RE: Modify a list of pure functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg70839] RE: [mg70812] Modify a list of pure functions*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 28 Oct 2006 23:38:46 -0400 (EDT)

What about... f = Sin[#] &; Function /@ Table[i Part[f, 1], {i, 1, 5}] {Sin[#1] &, 2 Sin[#1] &, 3 Sin[#1] &, 4 Sin[#1] &, 5 Sin[#1] &} That is, deconstruct the function, modify it, and then reconstruct the functions. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: . [mailto:ggroup at sarj.ca] To: mathgroup at smc.vnet.net Hi all, I have a problem where I need to build up a list of pure functions that have been modified from a base pure function. I'm not having much luck in getting it to work correctly, and was wondering if anyone had some good ideas. A toy version of the problem is: f = Sin[#]& listF = Table[(i f[##])&, {i, 5}] What I'd hope to get is listF containing: {Sin[##]&, (2 Sin[##])&, (3 Sin[##])&, (4 Sin[##])&, (5 Sin[##])&} But instead, I get something where neither i nor f have been evaluated. As I say, this is a toy example. One thing that does partially work for the toy case, but does not seem to work for more complicated situations is to use ReplaceAll: listF2 = Table[{j f[##])& /. j->i, {i,5}] This does give: {1 f[##1] &, 2 f[##1] &, 3 f[##1]&, 4 f[##1] &, 5 f[##1] &} However, all that has been done is the index has been inserted; no significant evaluation seems to have occurred. So this method doesn't work in more complicated situations. For example, suppose insted of using the index i directly, it actually referred to a list: coeffs = Reverse[ Range[5] ]; listF3 = Table[ (coeffs[[j]] f[##]) & /. j->i, {i, 5}] This just gives: {coeffs[[1]]*f[##1] & , coeffs[[2]]*f[##1] & , coeffs[[3]]*f[##1] & , coeffs[[4]]*f[##1] & , coeffs[[5]]*f[##1] & } Which is no good if coeffs is a temporary variable. Any suggestions would be most appreciated. Thanks!