Rational Algebraic Curves: A Computer Algebra Approach

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The central problem considered in this book is the determination of rational parametrizability of an algebraic curve, and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve, i.e. its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. Various optimality criteria for rational parametrizations of algebraic curves are discussed. This book is mainly intended for graduate students and researchers in constructive algebraic curve geometry.

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Algorithms and Computation in Mathematics • Volume 22 Editors Arjeh M. Cohen Henri Cohen David Eisenbud Michael F. Singer Bernd Sturmfels J. Rafael Sendra Franz Winkler Sonia Pérez-Díaz Rational Algebraic Curves A Computer Algebra Approach With 24 Figures and 2 Tables Authors J. Rafael Sendra Departamento de Matemáticas Universidad de Alcalá 28871 Alcalá de Henares, Madrid Spain E-mail: [email protected] Franz Winkler RISC-Linz J. Kepler Universität Linz 4040 Linz Austria E-mail: [email protected] Sonia Pérez-Díaz Departamento de Matemáticas Universidad de Alcalá 28871 Alcalá de Henares, Madrid Spain E-mail: [email protected] Library of Congress Control Number: 2007932190 Mathematics Subject Classification (2000): 14H50, 14M20, 14Q05, 68W30 ISSN 1431-1550 ISBN 978-3-540-73724-7 Springer Berl
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