Computing in Algebraic Geometry: A Quick Start using SINGULARThis 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. |
Contents
Introductory Remarks on Computer Algebra | 1 |
Basic Computational Problems and Their Solution | 37 |
An Introduction to SINGULAR 63 | 62 |
Practical Session I | 125 |
Homological Algebra I | 129 |
Homological Algebra II | 145 |
Practical Session III 167 | 166 |
Primary Decomposition and Normalization | 201 |
Practical Session IV 217 | 216 |
Computing in Local Rings | 235 |
Practical Session V | 271 |
| 311 | |
Other editions - View all
Computing in Algebraic Geometry: A Quick Start using SINGULAR Wolfram Decker,Christoph Lossen Limited preview - 2006 |
Computing in Algebraic Geometry: A Quick Start using SINGULAR Wolfram Decker,Christoph Lossen No preview available - 2006 |
Computing in Algebraic Geometry: A Quick Start using SINGULAR Wolfram Decker,Christoph Lossen No preview available - 2010 |
Common terms and phrases
active ring algebraic geometry algebraic set An(K apply associated primes bases Buchberger's algorithm codimension coefficient field Cohen-Macaulay components computer algebra Decker and Schreyer defined degree dimension Eisenbud elements elimination entry equations Example Exercise F₁ factorization fiber finitely generated graded flat free module free resolution given global monomial order Greuel and Pfister Gröbner basis Hamburger-Noether Hilbert function Hilbert series homogeneous homomorphism ideal of K[x implemented integer intersection irreducible kernel Koszul Lecture Let F lexicographic Gröbner basis lexicographic order matrix maximal ideal minimal free resolution monomial order multiplicity name space Noetherian Noetherian ring nonzero order on K[x output poly f polynomial f polynomial ring power series primary decomposition prime ideals problem procedure quotient ring R-module Remark respect result ring map Section setring SINGULAR command SINGULAR session solutions standard expression submodule subset syzygies Theorem variables vector zero zero-dimensional