atlas[Frame] - declaration of frame vectors 

Calling Sequence: 

    Frame(Id[j]) 

Parameters: 

    Id[j] -indexed variable the frame vectors 

Description: 

The Frame procedure allows one to declare frame vectors. If  E[j] is defined as a frame then vectors (n=dim) make the frame. Frame declaration is only possible if coframe has been defined (see atlas[Coframe]).  

Examples: 

>	restart: with(atlas):

 

Declare forms: 

>	Forms(e[j]=1,xi=1);

 

(2.1)

 

Declare vectors: 

>	Vectors(X,Y,Z,E[j]);

 

(2.2)

 

One can not declare frame before coframe declaration:
Frame(E[k]); 

Error, (in Frame) coframe is undefined

 

Declare coframe:
Coframe(e[j],j=1..n); 

(2.3)

 

Declare frame:
Frame(E[k]); 

(2.4)

 

It is obvious that
'iota[E[i]](e[j])'=iota[E[i]](e[j]); 

(2.5)

 

"To basis" decomposition 

>	X=ToBasis(X);

 

(2.6)

 

>	xi=ToBasis(xi);

 

(2.7)

 

>

 

See Also:  

atlas, atlas[Coframe], atlas[ToBasis].