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
| 1 | |
1 | 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 apply associated primes bases Betti Buchberger's algorithm codimension coefficient field Cohen-Macaulay components computer algebra Decker and Schreyer defined degree dimension Eisenbud elements elimination equations Example Exercise factorization finitely generated graded flat free module free resolution given global monomial order Greuel and Pfister Gröbner basis groebner Hamburger-Noether Hilbert function Hilbert series homogeneous homomorphism ideal of K[x imap implemented integer intersection irreducible Koszul Lecture lexicographic Gröbner basis lexicographic order matrix maximal ideal minimal free resolution monomial order name space Noetherian Noetherian ring nonzero order on K[x output poly f polynomial ring power series primary decomposition prime ideals problem procedure quotient ring R-module reduced Remark respect result ring map Section setring SINGULAR command SINGULAR session solutions standard expression submodule syzygies Theorem timer-aa Tjurina variables vector zero zero-dimensional