atlas[Vectors] - declaration of vectors 

Calling Sequence: 

    Vectors(V1, V2, ..., Vi, ..., Vn) 

Parameters: 

     Vi - vector identivier. 

Description: 

• In the atlas package any identifier is treated as 0-form i.e. as non-constant scalar (if it not declared as constant, p-form, tensor etc. (see atlas[types])).

 

• The Vectors procedure allows one to declare vectors. One can declare indexed vectors e.g. E[j] is treated as a set of vectors .

 

Examples: 

>	restart: with(atlas):

 

Declare f, h and z as functions:  

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

 

(2.1)

 

Verify that E[1] is vector using kind (see atlas[kind]) and type  procedures:  

>	kind(E[1]);

 

(2.2)

 

>	type(E[1],vect);

 

(2.3)

 

Construct new [2,0] tensors T[i,j] using tensor product operator (see atlas[`&.`]): 

>	T[i,j]:=E[i]&.E[j]+E[j]&.U[i]; 'kind(T[i,j])'=kind(T[i,j]);

 

 

	(2.4)

 

Calculation of Lie derivative (see atlas[L]): 

>	'L[X]'(f*Z+Y)=L[X](f*Z+Y);

 

(2.5)

 

Some more examples (see atlas[iota] and atlas[`&^`]): 

>	'iota[E[j]](d(x)&^d(y))'=iota[E[j]](d(x)&^d(y));

 

(2.6)

 

>	'iota[U[i],Z](d(x)&^d(y))'=iota[U[i],Z](d(x)&^d(y));

 

(2.7)

 

Let's see "who is who" 

>	Who([X,Y,Z,x,E[k],U[1]]);

 

X: vector Y: vector Z: vector x: 0 - form E[k]: vector U[1]: vector

 

>

Who();

 

(2.8)

 

>

 

See Also:  

atlas, atlas[Constants], atlas[Functions], atlas[Forms], atlas[Tensors], atlas[iota], atlas[`&^`], atlas[Who].