Algebraic geometry, central to pure mathematics, has important
applications in such fields as engineering, computer science,
statistics and computational biology, which exploit the
computational algorithms that the theory provides. Users get the
full benefit, however, when they know something of the underlying
theory, as well as basic procedures and facts. This book is a
systematic introduction to the central concepts of algebraic
geometry most useful for computation. Written for advanced
undergraduate and graduate students in mathematics and researchers
in application areas, it focuses on specific examples and restricts
development of formalism to what is needed to address these
examples. In particular, it introduces the notion of Grobner bases
early on and develops algorithms for almost everything covered. It
is based on courses given over the past five years in a large
interdisciplinary programme in computational algebraic geometry at
Rice University, spanning mathematics, computer science,
biomathematics and bioinformatics.
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