xTras: a field-theory inspired xAct package for Mathematica
Teake Nutma
TL;DR
xTras provides a cohesive, field-theory oriented extension to the xAct tensor algebra ecosystem in Mathematica, enabling practical construction of contractions, Ansätze, and tensor-equation solutions. The paper demonstrates core capabilities through Spin-2 on flat backgrounds and Gauss–Bonnet computations, and details a broad function suite spanning combinatorics, tensor algebra, and Young-tableaux tooling. Key contributions include AllContractions for contraction enumeration, MakeTraceless and ConstructDDIs for symmetry-based simplifications, EulerDensity for topological densities, and variational utilities VarL/VarD for efficient metric variations. Together, these tools streamline classical field theory tensor computations within a unified, freely available framework.
Abstract
We present the tensor computer algebra package xTras, which provides functions and methods frequently needed when doing (classical) field theory. Amongst others, it can compute contractions, make Ansätze, and solve tensorial equations. It is built upon the tensor computer algebra system xAct, a collection of packages for Mathematica.