Algebraic geometry is the study of geometric objects defined by polynomial equations, using algebraic means. Its roots go back to Descartes’ introduction of coordinates to describe points in Euclidean space and his idea of describing curves and surfaces by algebraic equations. Over the long history of the subject, both powerful general theories and detailed knowledge of many specific examples have been developed. Recently, with the development of computer algebra systems and the discovery (or rediscovery) of algorithmic approaches to many of the basic computations, the techniques of algebraic geometry have also found significant applications, for example in geometric design, combinatorics, integer programming, coding theory, and robotics. Our goal in Using Algebraic Geometry is to survey these algorithmic approaches and many of their applications.
KeywordsPrime Ideal Radical Ideal Total Degree Computer Algebra System Division Algorithm
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