atlas[delta] - Kronecker delta symbol

Calling Sequence:

     delta[i,j]

Parameters:

        i, j - variables or integers.

Description:

•  The delta  table is used as Kronecker's delta symbol. The main syntax is as follows: delta[i,j] i.e.  .
• The definition for Kronecker delta symbol is as follows:
• delta  is just the table:

Examples:
restart:
with(atlas):

Declare Functions
Functions(f=f(x,y,z));

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

Declare forms:
Forms(e[i]=1,omega=2,sigma=p);

Declare coframe:
Coframe(e[1]=d(x),e[2]=d(y),e[3]=d(z));

Declare frame:
Frame(E[k]);

Using delta  procedure:

Interior product of frame vector and coframe form:
'iota[E[j]](e[k])'=iota[E[j]](e[k]);

To basis decomposition:
X=ToBasis(X);

And then:
iota[X](e[k])=iota[ToBasis(X)](e[k]);

Some more examples:
'iota[E[n],E[i]](e[j]&^e[k])'=iota[E[n],E[i]](e[j]&^e[k]);

For function f:
'iota[E[k]](d(f))'=iota[E[k]](d(f));

For exterior product:
'iota[E[j]](e[k]&^d(f))'=iota[E[j]](e[k]&^d(f));

See Also:

atlas , atlas[iota] , atlas[Frame] , atlas[Coframe] , atlas[ToBasis] .