Tensor software
Encyclopedia
Tensor software is a class of mathematical software
Mathematical software
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.-Computer algebra systems:Many mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human...

 designed for manipulation and calculation with tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

s.

Standalone open-source software

  • Cadabra is a computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many more. The input format is a subset of TeX. Both a command-line and a graphical interface are available.
  • Tela is a software package similar to Matlab and Octave, but designed specifically for tensors.

Open-source packages for use with open-source algebra systems

  • Maxima is a free open source
    Open source
    The term open source describes practices in production and development that promote access to the end product's source materials. Some consider open source a philosophy, others consider it a pragmatic methodology...

     computer algebra system
    Computer algebra system
    A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...

     which can be used for tensor algebra calculations - it is particularly useful for calculations with abstract tensors (i.e. when one wishes to do calculations without defining all components of the tensor explicitly). It comes with three tensor packages: itensor for abstract (indicial) tensor manipulation, ctensor for component-defined tensors, and atensor for algebraic tensor manipulation. The itensor package guide

Software for use with Mathematica

  • MathTensor is a tensor analysis system written for the Mathematica system. It provides more than 250 functions and objects for elementary and advanced users.
  • Tensors in Physics is a tensor package written for the Mathematica system. It provides many functions relevant for General Relativity calculations in general Riemann-Cartan geometries.
  • Ricci is a system for Mathematica 2.x and later for doing basic tensor analysis, available for free.
  • TTC Tools of Tensor Calculus is a Mathematica package for doing tensor and exterior calculus on differentiable manifolds.
  • EDC and RGTC "Exterior Differential Calculus" and "Riemannian Geometry & Tensor Calculus" are free Mathematica packages for tensor calculus especially designed but not only for general relativity.
  • Tensorial "Tensorial 4.0" is a general purpose tensor calculus package for Mathematica.
  • xAct: Efficient Tensor Computer Algebra for Mathematica. xAct is a collection of packages for fast manipulation of tensor expressions.
  • GREAT: A free package for Mathematica that computes the Christoffel connection and the basic tensors of General Relativity from a given metric tensor.
  • atlas 2 for Mathematica: powerful Mathematica toolbox which allows to do a wide range of modern differential geometry calculations

Software for use with Maple

  • GRTensorII is a computer algebra package for performing calculations in the general area of differential geometry.

Software for use with Matlab

  • Tensor Toolbox Multilinear algebra MATLAB software.
  • MPCA and MPCA+LDA Multilinear subspace learning
    Multilinear subspace learning
    Multilinear subspace learning aims to learn a specific small part of a large space of multidimensional objects having a particular desired property. It is a dimensionality reduction approach for finding a low-dimensional representation with certain preferred characteristics of high-dimensional...

     software: Multilinear principal component analysis
    Multilinear principal component analysis
    Multilinear principal-component analysis is a mathematical procedure that uses multiple orthogonal transformations to convert a set of multidimensional objects into another set of multidimensional objects of lower dimensions. There is one orthogonal transformation for each dimension...

    .

Libraries

  • FTensor is a high performance tensor library written in C++.
  • TL is a multi-threaded tensor library implemented in C++ used in Dynare++. The library allows for folded/unfolded, dense/sparse tensor representations, general ranks (symmetries). The library implements Faa Di Bruno formula and is adaptive to available memory. Dynare++ is a standalone package solving higher order Taylor approximations to equilibria of non-linear stochastic models with rational expectations
    Rational expectations
    Rational expectations is a hypothesis in economics which states that agents' predictions of the future value of economically relevant variables are not systematically wrong in that all errors are random. An alternative formulation is that rational expectations are model-consistent expectations, in...

    .
  • Spartns is a Sparse Tensor framework for Common Lisp
    Common Lisp
    Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...

    .
  • FastMat is a thread-safe general tensor algebra library written in C++ and specially designed for FEM/FVM/BEM/FDM element/edge wise computations.
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