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];
{{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

is true. For example:

f[x_,y_] := {{x[[1]], y[[2]]},y[[1]]}
x=Range[3];y=10*Range[3];
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};
>

--
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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