相关论文: Tensor manipulation in GPL Maxima

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 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…

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…

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…

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…

Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…

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…

We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…

Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…

OpenTensor is a reproduction of AlphaTensor, which discovered a new algorithm that outperforms the state-of-the-art methods for matrix multiplication by Deep Reinforcement Learning (DRL). While AlphaTensor provides a promising framework for…

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…

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 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 Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing…

Recently, tensor algebra have witnessed significant applications across various domains. Each operator in tensor algebra features different computational workload and precision. However, current general accelerators, such as VPU, GPGPU, and…

Recently, deep learning has been an area of intense research. However, as a kind of computing-intensive task, deep learning highly relies on the scale of GPU memory, which is usually prohibitive and scarce. Although some extensive works…

In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct…

The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…

This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…