Mathematical Software - ICMS 2024

This book constitutes the proceedings of the 8th International Conference on Mathematical Software, ICMS 2024, held in Durham, UK, during July 2225, 2024.

The 37 full papers presented were carefully reviewed and selected from 46 submissions. The papers are organized in subject areas as follows: plenary lectures; number theory and related areas; novel formalisations of mathematics in lean; software for the applications of group theory to combinatorics; classical algebraic geometry & modern computer algebra: innovative software design and its applications; advancing computer algebra with massively parallel methods; computer algebra applications in the life sciences; machine learning within computer algebra systems; numerical software for special functions; mathematical research data; symbolic-numeric methods in algebraic geometry; Polyhedral geometry and combinatorics; general session.

Inhalt

.- Plenary Lectures.

.- The Reformation of Sage.

.- Algorithm and abstraction in formal mathematics.

.- Number theory and related areas.

.- Computing the Determinant of a Dense Matrix over Z.

.- FastECPP over MPI.

.- Attacking a Levelled Fully Homomorphic Encryption System with Topological Data Analysis.

.- Novel Formalisations of Mathematics in Lean.

.- Formalising Families of l-adic Galois Representations in Lean 4.

.- Formalization of the Existence of Frobenius Elements.

.- Formalising Analysis in Lean: Compactness and Dimensionality.

.- Formalisation of the Category of Hopf Algebras in Lean4.

.- Software for the applications of group theory to combinatorics.

.- Computing the Group of an Algebraic Variety over a Finite Field.

.- Computer classification of linear codes based on lattice point enumeration.

.- Software for proper vertex-colouring exploiting graph symmetry.

.- Classical Algebraic Geometry & Modern Computer Algebra: Innovative Software Design and Its Applications.

.- Localization in GromovWitten theory of toric varieties in a computer algebra system.

.- Advancing computer algebra with massively parallel methods.

.- Massively Parallel Methods for Free Resolutions.

.- Towards Parallel Methods in Birational Geometry.

.- Towards Parallel Algorithms for Gromov-Witten Invariants of Elliptic Curves.

.- Computer algebra applications in the life sciences.

.- A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks.

.- Machine learning within computer algebra systems.

.- Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs.

.- Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems.

.- Machine Learning for Variable Ordering in Cylindrical Algebraic Decomposition.

.- Machine learning for number theory.

.- Numerical software for special functions.

.- Approximation of an inverse of the incomplete beta function.

.- DLMF Standard Reference Tables on Demand.

.- Mathematical research data.

.- Integrating Mathematical Data and Resources: Advancements in zbMATH Open for Enhanced Mathematical Research Accessibility and Reproducibility.

.- A FAIR File Format for Mathematical Software.

.- Predefined Software Environment Runtimes As A Measure For Reproducibility.

.- Towards a FAIR Documentation of Workflows and Models in Applied Mathematics.

.- Symbolic-numeric methods in algebraic geometry.

.- Monodromy Coordinates.

.- Effective alpha theory certification using interval arithmetic: alpha theory over regions.

.- Gr¨obner Degenerations of Determinantal Ideals with an Application to Toric Degenerations of Grassmannians.

.- Polyhedral geometry and combinatorics.

.- Eigenvalue Methods for Sparse Tropical Polynomial Systems.

.- A framework for generalized tropical homotopy continuation.

.- Regular Flips in mptopcom.

.- Dynamic decomposition of tropical prevarieties for celestial mechanics.

.- General Session.

.- Integrating GeoGebra with React and WebAssembly: A Web-Based Approach for Mathematical Software Development.

.- DetGB: A Software Package for Computing Gr¨obner Bases of Determinantal Ideals.

.- Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy.