We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational axiomatisation for the class of algebras representable by partial functions. As a corollary, the same equations axiomatise the algebras representable by injective partial functions. For complete representations, we show that a representation is meet complete if and only if it is join complete. Then we show that the class of completely representable algebras is precisely the class of atomic and representable algebras. As a corollary, the same properties axiomatise the class of algebras completely representable by injective partial functions. The universal-existential-universal axiomatisation this yields for these complete representation classes is the simplest possible, in the sense that no existential-universal-existential axiomatisation exists.

我们研究了具有相对补和域限制特征的偏函数代数的表示和完全表示类。我们提供并证明了由偏函数表示的代数类的有限方程公理化的正确性。作为推论，相同的方程公理化了由内射偏函数表示的代数。对于完全表示，我们证明一个表示是满足完全的当且仅当它是连接完全的。然后我们证明完全可表示代数类正是原子可表示代数类。作为推论，相同的性质公理化了完全可以用单射偏函数表示的代数类。