Re: Question about subscripts and polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg107447] Re: [mg107355] Question about subscripts and polynomial
- From: Luca Zanotti Fragonara <Luca.Zanottifragonara at polito.it>
- Date: Fri, 12 Feb 2010 05:35:55 -0500 (EST)
- References: <201002100836.DAA21317@smc.vnet.net> <op.u7xj9seetgfoz2@bobbys-imac.local>
Forget the previous message. I get what is going wrong in my ordering. My polynomial is of this form: d[1]^2 v[1] + d[1]^2 v[3] + 2 d[1] d[3] v[1] + d[3]^2 v[1] + d[1]^2 v[5] + 2 d[1] d[5] v[1] + 2 d[1] d[3] v[3] + d[3]^2 v[3] + d[1]^2 v[7] + 2 d[3] d[5] v[1]+... and so on The problem with the command: order[term_] := term /. Times -> Plus /. Power -> Times /. Subscript[_, k_] :> k listSum = SortBy[basicSum /. Plus -> List, order] Is that I get a right order when I don't have a coefficient in front of the term, but when there is a coefficient it takes part in the calculation of the order of the term I guess. Do you have an idea of how to avoid this problem? Thank you in advance, Luca DrMajorBob ha scritto: > I'm not entirely sure what ordering you want, but here's something to > get you on the way. > > You can tweak the "order" function if needed. > > First, your original expansion: > > poly = d^2*v; > Subscript[q, 1] = > poly /. {d -> Sum[Subscript[d, i], {i, 1, 3}]} /. {v -> > Sum[Subscript[v, i], {i, 1, 3}]}; > basicSum = Expand[Subscript[q, 1]] > > (ugly output omitted; it looks fine in Mathematica) > > Here's the same thing transformed to a List and sorted by the total > order of each product: > > order[term_] := > term /. Times -> Plus /. Power -> Times /. Subscript[_, k_] :> k > listSum = SortBy[basicSum /. Plus -> List, order] > > (ugly output omitted; it looks fine in Mathematica) > > That's a List, not a sum; the following is also NOT a sum, but it > looks like one, sorted the same as listSum: > > displaySum = Infix[listSum, "+"] > > (ugly output omitted; it looks fine in Mathematica) > > To get back the original: > > backToBasics = Plus @@ displaySum[[1]]; > basicSum === backToBasics > > True > > Bobby > > On Wed, 10 Feb 2010 02:36:40 -0600, Luca Zanotti Fragonara > <Luca.Zanottifragonara at polito.it> 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!!! >> >> Thank you in advance. >> >> Luca >> >> >> > >
- References:
- Question about subscripts and polynomial
- From: Luca Zanotti Fragonara <Luca.Zanottifragonara@polito.it>
- Question about subscripts and polynomial