14 papers · ranked by Valyu relevance
L. Fekésházy, Bakar Chargeishvili, G. Somogyi, S. Van Thurenhout
We present LinApart, a routine designed for efficiently performing the univariate partial fraction decomposition of large symbolic expressions. Our method is based on an explicit closed formula for the decomposition of rational functions with fully factorized denominators. We provide implementations in both the Wolfram…
Oluwateniayo O. Ogunsan, Daniel Lobo
Mathematical models formally and precisely represent biological mechanisms with complex dynamics. To understand the possible behaviors of such systems, phase portrait diagrams can be used to visualize their overall global dynamics across a domain. However, producing these phase portrait diagrams is a laborious process…
Francesca Bertacchini, Carmelo Scuro, Pietro Pantano, Eleonora Bilotta
'Eleonora Bilotta'] An educational robotics lab has been planned for undergraduate students in an Electronic Engineering degree, using the Project Based Learning (PBL) approach and the NAO robot. Students worked in a research context, with the aim of making the functions of the NAO robot as social and autonomous as…
Robert Urbanczik
Background Despite recent algorithmic and conceptual progress, the stoichiometric network analysis of large metabolic models remains a computationally challenging problem. Results SNA is a interactive, high performance toolbox for analysing the possible steady state behaviour of metabolic networks by computing the…
Sebastiaan J. C. Joosten, René Thiemann, Akihisa Yamada
We formalize algebraic numbers in Isabelle/HOL. Our development serves as a verified implementation of algebraic operations on real and complex numbers. We moreover provide algorithms that can identify all the real or complex roots of rational polynomials, and two implementations to display algebraic numbers, an…
George I. Mias, Tahir Yusufaly, Raeuf Roushangar, Lavida R. K. Brooks + 2 more
Multiple omics data are rapidly becoming available, necessitating the use of new methods to integrate different technologies and interpret the results arising from multimodal assaying. The MathIOmica package for Mathematica provides one of the first extensive introductions to the use of the Wolfram Language to tackle…
Christian Bengs, Malcolm H. Levitt
SpinDynamica is a set of Mathematica packages for performing numerical and symbolic analysis of a wide range of magnetic resonance experiments and phenomena. An overview of the SpinDynamica architecture and functionality is given, with some simple representative examples.
Malcolm A. H. MacCallum
The complicated nature of calculations in general relativity was one of the driving forces in the early development of computer algebra (CA). CA has become widely used in gravity research (GR) and its use can be expected to grow further. Here the general nature of computer algebra is discussed, along with some aspects…
Ian Briggs, Yash Lad, Pavel Panchekha
Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately…
Éléa Thibault Greugny, Nicolas Ratto, Loïc Etheve, Jean-Baptise Gourlet + 2 more
Mathematical modeling of disease and drug action is becoming an indispensable component of drug development, underscored by recent examples of models predicting trial results. To be able to rely on such approaches, decision-makers need to be able to verify those results independently with in silico confirmatory…
Fredrik Johansson
We present an efficient implementation of hypergeometric functions in arbitraryprecision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error…
Daniel McKinley
Elementary cellular automata (ECA) are a set of simple binary programs in the form of truth tables called Wolfram codes that produce complex output when done repeatedly in parallel, and quaternions are an extension of complex numbers frequently used to represent 3D space and its rotations in computer graphics due to…
Authors not listed
An automatic code generated C++/HIP/CUDA implementation of the (auxiliary) Fock, or Kohn–Sham, matrix construction for execution in GPU-accelerated hardware environments is presented. The module is developed as part the quantum chemistry software package VeloxChem, employing localized Gaussian atomic orbitals. The per-…
Fergus R. Cooper, Ruth E. Baker, Alexander G. Fletcher
Mathematical modelling provides a useful framework within which to investigate the organization of biological tissues. With advances in experimental biology leading to increasingly detailed descriptions of cellular behaviour, models that consider cells as individual objects are becoming a common tool to study how…