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• catalog abstract ""Algebraic geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?" "The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory." "The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960s. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have led to some interesting applications - for example, in robotics and in geometric theorem proving."--Jacket.".
• catalog contributor b10145273.
• catalog contributor b10145274.
• catalog contributor b10145275.
• catalog created "1996.".
• catalog date "1996".
• catalog date "1996.".
• catalog dateCopyrighted "1996.".
• catalog description ""Algebraic geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?" "The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory." "The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960s. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have led to some interesting applications - for example, in robotics and in geometric theorem proving."--Jacket.".
• catalog description "1. Geometry, algebra, and algorithms -- 2. Groebner bases -- 3. Elimination theory -- 4. The algebra-geometry dictionary -- 5. Polynomial and rational functions on a variety -- 6. Robotics and automatic geometric theorem proving -- 7. Invariant theory of finite groups -- 8. Projective algebraic geometry -- 9. The dimension of a variety -- Appendixes: -- A. Some concepts from algebra -- B. Pseudocode -- C. Computer algebra systems -- D. Independent projects.".
• catalog description "Includes bibliographical references (p.523-526) and index.".
• catalog extent "xiii, 536 p. :".
• catalog identifier "0387946802 (alk. paper)".
• catalog isPartOf "Undergraduate texts in mathematics".
• catalog issued "1996".
• catalog issued "1996.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog subject "516.3/5 20".
• catalog subject "Commutative algebra Data processing.".
• catalog subject "Geometry, Algebraic Data processing.".
• catalog subject "QA564 .C688 1996".
• catalog tableOfContents "1. Geometry, algebra, and algorithms -- 2. Groebner bases -- 3. Elimination theory -- 4. The algebra-geometry dictionary -- 5. Polynomial and rational functions on a variety -- 6. Robotics and automatic geometric theorem proving -- 7. Invariant theory of finite groups -- 8. Projective algebraic geometry -- 9. The dimension of a variety -- Appendixes: -- A. Some concepts from algebra -- B. Pseudocode -- C. Computer algebra systems -- D. Independent projects.".
• catalog title "Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra / David Cox, John Little, Donal O'Shea.".
• catalog type "text".