• UFL

  • Referenced in 63 articles [sw11183]
  • problems, general differential operators and flexible tensor algebra. With these features, UFL has been used...
  • xAct

  • Referenced in 78 articles [sw07598]
  • suite of free packages for tensor computer algebra in Mathematica. xAct implements state...
  • xTras

  • Referenced in 48 articles [sw16622]
  • package for Mathematica. We present the tensor computer algebra package xTras, which provides functions ... equations. It is built upon the tensor computer algebra system xAct, a collection of packages...
  • xPerm

  • Referenced in 33 articles [sw01153]
  • xPerm: fast index canonicalization for tensor computer algebra. We present a very fast implementation ... linked from any other program or computer algebra system. We demonstrate with tests and timings ... recent investigations in large-scale tensor computer algebra...
  • DifferentialGeometry

  • Referenced in 29 articles [sw07593]
  • manifolds, differential 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 ... vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations...
  • TSFC

  • Referenced in 24 articles [sw20272]
  • lowering of finite element constructs to tensor algebra in the first stage, from the scheduling...
  • xTensor

  • Referenced in 33 articles [sw04984]
  • xTensor: Fast abstract tensor computer algebra. xTensor extends Mathematica capabilities in abstract tensor calculus, specially...
  • LieART

  • Referenced in 58 articles [sw08573]
  • frequently encountered in Lie Algebras and representation theory, such as tensor product decomposition and subalgebra ... handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight ... memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations...
  • LiE

  • Referenced in 164 articles [sw01075]
  • with elements of the Lie groups and algebras themselves; it rather computes with weights, roots ... similar objects. Some specialities of LiE are: tensor product decompositions, branching to subgroups, Weyl group ... about currently valid definitions and values. Computer algebra system...
  • xPert

  • Referenced in 20 articles [sw06827]
  • metric perturbation theory. We present the tensor computer algebra package xPert for fast construction ... order perturbation of curvature tensors and their gauge changes, and the use of highly efficient...
  • tproduct

  • Referenced in 23 articles [sw34460]
  • many others. The linear algebraic structure of tensors are similar to the matrix cases...
  • Maxima

  • Referenced in 169 articles [sw00560]
  • polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results ... data in two and three dimensions. Computer algebra system...
  • TensorLy

  • Referenced in 12 articles [sw27020]
  • perform tensor decomposition, tensor learning and tensor algebra. Its backend system allows to seamlessly perform...
  • xPand

  • Referenced in 12 articles [sw07599]
  • geometrical quantities only, using the tensor algebra package xTensor in the xAct distribution along with...
  • Invar

  • Referenced in 35 articles [sw00446]
  • Riemann tensors within seconds. It has been implemented both in Mathematica and Maple algebraic systems...
  • SHEEP

  • Referenced in 38 articles [sw00855]
  • computer algebra system for handling calculations of the components of tensors. Its main ... mechanics. It was based on the Lisp Algebraic Manipulator LAM (whence the name Sheep) written...
  • BIGEBRA

  • Referenced in 21 articles [sw00078]
  • direct calculations using symbolic manipulation and computer algebra system (CAS). We discuss problems which were ... CLIFFORD to handle tensor products, Graßmann and Clifford algebras, coalgebras and Hopf algebras. Recent results...
  • EinSum

  • Referenced in 7 articles [sw04212]
  • package primarily intended for tensor algebra, capable of supporting the Einstein summation convention. Details...
  • TenRes

  • Referenced in 5 articles [sw19993]
  • Algorithmic operator algebras via normal forms for tensors. We propose a general algorithmic approach ... parametrized) Gr”obner bases in noncommutative polynomial algebras as has been used ... basis-free analog in tensor algebras. This allows for a finite reduction system with unique ... illustrate both versions of the tensor setting using integro-differential operators as an example...
  • GRTensorII

  • Referenced in 49 articles [sw00393]
  • GRTensor II is a computer algebra package for performing calculations in the general area ... geometry. Its purpose is the calculation of tensor components on curved spacetimes specified in terms ... expandable by a facility for defining new tensors. Calculations can be carried out in spaces ... stand alone package, but requires an algebraic engine. The program was originally developed for MapleV.GRTensorII...