[GiNaC-devel] Matrices vs indexed

[Alejandro Limache]

according to Ginac-mini FAQ:
>The indexed class (and most derived classes) is intended for tensor 
>manipulation without >referring to a particular basis. Thus, the indexed 
>class is well suited for calculations >involving  (formally defined) tensor 
>algebra of "non-integer-dimensional space".
>....
>In that framework, unrolling ai*ai to a1^2+a2^2+a3^2+... is not possible, 
>since the dimension >is not integer!

I am physicist (not a relativist one though).. but, is there something more
useful than tensors representations (i.e tensor components) defined
for integer indexes?!!!.
Let us see... In two dimensions the tensor velocity vector V
can be written in cartesian cordinates (x,y) with basis vectors (e.x,e.y) 
as:
V.x e.x + V.y e.y
but aren't we finally more interested in the values of the "components":
V= [V.x ,V.y]   ===> a matrix with 2 integer indices.
But...let see in polar coordinates with basis vectors (e.r,e.theta) the same 
velocity
vector can be written as
V.r e.r + V.theta e.theta
but aren't we finally more interested in the values of the "components":
V= [V.r ,V.theta]   ===> a matrix of 2 integer indices.
but ....opps we always ended by looking at the multi-index
arrays of integer indeces!!!

It is because that I always want to get the components of tensors
(which can be arranged as multidimensional arrays/matrices)
is that I want to be able to unroll indexed objects.
So I agree with the type of interest reported by another newbie to Ginac:
(http://www.cebix.net/pipermail/ginac-list/2004-December/000576.html)
>I'd like to know if is it possible to unroll indexed
>objects. As example, I would like to do something like this
>a_i a~i = (a_1)^2 + (a_2)^2 + (a_3)^2 + ...
>or just substituting a_i values in a_i * b~i a_i = =(1,0,0)
>a_i b~i -> b~1
Definitely I like to be able to do things like the above.

Chris mentioned to me two things that could be very
useful in indexed expressions:
1)
ex_to<numeric>(e.subs(lst(i==0,j==0))).to_double()
This works in matrices but one should be abel to put numeric values
inside indexed expressions and do matrix type operations...

2) expand_dummy_sum(const ex & e, bool subs_idx)
there could be a similar function "expand_indexes"
that expand summed and not summed indices.
Example given
ex e=indexed(A,i,j)*indexed(v,j)
by applying the "expand_indices" function get:
e=[[A.1.1*v1 A.1.2*v.2],
      [A.2.1*v1 A.2.2*v.2]]

cheersss
Alejandro