Computing In Algebraic Geometry

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Computing In Algebraic Geometry

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Author : Wolfram Decker
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-01

Computing In Algebraic Geometry written by Wolfram Decker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-01 with Mathematics categories.

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

A First Course In Computational Algebraic Geometry

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Author : Wolfram Decker
language : en
Publisher:
Release Date : 2013

A First Course In Computational Algebraic Geometry written by Wolfram Decker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Curves, Algebraic categories.

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

Computations In Algebraic Geometry With Macaulay 2

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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Computations In Algebraic Geometry With Macaulay 2 written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

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 algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all.

Computer Algebra Handbook

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Author : Johannes Grabmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2003

Computer Algebra Handbook written by Johannes Grabmeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Computers categories.

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Applications Of Algebraic Geometry To Coding Theory Physics And Computation

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Author : Ciro Ciliberto
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-31

Applications Of Algebraic Geometry To Coding Theory Physics And Computation written by Ciro Ciliberto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-31 with Computers categories.

Proceedings of the NATO Advanced Research Workshop, held in Eilat, Israel, from 25th February to 1st March 2001

Computational Commutative Algebra 1

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Author : Martin Kreuzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-05

Computational Commutative Algebra 1 written by Martin Kreuzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-05 with Mathematics categories.

Hofstadter’s Law: It always takes longer than you think it will take, even if you take into account Hofstadter’s Law. (Douglas R. Hofstadter) Dear Reader, what you are holding in your hands now is for youabook. But for us, for our families and friends, it has been known as the book over the last three years. Three years of intense work just to ?ll three centimeters of your bookshelf! This amounts to about one centimeter per year, or roughly two-?fths of an inch per year if you are non-metric. Clearly we had ample opportunity to experience the full force of Hofstadter’s Law. Writing a book about Computational Commutative Algebra is not - like computing a Gr ̈ obner basis: you need unshakeable faith to believe that the project will ever end; likewise, you must trust in the Noetherianity of polynomial rings to believe that Buchberger’s Algorithm will ever terminate. Naturally, we hope that the ?nal result proves our e?orts worthwhile. This is a book for learning, teaching, reading, and, most of all, enjoying the topic at hand.

A Singular Introduction To Commutative Algebra

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Author : Gert-Martin Greuel
language : en
Publisher:
Release Date : 2002-08-07

A Singular Introduction To Commutative Algebra written by Gert-Martin Greuel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-07 with categories.

This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book's most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

Ideals Varieties And Algorithms

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Author : David Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Ideals Varieties And Algorithms written by David Cox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing a new edition of Ideals, Varieties and Algorithms the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple , Mathematica and REDUCE.

Computational Commutative And Non Commutative Algebraic Geometry

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Author : Svetlana Cojocaru
language : en
Publisher: IOS Press
Release Date : 2005

Computational Commutative And Non Commutative Algebraic Geometry written by Svetlana Cojocaru and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Electronic books categories.

Rational Algebraic Curves

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Author : J. Rafael Sendra
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-19

Rational Algebraic Curves written by J. Rafael Sendra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-19 with Mathematics categories.

The central problem considered in this introduction for graduate students 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: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.