Software Engineering and Complexity in Effective Algebraic Geometry

Details Software Engineering and Complexity in Effective Algebraic Geometry Software Engineering and Complexity in Effective Algebraic Geometry

2011-10-13

arxiv.org/abs/1110.3030v3

Computer Science

Computational Complexity

70 pages. arXiv admin note: substantial text overlap with arXiv:1201.4344

Scientific paper

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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