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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: [mg124454] 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: Fri, 20 Jan 2012 01:51:01 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201201181057.FAA16469@smc.vnet.net> <201201191010.FAA03651@smc.vnet.net> <CAO-JnY0vccWRr0puiMh6BSm8Hpcdd4oOPEZbqoXNjZHtpbuu=A@mail.gmail.com>

Well, actually both. The vector spaces R^n for n>1 have lots of 
different orders arising from the natural total order on R (the real 
numbers) and none of them is in any sense "canonical". In fact, of 
course, mathematica does have a default ordering, which is 
lexicographical, as you can see here:

OrderedQ[{1, 4}, {3, 3}]

True

and not the product ordering which is only a partial order. In any case, 
I don't think any of these ordering should by assumed when one applies 
the symbol <= etc.

Andrzej


On 19 Jan 2012, at 18:25, Ralph Dratman wrote:

> "Comparisons such as {3, 4} >= {2, 5} do not have a canonical meaning..."
>
> Andrej,
>
> Are you referring to a canonical meaning within Mathematica, or  to
> the canonical meaning in some wider realm of mathematics?
>
> I ask because I have seen the expression "canonical" used at Wolfram
> in the past, and I am not sure what is intended.
>
> How do we determine what the canonical meaning  (if any) of an expression is?
>
> Ralph
>
>
> On Thu, Jan 19, 2012 at 5:10 AM, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
>> 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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