atlas[Forms] - declaration of p-forms

Calling Sequence:

     Forms(F1=n, F2=k, ..., Fi=p)

Parameters:

      Fi=p  - equations where Fi - form identifier and p is a variable or an integer - the form's degree.

Description:

• In the atlas  package any identifier is treated as 0-form  i.e. as non-constant scalar  (if it not declared as constant, p-form, tensor etc. (see atlas[types] )).
• The Forms  procedure declares p-forms. One can declare indexed p-forms e.g. e[j]  is treated as a set of p-forms

Examples:
restart:
with(atlas):

Declare some forms:
Forms(e[i]=1,phi=1,z=1,omega=2,alpha=q,beta=p);

Varify that e[1] is 1-form using kind procedure (see atlas[kind] ):
kind(e[1]);

Using exterior product operator (see atlas[`&^`] ):
'omega&^beta'=omega&^beta;

'beta&^alpha'=beta&^alpha;

Some more examples:
'e[j]&^e[i]'=e[j]&^e[i];

'kind(d(beta))'=kind(d(beta));

And more:

p - was not declared as a constant!
'd(omega&^beta)'=d(omega&^beta);

'd(beta&^omega)'=d(beta&^omega);

Declare p as a constant:
Constants(p);

Thus:
'd(omega&^beta)'=d(omega&^beta);

Let's see "who is who"
Who([alpha,beta,omega,e[j],x,y,z,p]);

See Also:

atlas , atlas[Constants] , atlas[Functions] , atlas[Vectors] , atlas[Tensors] , atlas[d] , atlas[`&^`] , atlas[Who] .