This book provides a comprehensive treatment of Gr bner bases theory embedded in an introduction to commutative algebra from a computational point of view. The centerpiece of Gr bner bases theory is the Buchberger algorithm, which provides a common generalization of the Euclidean algorithm and the Gaussian elimination algorithm to multivariate polynomial rings. The book explains how the Buchberger algorithm and the theory surrounding it are eminently important both for the mathematical theory and for computational applications. A number of results such as optimized version of the Buchberger algorithm are presented in textbook format for the first time. This book requires no prerequisites other than the mathematical maturity of an advanced undergraduate and is therefore well suited for use as a textbook. At the same time, the comprehensive treatment makes it a valuable source of reference on Gr bner bases theory for mathematicians, computer scientists, and others. Placing a strong emphasis on algorithms and their verification, while making no sacrifices in mathematical rigor, the book spans a bridge between mathematics and computer science.
Gröbner Bases
and over one million other books are available for Amazon Kindle.
Learn more
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
First Sentence:
A mathematically rigorous definition of the number systems requires the use of axiomatic set theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
lexicographical term order, computable ring, abstract reduction relations, rational zeroes, noetherian reduction relation, different zeroes, squarefree decomposition, ideal membership test, finite generating system, total degree order, computable field, real zeroes, algebraically closed extension field, isolating intervals, multivariate polynomial rings, monic generator, normal form modulo, proper factorization, unique remainders, prime factor decomposition, commutative rings with unity, residue class rings, irreducible ideals, head coefficient, primary decomposition Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Hilbert Nullstellensatz, Zeroes of Ideals, Proof Assume, Computing Real Zeroes of Polynomial Systems, Proof Termination, Uniform Word Problems, Foundedness Properties, Squarefree Decomposition of Polynomials, Finitely Generated Algebras, Proof Suppose, Bases Corollary, Bases Exercise, Dimension of Ideals, Proof Condition, Some Special Orders, Unique Factorization Domains, Bases Lemma, Proof By Lemma, Proof Statement New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A mathematically rigorous definition of the number systems requires the use of axiomatic set theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
lexicographical term order, computable ring, abstract reduction relations, rational zeroes, noetherian reduction relation, different zeroes, squarefree decomposition, ideal membership test, finite generating system, total degree order, computable field, real zeroes, algebraically closed extension field, isolating intervals, multivariate polynomial rings, monic generator, normal form modulo, proper factorization, unique remainders, prime factor decomposition, commutative rings with unity, residue class rings, irreducible ideals, head coefficient, primary decomposition Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Hilbert Nullstellensatz, Zeroes of Ideals, Proof Assume, Computing Real Zeroes of Polynomial Systems, Proof Termination, Uniform Word Problems, Foundedness Properties, Squarefree Decomposition of Polynomials, Finitely Generated Algebras, Proof Suppose, Bases Corollary, Bases Exercise, Dimension of Ideals, Proof Condition, Some Special Orders, Unique Factorization Domains, Bases Lemma, Proof By Lemma, Proof Statement New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
See all 100 books this book cites
- Effective Methods in Algebraic Geometry (Progress in Mathematics) by T. Mora on 11 pages
- Symbolic and Algebraic Computation (Lecture Notes in Computer Science) by P. Gianni on 8 pages
- Computer Algebra (Lecture Notes in Computer Science) by Jacques Calmet on 6 pages
- Computer Algebra (Lecture Notes in Pure and Applied Mathematics) by Richard Jenks on 5 pages
- Rewriting Techniques and Applications by Author Unknown on 4 pages
See all 100 books this book cites
Books on Related Topics
(learn more)
|
Suggested Tags from Similar Products(What's this?)Be the first one to add a relevant tag (keyword that's strongly related to this product).
|
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
