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arXiv · 1905.10882

Decision problem for a class of univariate Pfaffian functions

Maria Laura Barbagallo·Gabriela Jeronimo·Juan Sabia
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Abstract

We address the decision problem for sentences involving univariate functions constructed from a fixed Pfaffian function of order $1$. 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.

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Maria Laura Barbagallo, Gabriela Jeronimo, Juan Sabia. 2019-05-26. Decision problem for a class of univariate Pfaffian functions. https://arxiv.org/abs/1905.10882

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