atlas[grad] - gradient operator

Calling Sequence:

     grad(expr)

Parameters:

         expr - any 0-form expression.

Description:

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);

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);

Using grad procedure:

Just definition:
'grad(z)'=grad(z);

For function f:
'grad(f)'=grad(f);

For h which depends on f:
'grad(h)'=grad(h);

For 0-form - coordinate x:
'grad(x)'=grad(x);

Some more examples:
'grad(cos(x)*sin(y)+x^2)'=grad(cos(x)*sin(y)+x^2);

'grad(x*ln(y))'=grad(x*ln(y));

See Also:

atlas , atlas[d] , atlas[cov] , atlas[div] , atlas[L] , atlas[dual] .