atlas[div] - divergence operator 

Calling Sequence: 

    div(expr) 

Parameters: 

       expr - any vector expression. 

Description: 

• The div - procedure allows one to calculate the divergence operator on a vector expression.

 

Examples: 

>	restart: with(atlas):

 

Declare constants:  

>	Constants(Lambda);

 

(2.1)

 

Declare functions:  

>	Functions(f=f(x,y),h=h(f));

 

(2.2)

 

Declare p-forms:  

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

 

(2.3)

 

Declare vectors:  

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

 

(2.4)

 

By definition:
'div(X+Y)'=div(X+Y);
'div(F*X)'=div(F*X); 

 

	(2.5)

 

Declare coframe:
Coframe(e[1]=d(x),e[2]=d(y)); 

(2.6)

 

Declare frame:
Frame(E[k]); 

(2.7)

 

Declare metric:
Metric(g=4*(d(x)&.d(x)+d(y)&.d(y))/(1+Lambda*(x^2+y^2))^2); 

(2.8)

 

Calculate connection:
Connection(omega); 

(2.9)

 

Divergence of frame vectors:
'div(E[1])'=div(E[1]); 

(2.10)

 

Divergence of vector X:
'div(X)'=div(ToBasis(X)); 

(2.11)

 

Divergence of "rotation" vector:
'div(y*E[1]-x*E[2])'=div(y*E[1]-x*E[2]); 

(2.12)

 

>

 

See Also:  

atlas, atlas[d], atlas[cov], atlas[`&.`], atlas[`&^`], atlas[iota].