Cat::PartialDifferentialRing
--
the category of partial differential ringsCat::PartialDifferentialRing
represents the category of
partial differential rings.
Cat::PartialDifferentialRing()
Cat::CommutativeRing
Cat::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)
.