• LiE

  • Referenced in 137 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 31 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 42 articles [sw04929]
  • computer package for symbolic computations in Weyl algebras...
  • MuPAD-Combinat

  • Referenced in 24 articles [sw04933]
  • some support for combinatorial Lie algebras, operads, (affine) Weyl groups, crystals, Schubert polynomials, ... The development...
  • coxeter

  • Referenced in 19 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...
  • NPspinor

  • Referenced in 12 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...
  • 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 q-Weyl algebras) over a field K. More detailled description...
  • LieART

  • Referenced in 34 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...
  • xTensor

  • Referenced in 23 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...
  • Affine

  • Referenced in 3 articles [sw08572]
  • theory of nite-dimensional 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 nite-dimensional...
  • Affine.m

  • Referenced in 2 articles [sw10836]
  • theory of finite-dimensional 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 finite-dimensional...
  • SageManifolds

  • Referenced in 1 article [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 564 articles [sw00143]
  • CoCoA is a system for Computations in Commutative...
  • GAP

  • Referenced in 2404 articles [sw00320]
  • GAP is a system for computational discrete algebra...
  • homalg

  • Referenced in 26 articles [sw00411]
  • homalg: a meta-package for homological algebra. The...
  • Macaulay2

  • Referenced in 1364 articles [sw00537]
  • Macaulay2 is a software system devoted to supporting...
  • Magma

  • Referenced in 2359 articles [sw00540]
  • Computer algebra system (CAS). Magma is a large...
  • Maple

  • Referenced in 4718 articles [sw00545]
  • The result of over 30 years of cutting...