>
|
|
| (1) |
First set the symbols and as prefixes identifying anticommutative variables (see Setup for details).
>
|
|
| (2) |
So the following is an anticommutative function of two anticommutative variables.
>
|
|
The second derivative with respect to the same anticommutative variable is equal to zero.
>
|
|
All second order mixed derivatives anticommute.
>
|
|
| (4) |
>
|
|
| (5) |
Convert to the D format.
Derivatives of composite anticommutative functions with respect to anticommutative variables:
>
|
|
| (7) |
| (8) |
Derivatives of anticommutative products with respect to an anticommutative variable:
>
|
|
| (9) |
| (10) |
The second derivative with respect to the same anticommutative variable is equal to zero.
The mixed second order derivatives anticommute. These operations sometimes require normalizing and expanding the noncommutative products; for that purpose, use the expand command (if the intention is to expand only noncommutative products, use Physics/Expand).
>
|
|
| (12) |
You can use C and AC variables together. If the output contains derivatives with respect to both C and AC variables, then they are displayed in separate groups.
>
|
|
| (14) |
When the derivand contains both commutative and anticommutative variables and functions, using the top level diff command may result in incorrect calculations, even when the differentiation variable is commutative.