• Magma

  • Referenced in 3137 articles [sw00540]
  • algebra, number theory, algebraic geometry and algebraic combinatorics. It provides a mathematically rigorous environment ... working with structures such as groups, rings, fields, modules, algebras, schemes, curves, graphs, designs, codes ... Magma is distributed by the Computational Algebra Group at the University of Sydney. Its development...
  • GAP

  • Referenced in 3068 articles [sw00320]
  • system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides ... well as large data libraries of algebraic objects. See also the overview and the description ... teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more...
  • LiE

  • Referenced in 160 articles [sw01075]
  • theory of complex semisimple (reductive) Lie groups and algebras, and on the structure of their ... directly with elements of the Lie groups and algebras themselves; it rather computes with weights ... tensor product decompositions, branching to subgroups, Weyl group orbits, reduced elements in Weyl groups, distinguished ... group theoretical concepts and about currently valid definitions and values. Computer algebra system...
  • OTTER

  • Referenced in 316 articles [sw02904]
  • finite semigroups, ternary Boolean algebra, logic calculi, combinatory logic, group theory, lattice theory, and algebraic...
  • CHEVIE

  • Referenced in 233 articles [sw04235]
  • groups of Lie type, Coxeter groups, Iwahori-Hecke algebras and other related structures...
  • CASA

  • Referenced in 102 articles [sw00108]
  • ongoing product of the Computer Algebra Group at the Research Institute for Symbolic Computation (RISC ... kernel of the widely used computer algebra system Maple. Computer algebra system...
  • LAGUNA

  • Referenced in 20 articles [sw08650]
  • LAGUNA: Lie AlGebras and UNits of group Algebras. The LAGUNA package replaces the LAG package ... normalized unit group of the modular group algebra of the finite p-group ... investigation of Lie algebra associated with group algebras and other associative algebras...
  • DifferentialGeometry

  • Referenced in 28 articles [sw07593]
  • geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces ... recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development ... Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein...
  • CAS

  • Referenced in 22 articles [sw07634]
  • constants of the centre of the group algebra; kernel of a character; p-blocks; power ... character theory, and for researchers in group theory. The CAS system makes a major contribution...
  • wedderga

  • Referenced in 13 articles [sw01019]
  • package Wedderga: Wedderburn Decomposition of Group Algebras. Wedderga is the package to compute the simple ... Wedderburn decomposition of semisimple group algebras of finite groups over finite fields and over subfields ... primitive central idempotents of semisimple group algebras and functions for computing Schur indices. Other functions ... construct crossed products over a group with coefficients in an associative ring with identity...
  • DISCRETA

  • Referenced in 32 articles [sw05937]
  • constructt-designs with prescribed automorphism groups. Computer algebra system...
  • MapReduce

  • Referenced in 257 articles [sw00546]
  • applications. The translation and optimization from relational algebra operators to MapReduce programs is still ... type of data analysis query, namely multiple group by query. We first study the communication...
  • GRAPE

  • Referenced in 89 articles [sw07516]
  • group and isomorphism testing functions, which use Brendan McKay’s nauty package. Computer algebra system...
  • SeDiMO

  • Referenced in 14 articles [sw07826]
  • connected reductive complex algebraic group and let V be a nontrivial irreducible module...
  • ATENSOR

  • Referenced in 12 articles [sw00055]
  • indexed objects arise. Solution method: The group algebra technique for permutation group is applied...
  • MuPAD-Combinat

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

  • Referenced in 12 articles [sw09237]
  • PyCox: computing with (finite) Coxeter groups and Iwahori-Hecke algebras. We introduce the computer algebra ... system, for working with Coxeter groups and Hecke algebras. This includes a new variation ... graphs, which works efficiently for all finite groups of rank ⩽8 (except...
  • BIGEBRA

  • Referenced in 19 articles [sw00078]
  • BIGEBRA package for Maple. Hopf algebraic structures will replace groups and group representations ... invariant theory, e.g., the Graßmann-Cayley bracket algebra, are all covered by the Hopf algebraic...
  • CREP

  • Referenced in 5 articles [sw30215]
  • algebras of this kind are the group algebras for finite groups or the finite-dimensional...
  • SymGroupAlgebra

  • Referenced in 5 articles [sw33420]
  • experimental package for computations in the group algebra of the symmetric group...