判别可分多项式与四元方程
Discriminantly separable polynomials and quad-equations
摘要：
我们分类的判别式可分多项式的次数为两个三个变量中的每一个，定义的一个属性，即所有的判别式作为两个变量的多项式因式分解为产品的两个多项式的一个变量。我们的分类是基于对判别式的多项式分量$P$的零点结构的研究。这种分类与二次曲线束的分类有微妙的关系。我们建立了我们的分类和分类之间的关系已建议最近由阿德勒，Bobenko和Suris的可积四方程。
英文摘要：
We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable each. Our classification is based on the study of structures of zeros of a polynomial component $P$ of a discriminant. This classification is related to the classification of pencils of conics in a delicate way. We establish a relationship between our classification and the classification of integrable quad-equations which has been suggested recently by Adler, Bobenko, and Suris.
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