diff and D notation - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

Home : Support : Online Help : Physics : diff and D notation

Conversions between diff, D, and Physics[diff] - convert derivatives between the diff and D notations

Calling Sequence

convert(expr, diff)

convert(expr, D)

Parameters

expr

-

any valid Maple object

Description

• 

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 , then with respect to  (or the opposite times ); and the right hand side is not interpreted as a commutative higher order derivative.

Examples

Load the Physics package and set a prefix to identify anticommutative variables (see Setup for more information).

(1)

(2)

Consider a commutative function depending on commutative and anticommutative variables, and one higher order derivative of it.

(3)

(4)

Note in the above that the commutative differentiation variables are collected as a group to be applied first, then the anticommutative ones.

Physics:-diff(Physics:-diff(Physics:-diff(diff(diff(diff(f(x,y,z,theta[1],theta[2],theta[3]),x),y),z),theta[1]),theta[2]),theta[3])

Rewrite this expression in D notation, then convert back to diff notation.

(5)

(6)

See Also

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


Download Help Document