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. As a by-product, we obtain a new oracle-free effective algorithm solving the same problem for univariate E-polynomials based on techniques that are simpler than the previous ones, and we 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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Partially supported by the following Grants: PIP 11220130100527CO (CONICET), UBACYT 20020160100039BA (2017-2020) and UBACYT 20020190100116BA (2020-2022).
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Barbagallo, M.L., Jeronimo, G. & Sabia, J. Decision problem for a class of univariate Pfaffian functions. AAECC 35, 207–232 (2024). https://doi.org/10.1007/s00200-022-00545-8
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DOI: https://doi.org/10.1007/s00200-022-00545-8