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Author : Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 40,91 MB
Release : 2002
Category : Mathematics
ISBN : 0821832514
Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
Author : Teo Mora
Publisher :
Page : 759 pages
File Size : 44,15 MB
Release : 2005
Category :
ISBN : 9781107264434
Author : Teo Mora
Publisher :
Page : 786 pages
File Size : 14,62 MB
Release : 2014-05-14
Category : Equations
ISBN : 9781107266902
The second volume of a comprehensive treatise. This part focuses on Buchberger theory and its application to the algorithmic view of commutative algebra.
Author : Teo Mora
Publisher : Cambridge University Press
Page : 792 pages
File Size : 12,48 MB
Release : 2003
Category : Mathematics
ISBN : 9780521811569
This volume focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. The presentation is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in its algorithmization.
Author : Alicia Dickenstein
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 14,14 MB
Release : 2005-04-27
Category : Computers
ISBN : 3540243267
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Author : Daniel J. Bates
Publisher : SIAM
Page : 372 pages
File Size : 15,82 MB
Release : 2013-11-08
Category : Science
ISBN : 1611972698
This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.
Author : Teo Mora
Publisher : Cambridge University Press
Page : 452 pages
File Size : 29,6 MB
Release : 2003-03-27
Category : Mathematics
ISBN : 9780521811545
Computational algebra; computational number theory; commutative algebra; handbook; reference; algorithmic; modern.
Author : Teo Mora
Publisher :
Page : pages
File Size : 31,20 MB
Release : 2015
Category :
ISBN : 9781316314814
Author : Teo Mora
Publisher : Cambridge University Press
Page : 833 pages
File Size : 31,73 MB
Release : 2016-04-01
Category : Mathematics
ISBN : 1316381382
In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Author : Lynn Marecek
Publisher :
Page : pages
File Size : 33,1 MB
Release : 2020-05-06
Category :
ISBN : 9781951693848