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This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations…
Cadabra is a new computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for…
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no…
Cadabra is a powerful computer program for the manipulation of tensor equations. It was designed for use in high energy physics but its rich structure and ease of use lends itself well to the routine computations required in General…
Computer Algebra Systems (CASs) like Cadabra Software play a prominent role in a wide range of research activities in physics and related fields. We show how Cadabra language is easily implemented in the well established Python programming…
The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight…
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately…
Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
In this paper we introduce Redberry --- an open source computer algebra system with native support of tensorial expressions. It provides basic computer algebra tools (algebraic manipulations, substitutions, basic simplifications etc.) which…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
We have been involved in the creation of multiple software systems for computer algebra, including Reduce, Maple, Axiom and Aldor as well as a number of smaller specialised programs. We relate observations on how the meaning of software…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into…
We discuss what is special about the reproducibility of workflows in computer algebra. It is emphasized how the programming language Julia and the new computer algebra system OSCAR support such a reproducibility, and how users can benefit…