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 allows one to declare 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);

 

(2.1)

 

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

>	kind(e[1]);

 

(2.2)

 

Using exterior product operator (see atlas[`&^`]): 

>	'omega&^beta'=omega&^beta;

 

(2.3)

 

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

 

(2.4)

 

Some more examples: 

>	'e[j]&^e[i]'=e[j]&^e[i];

 

(2.5)

 

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

 

(2.6)

 

And more: 

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

(2.7)

 

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

 

(2.8)

 

Declare p as a constant:
Constants(p); 

(2.9)

 

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

(2.10)

 

Let's see "who is who" 

>	Who([alpha,beta,omega,e[j],x,y,z,p]);

 

alpha: q - form beta: p - form omega: 2 - form e[j]: 1 - form x: 0 - form y: 0 - form z: 1 - form p: constant

 

>

Who();

 

(2.11)

 

>

 

See Also:  

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