It is proved that the field of complex algebraic numbers has an isomorphic presentation computable in polynomial time. A similar fact is proved for the ordered field of real algebraic numbers. The constructed polynomially computable presentations are based on a natural presentation of algebraic numbers by rational polynomials. Also new algorithms for computing values of polynomials on algebraic numbers and for solving equations in one variable with algebraic coefficients are presented.

中文翻译：

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多项式时间内可计算的代数数域。一世

证明复代数数域具有多项式时间内可计算的同构表示。对实代数数的有序域也证明了类似的事实。构造的多项式可计算表示基于代数数通过有理多项式的自然表示。还提出了用于计算代数数多项式值和求解具有代数系数的一个变量中的方程的新算法。