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Editorial Reviews
From the reviews:
"Four years ago the authors published the first volume of a projected series about computational commutative algebra a ] . Now they have gifted us with the second volume a ] . In this second volume the authors continue with the same style, as the first, an almost humorous one. a ] It was a pleasure to review this nice book a ] ." (Paulo F. Machado, Mathematical Reviews, Issue 2006 h)
"The book under review is the second volume of the authorsa (TM) a ~Computational commutative algebraa (TM). a ] the book altogether covers on its 586 pages a wealth of interesting material with several unexpected applications. a ] an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications." (Peter Schenzel, Zentralblatt MATH, Vol. 1090 (16), 2006)
Product Description
This book is the natural continuation of Computational Commutative Algebra 1 with some twists. The main part of this book is a breathtaking passeggiata through the computational domains of graded rings and modules and their Hilbert functions. Besides Gröbner bases, we encounter Hilbert bases, border bases, SAGBI bases, and even SuperG bases. The tutorials traverse areas ranging from algebraic geometry and combinatorics to photogrammetry, magic squares, coding theory, statistics, and automatic theorem proving. Whereas in the first volume gardening and chess playing were not treated, in this volume they are. This is a book for learning, teaching, reading, and most of all, enjoying the topic at hand. The theories it describes can be applied to anything from children's toys to oil production.
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minimal homogeneous presentation, apply your function, thesis polynomial, minimal homogeneous system, minimal homogeneous generators, minimal monomial generators, module terns, affine point set, delete their entries, homogeneous linear change, minimal graded free resolution, monomial system, residue class ideal, proper homogeneous ideal, graded subinodule, monoid orderings, finite dimensional homogeneous components, standard graded, pure binomials, graded free resolutions, whose residue classes form, toric ideal, subalgebra analog, finite homogeneous system, monomial ideal Key Phrases - Capitalized Phrases (CAPs): (learn more)
Computational Commutative Algebra, Basis Theorem, David Hilbert, Green's Reduction Theorem, Z-graded K-algebras, Compute the S-vector, Hilbert's Nullstellensatz, Krull's Intersection Theorem, Therefore Proposition, Classical Hilbert Numerator Algorithm, Hilbert Finictions, Albrecht Dürer, Basis Criterion, Gotzmann's Persistence Theorem, Homogeneous Prime Avoidance, Mark Green, Mullah Nasrudin, Running One, The Iloniogeneous Case New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
- Commutative Algebra: Geometric, Homological, Combinatorial and Computational Aspects (Lecture Notes in Pure and Applied Mathematics) by Alberto Corso in Back Matter
- Commutative Algebra (London Mathematical Society Lecture Note Series) by J. T. Knight on page 206
- Computers and Mathematics by Erich Kaltofen in Back Matter
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