Inheritance

Recall that we need to implement algebraic structures like: ring, commutative ring, euclidean domain, field, ... Moreover we want to say that an euclidean domain is a commutative ring. Hence we want INHERITANCE BETWEEN INTERFACES. Of course we need also INHERITANCE BETWEEN CONCRETE CLASSES. For instance:

• A prime finite field $\mbox{${\mathbb Z}$}$/p$\mbox{${\mathbb Z}$}$ is a particular ring of modular integers (whose characteristic is a prime). Hence its implementation should inherit from that of the modular integer ring $\mbox{${\mathbb Z}$}$/m$\mbox{${\mathbb Z}$}$ (where m is not necessarily a prime).
• A multivariate polynomial ring R[x₁, x₂,..., x_n] is a particular univariate polynomial ring (R[x₁, x₂,..., x_n-1])[x_n). Hence its implementation should be able to reuse that of a generic univariate polynomial ring.