Related papers: xTras: a field-theory inspired xAct package for Ma…
I present the tensor computer algebra package FieldsX, which extends the xAct suite of tensor algebra packages to perform computations in field theory with fermions and gauge fields. This includes the standard tools of curved-space $\gamma$…
We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…
In this paper we present a short overview of the new Wolfram Mathematica package intended for elementary "in-basis" tensor and differential-geometric calculations. In contrast to alternatives our package is designed to be easy-to-use,…
The Maxima computer algebra system, the open-source successor to MACSYMA, the first general-purpose computer algebra system that was initially developed at the Massachusetts Institute of Technology in the late 1960s and later distributed by…
We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but…
We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…
We present FormTracer, a high-performance, general purpose, easy-to-use Mathematica tracing package which uses FORM. It supports arbitrary space and spinor dimensions as well as an arbitrary number of simple compact Lie groups. While…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…
Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…
Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the…
Tensor calculation of suffix-contraction is carried out by a C-program. Tensors are represented graphically, and the algorithm makes use of the topology of graphs. Classical and quantum gravity, in the weak-field perturbative approach, is a…
We present a package for the computer algebra system Mathematica, which implements the parametrized post-Newtonian (PPN) formalism. This package, named xPPN, is built upon the widely used tensor algebra package suite xAct, and in particular…
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…
We present $\mathtt{bimEX}$, a Mathematica package for exact computations in 3$+$1 bimetric relativity. It is based on the $\mathtt{xAct}$ bundle, which can handle computations involving both abstract tensors and their components. In this…
CARTAN is an easy-to-use symbolic, tensor component package based on the popular Mathematica program. CARTAN makes use of the powerful formalism of rigid frames, and can return results both in this frame and in the coordinate basis. CARTAN…
We present a small computer algebra program for use in Maxwell's theory. The Maxwell equations and the energy-momentum current of the electromagnetic field are formulated in the language of exterior differential forms. The corresponding…
We describe TensoriaCalc, a tensor calculus package written to be smoothly consistent with the Wolfram Language, so as to ensure ease of usage. It allows multiple metrics to be defined in a given session; and, once a metric is computed,…