Related papers: A package for computations with classical resultan…
We discuss tableaux for the Implicational Propositional Calculus and show how they may be used to establish its completeness.
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
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…
This note presents the multivariate Hermite criterion: a practical and powerful algorithm for determining the number of distinct real and complex roots of a zero-dimensional system of polynomials in any finite number of variables. The final…
We describe TensoriaCalc, a tensor calculus package written to be smoothly consistent with the Wolfram Language, so as to ensure ease of usage. It allows multiple metrics to be defined in a given session; and, once a metric is computed,…
We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian field.…
In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
We introduce the \prog{Mathematica} package \prog{MT} which can be used to compute, both analytically and numerically, convolutions involving harmonic polylogarithms, polynomials or generalized functions. As applications contributions to…
The R package MfUSampler provides Monte Carlo Markov Chain machinery for generating samples from multivariate probability distributions using univariate sampling algorithms such as Slice Sampler and Adaptive Rejection Sampler. The sampler…
We compute Chow groups of moduli spaces of rank 2 vector bundles on curves with determinant of odd degree in terms of generators and relations.
We describe the qFunctions Mathematica package for $q$-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for $q$-shift equations and…
Quantum computer provides new opportunities for quantum chemistry. In this article, we present a versatile, extensible, and efficient software package, named Q$^2$Chemistry, for developing quantum algorithms and quantum inspired classical…
We propose an algebraic model of computation which formally relates symbolic listings, complexity of Boolean functions, and low depth arithmetic circuit complexity. In this model algorithms are arithmetic formula expressing symbolic…
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…
Predicting long-term outcomes of interventions is necessary for educational and social policy-making processes that might widely influence our society for the long-term. However, performing such predictions based on data from large-scale…
A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented.
The aim of this article is to show, how computer algebra can be used when applying Liu's procedure. Although Mathematica (a commercial product by Wolfram Research Inc.) is used, it is possible to use other computer algebra systems as well.
We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives w.r.t. several variables up to an arbitrary order in each variable, but excluding mixed derivatives. Arithmetic…