Homogeneous binary function products are often encountered in the sub-universes modeled by databases, from genealogical trees to sports, from education to healthcare, etc. Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility. The (Elementary) Mathematical Data Model provides 18 dyadic-type homogeneous binary function product constraint types. MatBase, an intelligent data and knowledge base management system prototype, allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them. This paper describes the algorithms that MatBase uses for enforcing all these 18 homogeneous binary function product constraint types, which may also be used by developers not having access to MatBase.

翻译：齐次二元函数乘积常见于由数据库建模的子宇宙中，从族谱树到体育赛事，从教育到医疗保健等领域。它们的性质必须由管理此类数据的软件应用发现并强制执行，以保证数据的合理性。（初等）数学数据模型提供了18种二项型齐次二元函数乘积约束类型。智能数据与知识库管理系统原型MatBase允许数据库设计者仅通过点击对应复选框来声明这些约束，并自动生成强制执行代码。本文描述了MatBase用于强制执行全部18种齐次二元函数乘积约束类型的算法，这些算法也可供未使用MatBase的开发者参考使用。