Search results for "symbolic computation"
showing 10 items of 124 documents
Application of modern computer algebra systems in food formulations and development: A case study
2017
Abstract Background Nutritional security determines the level of public health within a population while inadequate nutrition is one of the major factors in development of various health problems. This can be alleviated with sufficient and affordable access to currently available or newly designed nutritious foods. Scope and approach Formulation of new foods can be very costly, so methods able to lower design expanses are of utmost importance to the industry. Hence, the purpose of this work was to rationalize utilization of modern computerized algebraic systems (CAS) in solving traditional problems for formulating food mixtures by food combinatoric principles (FCP). Key findings and conclus…
"Table 5" of "Search for heavy charged long-lived particles in the ATLAS detector in 31.6 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} = 13…
2019
Expected signal yield and acceptance x efficiency, estimated background and observed number of events in data for the full range of simulated masses in the full-detector R-hadron search.
"Table 5" of "Search for heavy charged long-lived particles in the ATLAS detector in 31.6 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} = 13…
2019
Expected signal yield and acceptance x efficiency, estimated background and observed number of events in data for the full range of simulated masses in the full-detector R-hadron search.
Infinitesimal deformations of double covers of smooth algebraic varieties
2003
The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi--Yau threefolds which are non--singular models of do…
The History of Algebra in Mathematics Education
2006
In this chapter, we analyse key issues in algebra history from which some lessons can be extracted for the future of the teaching and learning of algebra. A comparative analysis of two types of pre-Vietan languages (before 16th century), and of the corresponding methods to solve problems, leads to conjecture the presence of didactic obstacles of an epistemological origin in the transition from arithmetic to algebraic thinking. This illustrates the value of historic and critical analysis for basic research design in mathematics education. Analysing the interrelationship between different evolution stages of the sign system of symbolic algebra and vernacular language supports the inference th…
Numerical evaluation of multiple polylogarithms
2004
Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for arbitrary complex arguments and without any restriction on the weight. We have implemented these algorithms with arbitrary precision arithmetic in C++ within the GiNaC framework.
On Meet-Complements in Cohn Geometries
1993
Within the frame of projective lattice geometry, the present paper investigates classes of meet-complements in Cohn geometries and especially in Ore and Bezout geometries. The algebraic background of these geometries is given by torsion free modules over domains — in particular Ore and Bezout domains. 1
A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches
2015
We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spin-free coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of non-antisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick's theorem. Each term is then put down in the form of a non-antisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying co…
Data for: Analytical induced force solution in conducting cylindrical bodies and rings due to a rotating finite permanent magnet
2019
Implementation of analytical current density solution in numerical calculations using Wolfram Mathematica software. THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOVE
MultivariateApart: Generalized partial fractions
2021
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 to terms of a sum separately. The package is designed to work in Mathematica, but also provides interfaces to the Form and Singular computer algebra systems.