etc.) xTensor does not perform component calculations...

ncfactor
 Referenced in 0 articles
[sw15060]
 both generated by two generators (Weyl and shift algebras) over ... field K. Recall, that the first Weyl algebra over K is generated...

WeylModules
 Referenced in 4 articles
[sw31472]
 with Weyl modules and simple modules for a given simplyconnected, semisimple, algebraic group...

Affine
 Referenced in 5 articles
[sw08572]
 theory of nitedimensional and ane Lie algebras and describe implemented algorithms. The algorithms ... based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible ... program is implemented in the popular computer algebra system Mathematica and works with nitedimensional...

Affine.m
 Referenced in 3 articles
[sw10836]
 theory of finitedimensional and affine Lie algebras and describe implemented algorithms. The algorithms ... based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible ... program is implemented in the popular computer algebra system Mathematica and works with finitedimensional...

lie_algebras
 Referenced in 2 articles
[sw34846]
 irreducible representation of a simple Lie algebra (mathfrak {g}) with highest weight (lambda ... formula is an alternating sum over the Weyl group and involves the computation ... compute (q)multiplicities for the simple Lie algebras...

SageManifolds
 Referenced in 2 articles
[sw27192]
 project aims at extending the modern computer algebra system SageMath towards differential geometry and tensor ... Riemann curvature tensor and associated tensors (Ricci, Weyl, Schouten and Cotton tensors) is implemented. SageManifolds...

CoCoA
 Referenced in 639 articles
[sw00143]
 CoCoA is a system for Computations in Commutative...

GAP
 Referenced in 3003 articles
[sw00320]
 GAP is a system for computational discrete algebra...

GRTensorII
 Referenced in 48 articles
[sw00393]
 GRTensor II is a computer algebra package for...

homalg
 Referenced in 30 articles
[sw00411]
 homalg: a metapackage for homological algebra. The...

Macaulay2
 Referenced in 1776 articles
[sw00537]
 Macaulay2 is a software system devoted to supporting...