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Cat::PartialDifferentialRing

Category of partial differential rings

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Description

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.

Methods

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Basic Methods

D(l, x)

diff(x, <v, …>)

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