English

Software Engineering and Complexity in Effective Algebraic Geometry

Computational Complexity 2012-04-26 v3

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.

Keywords

Cite

@article{arxiv.1110.3030,
  title  = {Software Engineering and Complexity in Effective Algebraic Geometry},
  author = {Joos Heintz and Bart Kuijpers and Andres Rojas Paredes},
  journal= {arXiv preprint arXiv:1110.3030},
  year   = {2012}
}

Comments

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

R2 v1 2026-06-21T19:19:56.154Z