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Re: Is there any efficient easy way to compare two lists with the same length with Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124421] Re: Is there any efficient easy way to compare two lists with the same length with Mathematica?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 19 Jan 2012 05:10:17 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201201181057.FAA16469@smc.vnet.net>

I do not think I would like Mathematica to automatically thread Greater 
etc over lists or automatically return False or True. Comparisons such 
as {3, 4} >= {2, 5} do not have a canonical meaning and they may arise 
in programs where the fact that they are kept unevaluated can be 
convenient e.g this
Min /@ ({3, 4} >= {2, 5})  is a convenient way to compare minima 
(Min@{3,5}>=Min@{2,5} is quite a lot longer...).
In general, there has to be a balance between the sort of things 
Mathematica does automatically and the sort of things that Mathematica 
leaves unevaluated until you make your intention more clear (by using 
Thread, for instance). In this particular case I think the second choice 
is the right one.

Andrzej Kozlowski



On 18 Jan 2012, at 11:57, Murray Eisenberg wrote:

> Over time more and more things like this have been extended to work
> automatically on lists. But so far, as you discovered, not GreaterEqual
> (nor Greater, etc.).  Here's one way without explicitly using Table:
>
>   a = RandomInteger[{0, 20}, 5];
>   b = RandomInteger[{0, 20}, 5];
>   And @@ MapThread[Greater, {a, b}]
>
> The key there is MapThread, which does what you (and I) would evidently
> like Mathematica to do automatically -- in effect, to make GreaterEqual
> have Listable as an Attribute.
>
> On 1/17/12 3:34 AM, Rex wrote:
>> Given two lists `A={a1,a2,a3,...an}` and `B={b1,b2,b3,...bn}`, I would
>> say `A>=B` if and only if all `ai>=bi`.
>>
>> There is a built-in logical comparison of two lists, `A==B`, but no
>> `A>B`.
>> Do we need to compare each element like this
>>
>> And@@Table[A[[i]]>=B[[i]],{i,n}]
>>
>> Any better tricks to do this?
>>
>
> --
> 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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