An Introduction to Grobner Bases
William Wells Adams ¡ Philippe Loustaunau
āĻāĻžāĻ¨ā§ ā§§ā§¯ā§¯ā§Ē ¡ American Mathematical Soc.
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As the primary tool for doing explicit computations in polynomial rings in many variables, GrÃļbner 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 GrÃļbner bases and their applications. Adams and Loustaunau cover the following topics: the theory and construction of GrÃļbner bases for polynomials with coefficients in a field, applications of GrÃļbner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and GrÃļbner bases in modules, and the theory of GrÃļbner bases for polynomials with coefficients in rings. With over 120 worked 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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