       Re: Question about subscripts and polynomial

• To: mathgroup at smc.vnet.net
• Subject: [mg107387] Re: [mg107355] Question about subscripts and polynomial
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 11 Feb 2010 05:20:07 -0500 (EST)
• References: <201002100836.DAA21317@smc.vnet.net>

```Luca Zanotti Fragonara wrote:
> 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!!!
>
>
> Luca

Poly = d^2*v;
Subscript[q, 1] =
Poly /. {d -> Sum[Subscript[d, i], {i, 1, 3}]} /. {v ->
Sum[Subscript[v, i], {i, 1, 3}]};
p2 = Expand[Subscript[q, 1]]

Then you can get in the vicinity of the desired ordering using
MonomialList with default (Lexicographic) term order, and a suitable
ordering of the variables. I rewrote to remove subscripting, so that
this could be readily depicted in email-friendly plain ascii.

mlist = MonomialList[p2,
Riffle[Table[Subscript[d, i], {i, 3}],
Table[Subscript[v, i], {i, 3}]]];

In:= mlist /. Subscript -> Compose

Out= {d^2 v, d^2 v, d^2 v, 2 d d v,
2 d d v, 2 d d v, 2 d d v,
2 d d v, 2 d d v, d^2 v, 2 d d v,
d^2 v, d^2 v, d^2 v, 2 d d v,
2 d d v, d^2 v, d^2 v}

Daniel Lichtblau
Wolfram Research

```

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