Related papers: Computations involving symbolic powers
Research on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) Number Theory in recent years. In this survey, we present the key tools…
MatchingTools is a Python library for doing symbolic calculations in effective field theory. It provides the tools to construct general models by defining their field content and their interaction Lagrangian. Once a model is given, the…
This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
The problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible decompositions is…
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
{\tt AbstractSimplicialComplexes.m2} is a computer algebra package written for the computer algebra system {\tt Macaulay2} \cite{M2}. It provides new infrastructure to work with abstract simplicial complexes and related homological…
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Searching for structural reasons behind old results and conjectures of Chudnovksy regarding the least degree of a nonzero form in an ideal of fat points in projective N-space, we make conjectures which explain them, and we prove the…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
Symbolic control techniques aim to satisfy complex logic specifications. A critical step in these techniques is the construction of a symbolic (discrete) abstraction, a finite-state system whose behaviour mimics that of a given…
We present {\tt RandomPoints}, a package in \emph{Macaulay2} designed mainly to identify rational and geometric points in a variety over a finite field. We provide tools to estimate the dimension of a variety. We also present methods to…
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the…
This paper introduces a novel method for the representation of images that is semantic by nature, addressing the question of computation intelligibility in computer vision tasks. More specifically, our proposition is to introduce what we…