atlas[`&d`] - codifferential operator 

Calling Sequence: 

    &d(expr) 

Parameters: 

    expr - any expression. 

Description: 

• The &d - procedure allows one to calculate codifferential on an expression that is p-form.

 

• The codifferential is the operator δ : ->  where is p-form and is (p-1)-form. The codifferential is defined as follows:

 

• If is  a p-form then

 

Examples: 

>	restart: with(atlas):

 

Declare p-forms:  

>	Forms(omega=n);

 

(2.1)

 

Using d- procedure: 

- declared as a p-form so we have:
'delta(omega)'=&d(omega);
 

(2.2)

 

>

 

See Also:  

atlas, atlas[Constants], atlas[Functions], atlas[Forms], atlas[`&^`],  atlas[`&**`], atlas[d], atlas[`&L`]. .