Computer Algebra and Polynomials: Applications of Algebra and Number Theory

✍ Scribed by Jaime Gutierrez, Josef Schicho, Martin Weimann (eds.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 222
• Series: Lecture Notes in Computer Science 8942 Theoretical Computer Science and General Issues
• Edition: 1
• Category: Library

✦ Synopsis

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life.

This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects.

The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

✦ Table of Contents

Front Matter....Pages I-IX
An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics....Pages 1-29
Moving Curve Ideals of Rational Plane Parametrizations....Pages 30-49
Survey on Counting Special Types of Polynomials....Pages 50-75
Orbit Closures of Linear Algebraic Groups....Pages 76-93
Symbolic Solutions of First-Order Algebraic ODEs....Pages 94-104
Ore Polynomials in Sage....Pages 105-125
Giac and GeoGebra – Improved Gröbner Basis Computations....Pages 126-138
Polar Varieties Revisited....Pages 139-150
A Note on a Problem Proposed by Kim and Lisonek....Pages 151-156
Fast Algorithms for Refined Parameterized Telescoping in Difference Fields....Pages 157-191
Some Results on the Surjectivity of Surface Parametrizations....Pages 192-203
Rational Normal Curves as Set-Theoretic Complete Intersections of Quadrics....Pages 204-212
Back Matter....Pages 213-213

✦ Subjects

Symbolic and Algebraic Manipulation; Numeric Computing; Algebra; Algorithm Analysis and Problem Complexity