Related papers: Symbolic tensor calculus on manifolds: a SageMath …
We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are…
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…
We introduce a new algorithm for computing the periods of a smooth complex projective hypersurface. The algorithm intertwine with a new method for computing an explicit basis of the singular homology of the hypersurface. It is based on…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
Bilinear pseudodifferential operators with symbols in the bilinear analog of all the H\"ormander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise…
The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given…
This article documents the free computer algebra system "gTybalt". The program is build on top of other packages, among others GiNaC, TeXmacs and Root. It offers the possibility of interactive symbolic calculations within the C++…
Nowadays interactive digital scientific environments have become an integral part of scientific computing in solving various scientific tasks in research, but also STEM education. We introduce SageMath or shortly Sage -- a free open…
Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
Symbolic integration is an important module of a typical Computer Algebra System. As for now, Mathematica, Matlab, Maple and Sage are all mainstream CAS. They share the same framework for symbolic integration at some points. In this book…
This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The…
Intuitively, an (implementation) automata is simulated by a (specification) automata if every externally observable transition by the implementation automata can also be made by the specification automata. In this work, we present a…
We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…
A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…
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 work presents a symbolic approach for estimating the energy consumption for nested loop programs when mapped and scheduled on parallel processor array accelerator architectures. Instead of simulation-based evaluation, we derive a…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
We treat the notion of principal symbol mapping on a compact smooth manifold as a $\ast$-homomorphism of $C^{\ast}$-algebras. Principal symbol mapping is built from the ground, without referring to the pseudodifferential calculus on the…