Computations in Algebraic Geometry with Macaulay 2
Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re cently developed algorit
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Springer-Verlag Berlin Heidelberg GmbH
David Eisenbud Daniel R. Grayson Michael Stillman Bernd Sturmfels (Eds.)
Computations in Algebraic Geometry with Macaulay 2
,
Springer
Editors David Eisenbud
Daniel R. Grayson
Mathematical Sciences Research Institute 1000 Centennial Drive Berkeley, CA 94720, USA e-mail: [email protected]
University of Illinois at Urbana-Champaign Department of Mathematics Urbana, IL 61801, USA e-mail: [email protected]
Michael Stillman
Bernd Sturmfels
Cornell University Department of Mathematics Ithaca, NY 14853, USA e-mail: [email protected]
University of California Department of Mathematics Berkeley, CA 94720, USA e-mail: [email protected]
Mathematics Subject Classification (2000): 13-04, 13P, 14-04, 14Q, 16Z05, 68W30, nY, 12Y05, 14P, 12DI0, 14M15, 14N15
Library of Congress Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Computations in algebraic geometry with macaulay 21 David Eisenbud ... (ed.). - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002 (Algorithms and computation in mathematics: Vol. 8)
ISBN 978-3-642-07592-6 ISBN 978-3-662-04851-1 (eBook) DOl 10.1007/978-3-662-04851-1 This work is subject to copyright. All rights are reserved. whether the whole or part of the material is concerned. specifically the rights of translation. reprinting. reuse of illustrations. recitation. broadcasting. reproduction on microfilm or in any other way. and storage in data banks. Duplication of this publication or parts thereofis permitted only under the provisions of the German Copyright Law of September 9. 1965. in its current version. and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.
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Preface
Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Recently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorithmic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solving problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield ne
