Tensor software

Key takeaways

Tensor software belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Tensor software to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Tensor software from memory before moving on to harder problems.

Reference excerpt

Tensor software is a class of mathematical software designed for manipulation and calculation with tensors.

Standalone software SPLATT is an open source software package for high-performance sparse tensor factorization. SPLATT ships a stand-alone executable, C/C++ library, and Octave/MATLAB API. 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 GNU Octave, but designed specifically for tensors.

Software for use with Mathematica Tensor 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 symbolic tensor expressions. GREAT is 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 is a powerful Mathematica toolbox which allows to do a wide range of modern differential geometry calculations GRTensorM is a computer algebra package for performing calculations in the general area of differential geometry. MathGR is a package to manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices to partially or completely explicit indices and convert partial derivatives into total derivatives. TensoriaCalc is a tensor calculus package written for Mathematica 9 and higher, aimed at providing user-friendly functionality and a smooth consistency with the Mathematica language itself. As of December 2025, given a metric and its coordinates, TensoriaCalc can compute the associated geometric objects such as Christoffel symbols, Riemann curvature tensor, Ricci tensor/scalar, etc. It allows for generic tensors to be defined and their indices moved readily. Furthermore, it is able to carry out differential geometric operations such as covariant, Lie and exterior derivatives; Hodge duals; coordinate transformations on generic tensors, including the use of orthonormal basis; etc. TensoriaCalc is continuously under development. OGRe is a modern free and open-source Mathematica package for tensor calculus, released in 2021 for Mathematica 12.0 and later. It is designed to be both powerful and user-friendly, and is especially suitable for general relativity. OGRe allows performing arbitrarily complicated tensor operations, and automatically transforms between index configurations and coordinate systems behind the scenes as needed for each operation.

Software for use with Maple GRTensorII is a computer algebra package for performing calculations in the general area of differential geometry. Atlas 2 for Maple is a modern differential geometry for Maple. DifferentialGeometry is a package which performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, General Relativity, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. It is included with Maple. Physics is a package developed as part of Maple, which implements symbolic computations with most of the objects used in mathematical physics. It includes objects from general relativity (tensors, metrics, covariant derivatives, tetrads etc.), quantum mechanics (Kets, Bras, commutators, noncommutative variables) etc.

Software for use with Matlab Tensorlab is a MATLAB toolbox for multilinear algebra and structured data fusion. Tensor Toolbox Multilinear algebra MATLAB software. MPCA and MPCA+LDA Multilinear subspace learning software: Multilinear principal component analysis. UMPCA Multilinear subspace learning software: Uncorrelated multilinear principal component analysis. UMLDA Multilinear subspace learning software: Uncorrelated multilinear discriminant analysis.

Software for use with Maxima Maxima is a free open source general purpose computer algebra system which includes several packages for tensor algebra calculations in its core distribution. 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.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Tensor software

Start with the simplest possible case. Write down what Tensor software claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Tensor software before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Tensor software ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Tensor software

In research: Tensor software appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Tensor software in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Tensor software is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer algebra systems, Tensors, so understanding it makes those chapters shorter.
In everyday life: Look for Tensor software outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Tensor software in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Tensor software means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Tensor software out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Tensor software in simple terms?

Tensor software is a class of mathematical software designed for manipulation and calculation with tensors. Standalone software SPLATT is an open source software package for high-performance sparse tensor factorization.

Why does Tensor software matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Tensor software?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Tensor software.