Effective Polynomial Computation

R E Zippel

ISBN 10: 0792393759 / ISBN 13: 9780792393757

Edité par Springer Us Jul 1993, 1993

A propos de cet article

Neuware - Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

N° de réf. du vendeur 9780792393757

Détails bibliographiques

• Titre: Effective Polynomial Computation
• Éditeur: Springer Us Jul 1993
• Date de parution: 1993
• Langue: anglais
• ISBN à 10 chiffres: 0792393759
• ISBN à 13 chiffres: 9780792393757
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 234 L x 156 H x 20 P (en millimètres) 234 millimètres de largeur par 156 millimètres de hauteur par 20 millimètres de profondeur
• Poids: 735 grammes

A propos de ce titre

Synopsis

Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained.
Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth.
Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers).
Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.