English

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 11. 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.

Keywords

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}
}
R2 v1 2026-06-23T09:25:06.761Z