The diff command is a differentiation command prepared to work with commutative (C) and anticommutative (AC) differentiation variables; that is, it takes into account the possible anticommutative character of the differentiation variables . Differentiation with respect to noncommutative (NC) variables is not implemented. Note that higher order derivatives with respect to AC variables do not commute, so their evaluation by the standard diff command would lead to an incorrect result. For the conventions adopted to represent NC and AC objects, see the Physics package conventions.

The %diff command is the inert form of diff; that is, it represents the same mathematical operation while displaying the operation unevaluated. To evaluate the operation, use the value command.

All of the differentiating knowledge of the top level diff command is taken into account when evaluating derivatives with diff, and all differentiation rules defined by the user as `diff/...` routines are also automatically taken into account.

The syntax for the input of diff is equal to that of the top level command, and a `print/diff` procedure is implemented in order to have the same display. Higher order derivatives with respect to commutative and anticommutative variables are displayed in separate groups. For example, set  to be the prefix identifying anticommutative variables:

Physics[Setup](anticommutativeprefix = theta);

Physics[diff](f(theta1, theta2, x, y), theta1, theta2, x$3, y$2);

As with the top level diff command, if the result of a requested derivative cannot be expressed in terms of diff, then the D operator is used to express it. The equivalence between derivatives written in terms of diff and D is as follows:

Physics[diff](f(theta1, theta2), theta1, theta2);

(3) = convert((3), D);

The derivative above should be interpreted as: first differentiate with respect to , then with respect to ; or perform the derivatives in the opposite order and multiply the result by . Thus, the right-hand side should not be interpreted as a commutative higher order derivative.

To convert between formats, use the convert command with diff, Diff, or D as the second argument. Although an equivalence between diff and D always exists, note that there is no equivalence between the Physics and top level versions of diff when there are anticommutative objects in the derivand.

Cheb-Terrab, E.S. "Symbolic Computing with Anti-commutative and Non-commutative Variables." MapleTech, Vol. 5, No. 1. (1998): 16-22.