Computer Algebra in Scientific Computing : 22nd International Workshop, CASC 2020, Linz, Austria, September 14-18, 2020, Proceedings

Computer Algebra in Scientific Computing : 22nd International Workshop, CASC 2020, Linz, Austria, September 14-18, 2020, Proceedings / edited by François Boulier, Matthew England, Timur M. Sadykov, Evgenii V. Vorozhtsov.

This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020, held in Linz, Austria, in September 2020. The conference was held virtually due to the COVID-19 pandemic. The 34 full papers presented together with 2 invited tal...

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Bibliographic Details
Corporate Author: International Workshop on Computer Algebra in Scientific Computing Online
Other Authors: Boulier, François, England, Matthew, Sadykov, Timur M., Vorozhtsov, E. V. (Evgenii Vasilʹevich), 1946-
Format: eBook
Language:English
Published: Cham : Springer, 2020.
Series:Lecture notes in computer science ; 12291.
LNCS sublibrary. Theoretical computer science and general issues.
Subjects:
Computer science > Congresses.
Computers, Special purpose > Congresses.
Software engineering > Congresses.
Algorithms > Congresses.
Computer logic > Congresses.
Computer science > Mathematics > Congresses.
Management information systems > Congresses.
Algorithms
Computer logic
Computer science
Computer science > Mathematics
Computers, Special purpose
Management information systems
Software engineering
proceedings (reports)
Conference papers and proceedings
Conference papers and proceedings.
Actes de congrès.
Online Access:Click for online access
Table of Contents:
  • Intro
  • Preface
  • CASC 2020 Venue
  • Overview of the Volume
  • Acknowledgments
  • Organization
  • Contents
  • Tropical Geometry of Biological Systems (Invited Talk)
  • 1 Introduction
  • 2 Models of Biological Systems and Their Reductions
  • 3 Tropical Geometry Approaches
  • 4 Scaling and Singular Perturbation Schemes
  • 5 Approximate Conservation Laws
  • 6 Metastability
  • 7 Conclusion
  • References
  • Algebraic and Geometric Analysis of Singularities of Implicit Differential Equations (Invited Talk)
  • 1 Introduction
  • 2 Differential Systems and Algebraic Differential Equations
  • 3 Singularities of Algebraic Differential Equations
  • 4 Regularity Decompositions
  • 5 Semialgebraic Differential Equations
  • 6 Analysis of Geometric Singularities
  • 7 Quasilinear Equations
  • 8 Analysis of Algebraic Singularities
  • 9 Conclusions
  • References
  • On the Complexity of Computing Integral Bases of Function Fields
  • 1 Introduction
  • 2 Van Hoeij's Algorithm
  • 2.1 Puiseux Series
  • 2.2 Description of van Hoeij's Algorithm
  • 2.3 Complexity Analysis
  • 2.4 An Improvement in the Case of Low-Degree Singularities
  • 3 Trager's Algorithm
  • 3.1 A Description of Trager's Algorithm
  • 3.2 Complexity Analysis
  • 4 Integral Bases Through Weierstrass Factorization and Truncations of Puiseux Series
  • 4.1 Computing Normalization at One Branch
  • 4.2 Branch-Wise Splitting for Integral Bases
  • 4.3 Contribution of the Invertible Factor f0
  • 4.4 Proof of Theorem 3
  • 5 Conclusion
  • References
  • Truncated and Infinite Power Series in the Role of Coefficients of Linear Ordinary Differential Equations
  • 1 Introduction
  • 2 The Equation Threshold
  • 3 Induced Recurrence Equations
  • 4 Computing Coefficients of Truncated Laurent Solutions
  • 5 Algorithm
  • 6 Implementation
  • Examples of Use
  • 7 Concluding Remarks
  • References
  • On Periodic Approximate Solutions of the Three-Body Problem Found by Conservative Difference Schemes
  • 1 Basic Definitions
  • 2 Inheritance of the Exact Solution Properties
  • 3 Conservative Schemes for the Problem of Many Bodies
  • 4 Lagrange Problem
  • 5 Triangular Solution
  • References
  • Univariate Polynomials with Long Unbalanced Coefficients as Bivariate Balanced Ones: A Toom-Cook Multiplication Approach
  • 1 Introduction
  • 2 Multiplication of Polynomials with Unbalanced Long Coefficients
  • 2.1 A Note About the Kronecker Trick
  • 3 Sparse Univariate Toom-Cook
  • 4 Using Toom-Cook Bivariate Multiplication
  • 4.1 Evaluation Phase
  • 4.2 Interpolation Phase
  • 5 Experimental Results
  • 6 Conclusions
  • References
  • Power Series Arithmetic with the BPAS Library
  • 1 Introduction
  • 2 Background
  • 3 The Design and Implementation of Lazy Power Series
  • 3.1 The Power Series Data Structure, Generators, and Ancestors
  • 3.2 Implementing Power Series Arithmetic
  • 4 Univariate Polynomials over Lazy Power Series
  • 5 Lazy Weierstrass Preparation
  • 6 Lazy Factorization via Hensel's Lemma
  • 7 Conclusions and Future Work

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