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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
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