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：齐次二元函数乘积在数据库建模的子宇宙中频繁出现，从家谱树到体育领域，从教育到医疗保健等。其属性必须由管理此类数据的软件应用程序发现并强制实施，以保证数据合理性。（初等）数学数据模型提供了18种二元型齐次函数乘积约束类型。MatBase是一种智能数据与知识库管理系统原型，允许数据库设计者仅通过勾选对应复选框即可简单声明这些约束，并自动生成强制实施代码。本文描述了MatBase用于强制实施全部18种齐次函数乘积约束类型的算法，这些算法也可供无法访问MatBase的开发者使用。