Computer Algebra and Polynomials : Applications of Algebra and Number Theory / edited by Jaime Gutierrez, Josef Schicho, Martin Weimann.

Format:

Book

Contributor:

Gutiérrez Vallejo, Jaime, editor.

Schicho, Josef, 1964- editor.

Weimann, Martin, editor.

SpringerLink (Online service)

Series:

Computer Science (Springer-11645)

LNCS sublibrary. Theoretical computer science and general issues ; SL 1, 8942.

Theoretical Computer Science and General Issues ; 8942

Language:

English

Subjects (All):

Computer science--Mathematics.

Computer science.

Numerical analysis.

Algebra.

Algorithms.

Symbolic and Algebraic Manipulation.

Numeric Computing.

Algorithm Analysis and Problem Complexity.

Local Subjects:

Symbolic and Algebraic Manipulation.

Numeric Computing.

Algebra.

Algorithm Analysis and Problem Complexity.

Physical Description:

1 online resource (IX, 213 pages) : 29 illustrations.

Edition:

First edition 2015.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

System Details:

text file PDF

Summary:

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, et cetera 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.

Contents:

An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics

Moving Curve Ideals of Rational Plane Parametrizations

Survey on Counting Special Types of Polynomials

Orbit Closures of Linear Algebraic Groups

Symbolic Solutions of First-Order Algebraic ODEs

Ore Polynomials in Sage

Giac and GeoGebra - Improved Gröbner Basis Computations

Polar Varieties Revisited

A Note on a Problem Proposed by Kim and Lisonek

Fast Algorithms for Refined Parameterized Telescoping in Difference Fields

Some Results on the Surjectivity of Surface Parametrizations

Rational Normal Curves as Set-Theoretic Complete Intersections of Quadrics.

Other Format:

Printed edition:

ISBN:

978-3-319-15081-9

9783319150819

Access Restriction:

Restricted for use by site license.