Decision problem for a class of univariate Pfaffian functions

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 funct...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing Vol. 35; no. 2; pp. 207 - 232
Main Authors: Barbagallo, María Laura, Jeronimo, Gabriela, Sabia, Juan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2024
Springer Nature B.V
Subjects:
Algebra
Algorithms
Artificial Intelligence
Computation
Computer Hardware
Computer Science
Estimates
Original Paper
Partial differential equations
Polynomials
Sequences
Symbolic and Algebraic Manipulation
Theory of Computation
68W30
Pfaffian functions
14P15
Decision problem
Sturm sequences
Complexity
ISSN:0938-1279, 1432-0622
Online Access:Get full text
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Summary: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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ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-022-00545-8