We study questions of existence and uniqueness of quadrature domains using computational tools from real algebraic geometry. These problems are transformed into questions about the number of solutions to an associated real semi-algebraic system, which is analyzed using the method of real comprehensive triangular decomposition.

中文翻译：

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关于正交域的唯一性问题

我们使用来自实际代数几何的计算工具研究正交域的存在性和唯一性问题。这些问题转化为有关关联的实际半代数系统的解数的问题，使用实数全面三角分解的方法对其进行了分析。