利用赋值映射构造隐函数
Constructing elusive functions with help of evaluation mappings
摘要：
我们开发了一种方法来构造难以捉摸的功能，使用交换代数和代数几何的技术。这种方法的关键概念是难以捉摸的子集和评估映射。为了构造多项式映射象外的具体点，我们还结合代数数域理论发展了有效消元理论。使用所开发的方法，对于$F = C \text{or} F = R$，我们构造了$(s,r)$ -难以捉摸的功能，其单项系数是代数数，这给出了大电路尺寸的代数数系数的多项式的例子。
英文摘要：
We develop a method to construct elusive functions using techniques of commutative algebra and algebraic geometry. The key notions of this method are elusive subsets and evaluation mappings. We also develop the effective elimination theory combined with algebraic number field theory in order to construct concrete points outside the image of a polynomial mapping. Using the developed methods, for $F = C \text{or} F = R$, we construct examples of $(s,r)$-elusive functions whose monomial coefficients are algebraic numbers, which give polynomials with algebraic number coefficients of large circuit size.
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