Decision problem for a class of univariate Pfaffian functions
Algebraic Geometry
2019-05-29 v2
Abstract
We address the decision problem for sentences involving univariate functions constructed from a fixed Pfaffian function of order . We present a new symbolic procedure solving this problem with a computable complexity based on the computation of suitable Sturm sequences. For a general Pfaffian function, we assume the existence of an oracle to determine the sign that a function of the class takes at a real algebraic number. For E-polynomials, we give an effective algorithm solving the problem without using oracles and apply it to solve a similar decision problem in the multivariate setting. Finally, we introduce a notion of Thom encoding for zeros of an E-polynomial and describe an algorithm for their computation.
Cite
@article{arxiv.1905.10882,
title = {Decision problem for a class of univariate Pfaffian functions},
author = {Maria Laura Barbagallo and Gabriela Jeronimo and Juan Sabia},
journal= {arXiv preprint arXiv:1905.10882},
year = {2019}
}