As the primary tool for doing explicit computations in polynomial rings in many variables, Gröbner bases are an important component of all computer algebra systems. They are also important in computational commutative algebra and algebraic geometry. This book provides a leisurely and fairly comprehensive introduction to Gröbner bases and their applications. Adams and Loustaunau cover the following topics: the theory and construction of Gröbner bases for polynomials with coefficients in a field, applications of Gröbner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and Gröbner bases in modules, and the theory of Gröbner bases for polynomials with coefficients in rings. With over 120 worked out examples and 200 exercises, this book is aimed at advanced undergraduate and graduate students. It would be suitable as a supplement to a course in commutative algebra or as a textbook for a course in computer algebra or computational commutative algebra. This book would also be appropriate for students of computer science and engineering who have some acquaintance with modern algebra.
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Editorial Reviews
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"A very carefully crafted introduction to the theory and some of the applications of Grbner bases ... contains a wealth of illustrative examples and a wide variety of useful exercises, the discussion is everywhere well-motivated, and further developments and important issues are well sign-posted ... has many solid virtues and is an ideal text for beginners in the subject ... certainly an excellent text." -- Bulletin of the London Mathematical Society
"Clearly written and has a great collection of exercises. It is the best textbook at this level ... recommend it to colleagues -- O. M. G. Jenda, Auburn University
"The book is self-contained and does not assume an extensive knowledge of algebra. The style of the book is as elementary as the subject allows. All chapters are enriched by a large number of examples and exercises, the total number is over 120 worked-out examples and over 200 exercises. All these features make it an excellent textbook for a first course in the theory of Grbner bases for advanced undergraduate or beginning graduate students. The reviewer also warmly recommends the book for independent study by students and researchers looking for a theoretical introduction to Grbner bases." -- Mathematical Reviews
"The rich set of applications and exercises concentrates on pure higher algebra ... The book is intended as a textbook for advanced undergraduates." -- Zentralblatt fr Mathematik
"Clearly written and has a great collection of exercises. It is the best textbook at this level ... recommend it to colleagues -- O. M. G. Jenda, Auburn University
"The book is self-contained and does not assume an extensive knowledge of algebra. The style of the book is as elementary as the subject allows. All chapters are enriched by a large number of examples and exercises, the total number is over 120 worked-out examples and over 200 exercises. All these features make it an excellent textbook for a first course in the theory of Grbner bases for advanced undergraduate or beginning graduate students. The reviewer also warmly recommends the book for independent study by students and researchers looking for a theoretical introduction to Grbner bases." -- Mathematical Reviews
"The rich set of applications and exercises concentrates on pure higher algebra ... The book is intended as a textbook for advanced undergraduates." -- Zentralblatt fr Mathematik
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Inside This Book
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In this chapter we give a leisurely introduction to the theory of Gröbner bases. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
deglex term, using deglex, homogeneous generating set, lex term order, same syzygy, whose leading power product, homogeneous syzygy, leading term ideal, syzygy module, only irreducible factor, saturated subsets, given term order, computing generators, compute generators, elimination order, computing syzygies, leading power products, lex order, terra order, irreducible ideals, saturated set, using lex, finite generating set, primary decomposition, ideal quotient Key Phrases - Capitalized Phrases (CAPs): (learn more)
Buchberger's Algorithm, Hilbert Basis Theorem, Computer Algebra System, Prove Theorem, Euclidean Algorithm, Prove Proposition, Prove Lemma, Buchberger's Theorem, Consider the Z-algebra, Gröbner Basis Algorithm, Prove Corollary, Xij Xij New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we give a leisurely introduction to the theory of Gröbner bases. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
deglex term, using deglex, homogeneous generating set, lex term order, same syzygy, whose leading power product, homogeneous syzygy, leading term ideal, syzygy module, only irreducible factor, saturated subsets, given term order, computing generators, compute generators, elimination order, computing syzygies, leading power products, lex order, terra order, irreducible ideals, saturated set, using lex, finite generating set, primary decomposition, ideal quotient Key Phrases - Capitalized Phrases (CAPs): (learn more)
Buchberger's Algorithm, Hilbert Basis Theorem, Computer Algebra System, Prove Theorem, Euclidean Algorithm, Prove Proposition, Prove Lemma, Buchberger's Theorem, Consider the Z-algebra, Gröbner Basis Algorithm, Prove Corollary, Xij Xij 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 12
books:
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2
books
cite this book:
- Symbolic and Algebraic Computation (Lecture Notes in Computer Science) by P. Gianni in Back Matter
- Introduction To Commutative Algebra by Michael Atiyah in Back Matter
- Algorithmic Algebra (Monographs in Computer Science) by Bhubaneswar Mishra in Back Matter
- Topics in Algebra by I. N. Herstein in Back Matter
- A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics) by H. Cohen in Back Matter
See all 12 books this book cites
- A First Course in Abstract Algebra (6th Edition) by John B. Fraleigh in Back Matter
- Advances in Robot Kinematics: Theory and Applications by Jadran Lenarcic on page 472
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