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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…
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using Cadabra as the main computer algebra system for several…
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…
ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…
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…
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,…
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…
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…
GRTensorJ - Books is an active interface to a small part of the computer algebra systems GRTensorII (for Maple) and GRTensorM (for Mathematica) with the specific intent of providing students of General Relativity with an advanced…
Model-based approaches to imaging, like specialized image enhancements in astronomy, facilitate explanations of relationships between observed inputs and computed outputs. These models may be expressed with extended matrix-vector (EMV)…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
Detailed notes on the functions included in the DMRjulia library are included here. This discussion of how to program functions for a tensor network library are intended to be a supplement to the other documentation dedicated to explaining…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
We introduce Strawberry Fields, an open-source quantum programming architecture for light-based quantum computers, and detail its key features. Built in Python, Strawberry Fields is a full-stack library for design, simulation, optimization,…
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,…
An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…
Tensor algebra lies at the core of computational science and machine learning. Due to its high usage, entire libraries exist dedicated to improving its performance. Conventional tensor algebra performance boosts focus on algorithmic…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…