Related papers: TensoriaCalc: A User-Friendly Tensor Calculus Pack…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
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…
FormCalc is a Mathematica package for the automatic computation of tree-level and one-loop Feynman amplitudes. It accepts diagrams generated by FeynArts, simplifies them, and generates a complete Fortran code for their numerical evaluation.…
Theoretical spectroscopy is a powerful tool to describe and predict optical properties of materials. While nowadays routinely performed, first-principles calculations only provide bulk dielectric tensors in Cartesian coordinates. These…
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact…
The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…
We introduce SignatureTensors.jl, a new package for computing signature tensors of paths in julia. We present its core functionality and demonstrate its use through illustrative examples. The package is compatible with the computer algebra…
We present a user-friendly, open-source Wolfram Language package that automates the construction of an effective homogeneous generalized Voigt rheology for a spherically symmetric, incompressible layered body with Maxwell solid layers. It…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
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,…
This paper describes a package for calculations of expressions with Dirac matrixes. Advantages to existing similar packages are described. MatrixExp package is intended for simplification of complex expressions involving $\gamma$-matrixes,…
Computations with tensors are ubiquitous in fundamental physics, and so is the usage of Einstein's dummy index convention for the contraction of indices. For instance, $T_{ia}U_{aj}$ is readily recognized as the same as $T_{ib}U_{bj}$, but…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
TextDescriptives is a Python package for calculating a large variety of metrics from text. It is built on top of spaCy and can be easily integrated into existing workflows. The package has already been used for analysing the linguistic…
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…