Re: Re: Question about subscripts and
- To: mathgroup at smc.vnet.net
- Subject: [mg107454] Re: [mg107447] Re: [mg107355] Question about subscripts and
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Sat, 13 Feb 2010 05:22:03 -0500 (EST)
- References: <201002100836.DAA21317@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
OK, try this: 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]] (* output suppressed *) Subscript[_, k_] :> k Clear[order] order[term_] := Replace[term, x_?(FreeQ[#, Subscript] &) :> 1, {1}] /. Times -> Plus /. Power -> Times /. Subscript[_, k_] :> k listSum = SortBy[basicSum /. Plus -> List, order] (* output suppressed *) displaySum = Infix[listSum, "+"] (* output suppressed *) backToBasics = Plus @@ displaySum[[1]]; basicSum === backToBasics True Bobby On Fri, 12 Feb 2010 04:35:55 -0600, Luca Zanotti Fragonara <Luca.Zanottifragonara at polito.it> wrote: > 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 >>> >>> >>> >> >> > -- DrMajorBob at yahoo.com
- References:
- Question about subscripts and polynomial
- From: Luca Zanotti Fragonara <Luca.Zanottifragonara@polito.it>
- Question about subscripts and polynomial