Computational Commutative Algebra 1Hofstadter’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. |
Contents
Foreword | 1 |
Foundations | 15 |
Gröbner Bases | 85 |
First Applications | 145 |
A How to Get Started with CoCoA 275 | 274 |
B How to Program CoCoA | 283 |
A Potpourri of CoCoA Programs 293 | 292 |
Hints for Selected Exercises | 305 |
Bibliography | 313 |
Other editions - View all
Computational Commutative Algebra 2, Volume 1 Martin Kreuzer,Lorenzo Robbiano No preview available - 2005 |
Common terms and phrases
affine K-algebra Apply your function Buchberger's Algorithm called CoCoA function CoCoA program colon ideal Commutative Algebra Computational Commutative Algebra conditions are equivalent consider Corollary defined Definition DegRevLex denoted Division Algorithm element elimination ordering EndDefine example Exercise exists field finitely given Gröbner basis Hilbert's Nullstellensatz Hint homogeneous implies indeterminates integer integral domain irreducible isomorphism K-algebra K-algebra homomorphism leading term Lemma let f let G linear LT(M m₁ matrix maximal ideals minimal polynomial module ordering module term ordering monoid ordering monomial multiple non-zero ordering on Tn P-linear map P-submodule of Pr polynomial f polynomial ring portfolio Pr/M principal ideal Proof Proposition prove R-module radical ideal reduced Gröbner representation residue class respect satisfies sequence Show step submodule subset surjective Syz(G Syz(LM(G syzygy syzygy module t₁ Tn e1 tuple Tutorial unique vectors Write a CoCoA zero zero-dimensional