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Question about subscripts and polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg107355] Question about subscripts and polynomial
  • From: Luca Zanotti Fragonara <Luca.Zanottifragonara at polito.it>
  • Date: Wed, 10 Feb 2010 03:36:40 -0500 (EST)
Hello everybody,

I would like to write a Polynomial, in this way:

Poly = d^2*v
Subscript[q, 1] =
 Poly /. {d -> Sum[Subscript[d, i], {i, 1, 3}]} /. {v ->Sum[Subscript[v, 
i], {i, 1, 3}]}
Expand[Subscript[q, 1]]

In this way I will obtain a polynomial in this form:

d_1^2 v_1+2 d_1 d_2 v_1+d_2^2 v_1+2 d_1 d_3 v_1+2 d_2 d_3 v_1+d_3^2 
v_1+d_1^2 v_2+2 d_1 d_2 v_2+d_2^2 v_2+2 d_1 d_3 v_2+2 d_2 d_3 v_2+d_3^2 
v_2+d_1^2 v_3+2 d_1 d_2 v_3+d_2^2 v_3+2 d_1 d_3 v_3+2 d_2 d_3 v_3+d_3^2 v_3

I would like to reorder the expanded polynomial in a way such that the 
terms with lower subcripts indexes will be at the beginning of the 
polynomial, and the terms with higher order of subscripts will be at the 
end (a sort of order due to the subscript instead of the power terms). 
So the order should be something:

Order 3: d_1^2 v_1
Order 4: 2 d_1 d_2 v_1+d_1^2 v_2+...
Order 5: d_2^2 v_1+2 d_1 d_3 v_1+...
Order 6: 2 d_2 d_3 v_1+...

I've tried to figure it out but I don't know which way to turn!!!

Thank you in advance.

Luca
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