Cat::PartialDifferentialRing --
the category of partial differential rings
IntroductionCat::PartialDifferentialRing represents the category of
partial differential rings.
Generating
the categoryCat::PartialDifferentialRing()
Cat::CommutativeRing
DetailsCat::PartialDifferentialRing is a commutative ring
with a finite set of derivation operators D_i.D_i(f * g) equals D_i(f) * g + f * D_i(g) for
all f and g."diff" exists, such that diff(f, x) returns
the partial derivation of f with respect to the
indeterminate x.D(Type::ListOf(Type::PosInt) l, dom x)x which is given by the
indices in l:
l is empty then x must be
returned.l contains one integer i then the
i-th derivative D_i(x) must be returned. If
the i-th derivativation does not exist
dom::zero must be returned.l contains more than one integer
i1,...,in than the derivative
D_i1(...D_in(x)...) must be returned.diff(dom x <, variable v...>)x with respect to the
variables v:
diff(x) must return x.diff(x, v) must return the partial derivative of
x with respect to v.diff(x, v1,..., vn) must return diff(...diff(x,
v1),...vn).