Category of partial differential rings
Cat::PartialDifferentialRing represents the category of partial differential rings.
A Cat::PartialDifferentialRing is a commutative ring with a finite set of derivation operators D_i.
A derivation is a linear operator with product rule, i.e. D_i(f * g) equals D_i(f) * g + f * D_i(g) for all f and g.
For many partial differential rings the derivations are differentiations with respect to some indeterminates. Thus in order to support a natural notion it is also supposed that a method "diff" exists, such that diff(f, x) returns the partial derivation of f with respect to the indeterminate x.