Conversions between diff, D, and Physics[diff] - convert derivatives between the diff and D notations
any valid Maple object
The Physics package provides a framework for computing with commutative, anticommutative, and noncommutative objects at the same time. Accordingly, it is possible to differentiate with respect to anticommutative variables; the command used to perform these derivatives is the diff command of the Physics package. (herein referred to as diff).
convert/D and convert/diff are converter routines between the D and diff formats for representing derivatives. The equivalence for anticommutative high order derivatives written in the D format and diff format of the Physics package is as in:
where the derivative above should be interpreted as: first differentiate with respect to θ1, then with respect to θ2 (or the opposite times −1); and the right hand side is not interpreted as a commutative higher order derivative.
Load the Physics package and set a prefix to identify anticommutative variables (see Setup for more information).
Setup(mathematicalnotation = true);
Setup(anticommutativepre = theta);
* Partial match of 'anticommutativepre' against keyword 'anticommutativeprefix'
Consider a commutative function depending on commutative and anticommutative variables, and one higher order derivative of it.
f(x, y, z, theta, theta, theta);
diff((3), x, theta, y, theta, z, theta);
Note in the above that the commutative differentiation variables are collected as a group to be applied first, then the anticommutative ones.
Rewrite this expression in D notation, then convert back to diff notation.
convert/D, convert/diff, D, diff, Physics, Physics conventions, Physics examples, Physics Updates, Tensors - a complete guide, Mini-Course Computer Algebra for Physicists, Physics,diff, Physics,diff,anticommutative, Setup
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