# Documentation

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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`.

## Categories

`Cat::CommutativeRing`

## Methods

expand all

#### Basic Methods

`D(l, x)`

`diff(x, <v, …>)`