A numerical description of an algebraic subvariety of projective space is given by a general linear section, called a witness set. For a subvariety of a product of projective spaces (a multiprojective variety), the corresponding numerical description is given by a witness collection, whose structure is more involved. We build on recent work to develop a toolkit for the numerical manipulation of multiprojective varieties that operates on witness collections, and use this toolkit in an algorithm for numerical irreducible decomposition of multiprojective varieties. The toolkit and decomposition algorithm are illustrated throughout in a series of examples.

中文翻译：

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多投影变体的数值工具包

射影空间的代数子变体的数值描述由称为见证集的一般线性部分给出。对于射影空间乘积的子变体（多射影变体），对应的数值描述由结构更复杂的witness collection给出。我们在最近的工作的基础上开发了一个工具包，用于对见证集合进行操作的多投影变体的数值操作，并将该工具包用于多投影变体的数值不可约分解的算法中。工具包和分解算法在整个示例中都有说明。