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 declares 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]);

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

type(E[1],vect);

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]);

Calculation of Lie derivative (see atlas[L] ):
'L[X]'(f*Z+Y)=L[X](f*Z+Y);

Some more examples (see atlas[iota]  and atlas[`&^`] ):
'iota[E[j]](d(x)&^d(y))'=iota[E[j]](d(x)&^d(y));

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

Let's see "who is who"
Who([X,Y,Z,x,E[k],U[1]]);

See Also:

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