实代数数的代数表达式的符号判定

Determining the Signs of Real Algebraic Numbers

将符号计算方法与数值计算方法结合起来应用于计算机代数领域，构造了一种判定实代数数的代数表达式的符号的算法，并在计算机数学系统上加以实现．算法的基本思想是对每一个实代数数α定义了一个二元组（Ｉ，ｆ（ｘ）），其中Ｉ是包含α的区间，ｆ（ｘ）是α所满足的多项式，并将代数数的运算转化为对应的二元组的运算，同时结合多项式的根的最短距离估计式，从而达到对代数数的代数表达式进行符号判定的目的．

A numerical computation method is used to get some results about symbolic computation.An algorithm is created for determining the signs of arithmetic expressions of real algebraic numbers.We use an ordered pair (I,f(x)) instead of a real algebraic number α,where I is an interval containing α and f(x) is a polynomial satisfied by α.With some skills, the computation of algebraic numbers' expression is changed into the computation of their ordered pairs.By using the estimation of the shortest distance of roots of a polynomial , the sign of this expression can be determined within finite steps.