This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polymial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
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Algorithms and Computation in Mathematics
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Springer-Verlag Berlin and Heidelberg GmbH & Co. K