The computational complexity of the Chow form
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Abstract
We present a bounded probability algorithm for the computation of the Chow forms of the equidimensional components of an algebraic variety. Its complexity is polynomial in the length and in the geometric degree of the input equation system defining the variety. In particular, it provides an alternative algorithm for the equidimensional decomposition of a variety. As an application we obtain an algorithm for the computation of a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As a further application, we derive an algorithm for the computation of the (unique) solution of a generic over-determined equation system.
Cite
@article{arxiv.math/0210009,
title = {The computational complexity of the Chow form},
author = {Gabriela Jeronimo and Teresa Krick and Juan Sabia and Martin Sombra},
journal= {arXiv preprint arXiv:math/0210009},
year = {2007}
}
Comments
60 pages, Latex2e