On enforcing function diagram commutativity and anti-commutativity constraints in MatBase

Presented are algorithms for enforcing function diagram commutativity and anti-commutativity database constraints, using the database software application constraint-driven design and development methodology, in the realm of the (Elementary) Mathematical Data Model ((E)MDM). MatBase, an intelligent data and knowledge management system prototype mainly based on the (E)MDM, uses these algorithms to automatically generate corresponding code in both its versions (i.e., the MS Access and the .NET and SQL Server ones). Of course, any software developer may also use these algorithms manually. The paper also discusses the code generated to enforce two such constraints from a Geography database.