Mathematica packages that do certain types of symbolic mathematics such as indefinite integral evaluation.

## Analytica

A theorem prover that can be used to prove nontrivial theorems.

Last updated October 31, 2016 symbolic

## ConstantsGrouping

Simple package for replacing combinations of constants with single constants.

Last updated March 12, 2016 symbolic

## DifferentialOperator

DIfferential operators that mimic traditional notation.

Last updated October 1, 2018 symbolic calculus

## Exploring Abstract Algebra with Mathematica

The AbstractAlgebra package is a freely available complement to the book Exploring Abstract Algebra with Mathematica. The package supports working with (finite) groups, rings, fields, and morphisms and functions related to each of these objects. There are a large number of built-in groups (including such standard groups as $Z_n$, $U_n$ (units of $Z_n$), $S_n$, and $D_n$, as well as direct products and quotients of these) and rings (including $Z_n$, Boolean rings and lattice rings, as well as polynomial, matrix and function extension rings). One can also create functions between groups or rings and investigate if these are morphisms.

Last updated September 27, 2015 algebra symbolic

## HolonomicFunctions

The HolonomicFunctions package allows to deal with multivariate holonomic functions and sequences. For this purpose the package can compute annihilating ideals and execute closure properties (addition, multiplication, substitutions) for such functions. An annihilating ideal represents the set of linear differential equations, linear recurrences, q-difference equations, and mixed linear equations that a given function satisfies. Summation and integration of multivariate holonomic functions can be performed via creative telescoping. As subtasks, the following functionalities have been implemented in HolonomicFunctions: computations in Ore algebras (noncommutative polynomial arithmetic with mixed difference-differential operators), noncommutative Gröbner bases, and solving of coupled linear systems of differential or... Read more.

## HypExp

Expands hypergeometric JFJ-1 functions around their parameters. Detailed descriptions are available at hep-ph/0507094 and arXiv:0708.2443 .

Last updated October 18, 2015 symbolic algebra

## Lambda

A Mathematica-package for OPEs in vertex algebras. The package Lambda is designed for calculating λ-brackets in both vertex algebras, and in SUSY vertex algebras. This is equivalent to calculating operator product expansions in two-dimensional conformal field theory. For an introduction, see http://arxiv.org/abs/1004.5264 .

Last updated October 11, 2015 hep physics symbolic

Seven different packages related to mathematical physics; a package for GR-type tensor algebra, one for Virasoro algebra, one for algebra with Grassman variables, a package for Polchinski theta-function conventions, a package specialized at inverting diagonal matrices by inverting each diagonal entry separately, and two packages that deal with approximations to the Ricci-flat metric on the algebraic Calabi-Yau manifold.

Last updated September 27, 2015 physics symbolic algebra

## Ricci

A package for doing tensor calculations in differential geometry.

Last updated September 12, 2015 tensors differential geometry symbolic

## RISCErgoSum

RISCErgoSum is a collection of packages created at the Research Institute for Symbolic Computation (RISC), Linz, Austria. The included packages are: Asymptotics for computing asymptotic series expansions of univariate holonomic sequences; Dependencies for computing algebraic relations of C-finite sequences and multi-sequences; Engel is an implementation of q-Engel Expansion; fastZeil, the Paule/Schorn Implementation of Gosper’s and Zeilberger’s Algorithms; GeneratingFunctions for manipulations of univariate holonomic functions and sequences; GenOmega, Guo-Niu Han’s general Algorithm for MacMahon’s Partition Analysis; Guess for guessing multivariate recurrence equations; HolonomicFunctions for dealing with multivariate holonomic functions, including closure properties, summation, and integration; MultiSum for proving hypergeometric multi-sum... Read more.

Last updated January 6, 2018 symbolic

## RUBI

RUBI is a RUle Based Integrator. It computes indefinite integrals symbolically.

Last updated September 9, 2015 integrals symbolic

## Singular.m

This packages is for interfacing with the Singular computer algebra system. Singular is an open-source computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.

Last updated February 24, 2018 interface singular symbolic polynomial

## VEST

A package for carrying out vector calculus calculations. Related paper: http://arxiv.org/abs/1309.2561.

Last updated September 9, 2015 symbolic vector

## WuRittSolva

WuRittSolva is a standard application package for computer algebra system Mathematica(TM) developed by Liu Hua-Shan for mechanization mathematics education purpose at present. It introduces the Wu-Ritt Well-Order Principle and Zero-Decompostion Theorem as its key theory considering points, and has implemented the most operation for normal polynomials processing, such as fixing CLASS, MAIN VARIABLE, SEPARANT, POLYNOMIAL RANK, BASIC SET, CHARACTERISTIC SET and so on. What is more, it supplies smart functions for elementary geometry theorems proving, promising theorem proving in a smart way. It strongly advises that the polynomials appearing for functions in WuRittSolva are belong to polynomial ring K[u_1,u_2,...,u_n;x_1,x_2,...,x_n] such that... Read more.

Last updated November 25, 2018 Polynomials geometry symbolic

## xAct: Efficient tensor computer algebra for Mathematica

xAct is a suite of free and actively maintained packages for tensor computer algebra in Mathematica. xAct implements state-of-the-art algorithms for fast manipulations of indices and has been modelled on the current geometric approach to General Relativity. It is highly programmable and configurable. Since its first public release in March 2004, xAct has been intensively tested and has solved a number of hard problems in GR.

Last updated April 22, 2018 tensors symbolic