Computing In Algebraic Geometry


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Computing in Algebraic Geometry


Computing in Algebraic Geometry

Author: Wolfram Decker

language: en

Publisher: Springer Science & Business Media

Release Date: 2006-05-01


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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.

Computational Algebraic Geometry


Computational Algebraic Geometry

Author: Hal Schenck

language: en

Publisher: Cambridge University Press

Release Date: 2003-10-06


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The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).

A First Course in Computational Algebraic Geometry


A First Course in Computational Algebraic Geometry

Author: Wolfram Decker

language: en

Publisher: Cambridge University Press

Release Date: 2013-02-07


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