atlas[div] - divergence operator

Calling Sequence:

     div(expr)

Parameters:

         expr - any vector expression.

Description:

•  The div procedure calculates the divergence operator on a vector expression.

Examples:
restart:
with(atlas):

Declare constants:
Constants(Lambda);

Declare functions:
Functions(f=f(x,y),h=h(f));

Declare p-forms:
Forms(e[k]=1,xi=1);

Declare vectors:
Vectors(E[j],X,Y,Z);

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

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

Declare frame:
Frame(E[k]);

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

Calculate connection:
Connection(omega);

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

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

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

See Also:

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