Related papers: xTras: a field-theory inspired xAct package for Ma…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
Monte Carlo Tree Search (MCTS) algorithms such as AlphaGo and MuZero have achieved superhuman performance in many challenging tasks. However, the computational complexity of MCTS-based algorithms is influenced by the size of the search…
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…
In this work we present recent results on application of low-rank tensor decompositions to modelling of aggregation kinetics taking into account multi-particle collisions (for three and more particles). Such kinetics can be described by…
A complete contraction on a C*-algebra A, which preserves all closed two sided ideals J, can be approximated pointwise by elementary complete contractions if and only if the induced map on the tensor product of B with A/J is contractive for…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
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…
ASTRA is a Python package that provides a modular, instrument-independent interface for working with high-resolution stellar spectra. Designed to support data from multiple spectrographs, including ESPRESSO (Pepe et al., 2021), HARPS (Mayor…
We present some methods and results in the application of algebraic geometry and computer algebra to the study of algebraic vector bundles, foliations and zeta functions. A connection of the methods and results with noncommutative geometry…
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…
A Galilean contraction is a way to construct Galilean conformal algebras from a pair of infinite-dimensional conformal algebras, or equivalently, a method for contracting tensor products of vertex algebras. Here, we present a generalisation…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for…
The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had succesful applications in both mathematics and theoretical physics. This work deals with generalizations of the…
This article introduces the Mathematica package \emph{HEPMath} which provides a number of utilities and algorithms for High Energy Physics computations in Mathematica. Its functionality is similar to packages like FormCalc or FeynCalc, but…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
The discrete cosine transform (DCT) is a widely-used and important signal processing tool employed in a plethora of applications. Typical fast algorithms for nearly-exact computation of DCT require floating point arithmetic, are multiplier…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
We provide an explicit algorithm to calculate invariant tensors for the adjoint representation of the simple Lie algebra $sl(n)$, as well as arbitrary representation in terms of roots. We also obtain explicit formulae for the adjoint…
Equivariant atomistic machine learning models have largely been built on spherical-tensor representations, where explicit angular-momentum coupling introduces substantial complexity and systematic extensions beyond energies and forces…