Abstract In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective witness sets which encode the multidegree information of an irreducible multiprojective variety. Our main results generalise the regeneration solving procedure, a trace test, and numerical irreducible decomposition to the multiprojective case. Examples are included to demonstrate this new approach.

中文翻译：

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多投影见证集和踪迹检验

摘要 在数值代数几何领域，多项式方程组的正维解集是用见证集来描述的。在本文中，我们定义了多投影见证集，它对不可约多投影多样性的多度信息进行编码。我们的主要结果将再生求解程序、迹测试和数值不可约分解推广到多投影情况。包括示例以演示这种新方法。