Software Engineering and Complexity in Effective Algebraic Geometry

Joos Heintz; Bart Kuijpers; Andres Rojas Paredes

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arXiv · 1110.3030

Software Engineering and Complexity in Effective Algebraic Geometry

Joos Heintz·Bart Kuijpers·Andres Rojas Paredes

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Abstract

We introduce the notion of a robust parameterized arithmetic circuit for the evaluation of algebraic families of multivariate polynomials. Based on this notion, we present a computation model, adapted to Scientific Computing, which captures all known branching parsimonious symbolic algorithms in effective Algebraic Geometry. We justify this model by arguments from Software Engineering. Finally we exhibit a class of simple elimination problems of effective Algebraic Geometry which require exponential time to be solved by branching parsimonious algorithms of our computation model.

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Joos Heintz, Bart Kuijpers, Andres Rojas Paredes. 2012-04-25. Software Engineering and Complexity in Effective Algebraic Geometry. https://arxiv.org/abs/1110.3030

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