Re: Re: {x},{y} -> {x,y} ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg68319] Re: [mg68275] Re: {x},{y} -> {x,y} ?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Tue, 1 Aug 2006 06:59:47 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <eaht5b$or5$1@smc.vnet.net> <200607310745.DAA26835@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

This solution (also posted by Bob Hanlon [mg68257] and Oleksandr Pavlyk [mg68254], and appearing as well in Michael Trott's "The Mathematica Guidebook for Programming") is very interesting, because Thread is its own functional inverse here: x = Range[3]; y = 10*Range[3]; Thread[{x, y}] Thread[%] {{1, 10}, {2, 20}, {3, 30}} {{1, 2, 3}, {10, 20, 30}} In general, if x and y are any lists of the same length, then: Thread @ Thread[List[x, y]] == List[x, y] True (And similarly for n instead of 2 such lists). But for functions f other than List, it is not necessarily the case that Thread@Thread[f[x, y]] == f[x, y] is true. For example: f[x_,y_] := {{x[[1]], y[[2]]},y[[1]]} x=Range[3];y=10*Range[3]; f[x,y] Thread[f[x,y]] Thread@Thread[f[x,y]] {{1,20},10} {{1, 10}, {20, 10}} {{1,20},{10,10}} What more can be said about such counterexamples? Stratocaster wrote: > "AngleWyrm" <anglewyrm at yahoo.com> wrote in message > news:eaht5b$or5$1 at smc.vnet.net... >> Hi, >> I have two lists, a set of x values and a set of y values. How do I >> convert >> them to one list of { {x1,y1},{x2,y2} } pairs? >> > > x = {set of X values}; > y = {set of Y values}; > > Thread[{x,y}] -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**Follow-Ups**:**Re: Re: Re: {x},{y} -> {x,y} ?***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>