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 $R[x_1, x_2, \ldots, x_n]$ is a particular univariate polynomial ring $(R[x_1, x_2, \ldots, x_{n-1}])[x_n)$ . Hence its implementation should be able to reuse that of a generic univariate polynomial ring.