Mathematical Software - ICMS 2024 : 8th International Conference, Durham, UK, July 22-25, 2024, Proceedings

• Record Nr.: UNINA9910874694803321
• Autore: Buzzard Kevin
• Pubbl/distr/stampa: Cham : , : Springer, , 2024; ©2024
• ISBN: 9783031645297
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (377 pages)
• Collana: Lecture Notes in Computer Science Series ; ; v.14749
• Altri autori (Persone): DickensteinAlicia; EickBettina; LeykinAnton; RenYue
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Organization -- Plenary Lectures -- The Reformation of Sage -- Algorithm and Abstraction in Formal Mathematics -- Polynomial System Solving with the Msolve Library -- Contents -- Plenary Lectures -- The Reformation of Sage -- 1 Introduction: What Is Sage? -- 2 The Modularization Project -- 2.1 Problem Description and Goals -- 2.2 Origins -- 2.3 The Tools -- 2.4 The Rules -- 2.5 The Blocks -- References -- Algorithm and Abstraction in Formal Mathematics -- 1 Introduction -- 2 Computation -- 2.1 Classification of Wallpaper Groups -- 2.2 The Kochen-Specker Paradox -- 2.3 Multiplication of Chebyshev Polynomials -- 3 Abstraction -- 3.1 Lax-Milgram Theorem -- 3.2 Smooth Vector Bundles -- 4 Conclusion -- References -- Number Theory and Related Areas -- Computing the Determinant of a Dense Matrix over Z -- 1 Introduction -- 1.1 Uniform Dense Matrices -- 2 Notation, Terminology, Preliminaries -- 2.1 Unimodular Matrices -- 2.2 Unimodularity Verification -- 3 Determinant Algorithms for Integer Matrices -- 3.1 Using the Modular HNF -- 4 Algorithm for Computing Determinant -- 5 Practical Tests -- 6 Conclusion -- References -- FastECPP over MPI -- 1 FastECPP and Its Complexity -- 2 ; Implementation Choices -- 3 Details of the 86453 Digit Record -- 4 Sizes of Smooth Parts -- 5 Comparison -- References -- Attacking a Levelled Fully Homomorphic Encryption System with Topological Data Analysis -- 1 Introduction -- 2 Background -- 2.1 Helper Functions -- 2.2 Cryptosystem -- 3 Cryptanalysis -- 3.1 Basic Idea -- 3.2 Methodology -- 4 Results and Discussion -- 5 Conclusions -- References -- Novel Formalisations of Mathematics in Lean -- Formalising Families of -adic Galois Representations in Lean 4 -- 1 Introduction -- 1.1 Mathematical Definitions -- 2 Formalisation -- 2.1 Definitions and Initial Challenges -- 2.2 Trivial Example.; 2.3 A Further Example -- 2.4 Compatibility -- 3 Conclusion -- References -- Formalization of the Existence of Frobenius Elements -- 1 Introduction -- 2 Mathematical Background -- 2.1 leanA K L B Setup. -- 2.2 Characteristic of Finite Fields -- 2.3 Galois Correspondence -- 2.4 Integral Closure -- 3 Survey of Lean Code -- 3.1 leangalactionIdeal' and leandecompositionsubgroupIdeal' -- 3.2 leanexistsgenerator -- 3.3 [escapeinside=||]lean|| ||, || q [escapeinside=||]lean || || || mod Q (leanpowqisconjugate) -- 4 Discussion -- References -- Formalising Analysis in Lean: Compactness and Dimensionality -- 1 Introduction -- 2 Mathematical Proof -- 3 Proof in Lean -- 4 Conclusions -- References -- Formalisation of the Category of Hopf Algebras in Lean4 -- 1 Introduction -- 2 Group Structure on the `3́9`42`"̇613A``45`47`"603AHom Set -- 2.1 Mathematical Details -- 2.2 Formalisation -- 3 Affine Group Scheme -- 3.1 Mathematical Details -- 3.2 Formalisation -- 4 Conclusion -- References -- Software for the Applications of Group Theory to Combinatorics -- Computing the Group of an Algebraic Variety over a Finite Field -- 1 Introduction -- 2 Groups and Geometries -- 3 The Algorithm -- 4 Implementation in Orbiter -- 5 Tactical Decompositions -- 6 Example 1: The Edge Quartic -- 7 Comparison with Classification -- References -- Computer Classification of Linear Codes Based on Lattice Point Enumeration -- 1 Introduction -- 2 Preliminaries -- 2.1 Geometric Representation of Linear Codes -- 2.2 Extending Linear Codes Using Lattice Point Enumeration -- 3 Enhancing the Algorithmic Approach via Integer Linear Programming Computations -- 4 Computational Results -- References -- Software for Proper Vertex-Colouring Exploiting Graph Symmetry -- 1 Introduction -- 2 Proper Vertex-Colouring and Cliques -- 3 The Main Tools.; 4 A Total Ordering of Finite Sequences of Subsets of {1,…,n} -- 5 The Backtrack Search -- 5.1 Constraints on Partial Solutions -- 6 Examples -- References -- Classical Algebraic Geometry and Modern Computer Algebra: Innovative Software Design and Its Applications -- Localization in Gromov-Witten Theory of Toric Varieties in a Computer Algebra System -- 1 Introduction -- 2 Atiyah-Bott Formula -- 3 The Algorithm -- 3.1 Generation of the Decorated Graphs -- 3.2 Equivariant Classes -- 4 Generalization -- References -- Advancing Computer Algebra with Massively Parallel Methods -- Massively Parallel Methods for Free Resolutions -- 1 Introduction -- 2 Gröbner Bases and Syzygies -- 2.1 Finitely Generated Modules and Their Syzygies -- 2.2 Induced Ordering and Schreyer's Algorithms -- 3 Singular/GPI-Space Framework and Petri Nets -- 4 Modelling Free Resolutions -- References -- Towards Parallel Methods in Birational Geometry -- 1 Introduction -- 2 Example: Determining Images of Rational Maps -- 3 Covering a Scheme with Complete Intersection Charts -- References -- Towards Parallel Algorithms for Gromov-Witten Invariants of Elliptic Curves -- 1 Introduction -- 2 Gromov-Witten Invariants and Feynman Integrals -- 2.1 Theoretical Background and Elementary Algorithm -- 2.2 Improvement of the Algorithm -- 3 Petri Nets and GPI-Space -- 4 ; Parallel Enumeration of Combinatorial Objects -- References -- Computer Algebra Applications in the Life Sciences -- A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks -- 1 Elementary Vectors of a Subspace -- 2 Applications to Chemical Reaction Networks -- References -- Machine Learning Within Computer Algebra Systems -- Symbolic Integration Algorithm Selection with Machine Learning: LSTMs Vs Tree LSTMs -- 1 Introduction -- 2 Literature Review -- 3 Machine Learning -- 3.1 LSTM.; 3.2 TreeLSTM -- 4 Generating Data -- 4.1 Existing Methods -- 4.2 New Methods -- 4.3 Datasets of Integrals -- 5 Experimental Results -- 5.1 Experiment Setup -- 5.2 Experiment Results -- 6 Conclusion -- References -- Exploring Alternative Machine Learning Models for Variable Ordering in Cylindrical Algebraic Decomposition -- 1 Introduction -- 2 Background -- 2.1 CAD and Variable Ordering -- 2.2 Machine Learning in CAD -- 3 Our Methodology -- 3.1 Datasets -- 3.2 Training and Features -- 3.3 Implementation of General Models -- 3.4 Implementation of GNN Models -- 3.5 Exploration of Data Pollution -- 4 Results -- 5 Conclusion and Future Work -- References -- Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems -- 1 Introduction -- 1.1 Machine Learning Within Computer Algebra Systems -- 1.2 Gaining Additional Mathematical Insight from Machine Learning -- 1.3 Explainable AI -- 1.4 Plan of the Paper -- 2 Our Application: Variable Ordering Choice for CAD -- 2.1 Cylindrical Algebraic Decomposition -- 2.2 CAD Variable Ordering -- 3 Feature Generation Process -- 3.1 Formalising Brown's Heuristic -- 3.2 Generating Similar Features -- 4 Interpreting Brown's Heuristic as a Neural Network -- 5 Searching Through Similar Constrained Neural Networks -- 5.1 Feature Selection -- 5.2 Weight Tuning -- 6 Final Thoughts -- References -- Machine Learning for Number Theory: Unsupervised Learning with L-Functions -- 1 Introduction -- 2 A Crash Course in L-Functions -- 3 Unsupervised Learning with RStudio -- 3.1 Data Summary -- 3.2 Hierarchical Clustering with RStudio -- 3.3 PCA with RStudio -- 4 Outlook -- References -- Numerical Software for Special Functions -- Approximation of an Inverse of the Incomplete Beta Function -- 1 Introduction -- 2 Normal Asymptotic Approximation -- 3 GST Asymptotic Approximation -- 4 Conclusions.; References -- DLMF Standard Reference Tables on Demand -- 1 Introduction -- 2 MpIeee -- 3 Design of DLMF Tables -- 3.1 Tabulation -- 3.2 Comparison -- 4 Future Directions -- References -- Mathematical Research Data -- Integrating Mathematical Data and Resources: Advancements in zbMATH Open for Enhanced Mathematical Research Accessibility and Reproducibility -- 1 The swMATH Journey -- 1.1 On the Importance of Metadata for Software -- 1.2 swMATH as an Extension of zbMATH Open -- 2 swMATH in the EOSC -- 2.1 Protecting Source Code and Indexing It, a Fruitful Collaboration with Software Heritage -- 2.2 Disseminating Software Metadata for the Advancement of Open Science -- 2.3 swMATH: Towards a Connected Resource into the EOSC Ecosystem -- 2.4 swMATH Adopted CodeMeta as the Standard Format to Display Software Metadata -- 3 Conclusion -- References -- A FAIR File Format for Mathematical Software -- 1 The File Format by Example -- 2 More Examples -- 3 Format Specification -- 4 Beyond OSCAR -- 5 Concluding Remarks -- References -- Predefined Software Environment Runtimes as a Measure for Reproducibility -- 1 Introduction -- 1.1 Organization -- 2 MaRDI Packaging System: An Overview -- 3 Technical Details -- 3.1 Bubblewrap -- 3.2 Libostree -- 3.3 Fuse-Overlayfs -- 3.4 MaPS -- 3.5 Comparison with Competing Methods -- 3.6 Compatibility -- 4 ; Examples -- 4.1 AccurateArithmetic.jl -- 4.2 OSCAR -- 5 Beyond Mathematical Software -- 5.1 VIBRANT -- 6 Concluding Remarks -- References -- Towards a FAIR Documentation of Workflows and Models in Applied Mathematics -- 1 Introduction -- 2 MaRDMO, MathModDB and Their Connection -- 3 A Semantic Representation of an Algebraic Modeling Workflow -- 4 Conclusion and Outlook -- References -- Symbolic-Numeric Methods in Algebraic Geometry -- Monodromy Coordinates -- 1 Introduction -- 2 Monodromy Background -- 3 Monodromy Solving.; 4 Monodromy Coordinates: Compression.