atlas[delta] - Kronecker's delta symbol 

Calling Sequence: 

    delta[i,j] 

Parameters: 

       i, j - variables or integers. 

Description: 

• The delta table allows one to use Kronecker's delta symbol. The main syntax is as follows: delta[i,j] i.e. .

 

• The definition for Kronecker's delta symbol is as follows:

 

• delta is just the table:

 

Examples: 

>	restart: with(atlas):

 

Declare Functions  

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

 

(2.1)

 

Declare Vectors  

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

 

(2.2)

 

Declare forms:  

>	Forms(e[i]=1,omega=2,sigma=p);

 

(2.3)

 

Declare coframe:  

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

 

(2.4)

 

Declare frame:  

>	Frame(E[k]);

 

(2.5)

 

Using delta procedure: 

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

(2.6)

 

To basis decomposition:
X=ToBasis(X); 

(2.7)

 

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

(2.8)

 

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

(2.9)

 

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

(2.10)

 

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

(2.11)

 

>

 

See Also:  

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