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.

我们解决了涉及从 1 阶固定 Pfaffian 函数构造的单变量函数的句子的决策问题。我们提出了一种新的符号程序，该程序基于合适的 Sturm 序列的计算以可计算的复杂性解决了这个问题。对于一般的 Pfaffian 函数，我们假设存在一个预言来确定该类的函数在实代数数处所取的符号。作为一个副产品，我们基于比以前更简单的技术，获得了一种新的无预言机有效算法来解决单变量 E 多项式的相同问题，并将其应用于解决多变量设置中的类似决策问题。最后，我们为 E 多项式的零点引入了 Thom 编码的概念，并描述了一种计算它们的算法。