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Re: Re: Re: When is a List not a List?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91001] Re: [mg90968] Re: [mg90956] Re: [mg90947] When is a List not a List?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 2 Aug 2008 03:28:10 -0400 (EDT)
  • References: <200807310656.CAA07700@smc.vnet.net> <200808010659.CAA25763@smc.vnet.net>

I am not sure about the "no argument part". First, it seems to me  
obvious that one should try to learn Mathematica before trying to use  
it, and reading the documentation is a pretty basic part of learning.  
Why should you then call something a "quirk" if it is both documented  
and even exemplified.
However, there is more to that. In view of what you have been arguing,  
perhaps you could tell us if it "seems odd to you"  that Plot does not  
use different colors in the example below. It does not seem odd to me  
at all, and I doubt that even beginners (AES excepting, of course)  
will find it "a quirk".


Plot[x /. Solve[x^3 - 3 x + a x == 0, x], {a, -3, 3}]

Andrzej Kozlowski


On 1 Aug 2008, at 08:59, DrMajorBob wrote:

> No argument here. That's the behavior, and we've seen it a thousand  
> times.
> A "quirk" is only a quirk the first 100 times we see it, or  
> thereabouts.
> (Pick a number.)
>
> Plot COULD assign colors after evaluation, OTOH... the fact that it
> doesn't is a design choice/artifact, not a necessity preordained by  
> fate.
>
> That being so, users are entitled to find it odd at first glance.  
> (Or even
> second... maybe third.)
>
> Bobby
>
> On Thu, 31 Jul 2008 13:56:56 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl 
> >
> wrote:
>
>> When I wrote "Plot does not evaluate its arguments" I meant it in the
>> usual (although inaccurate) sense that people frequently  use in this
>> context, namely: that the so called Evaluator does not pre-evaluate  
>> the
>> arguments of Plot  (if you do not like to thing of "the Evaluator",
>> another way of saying this is that "Mathematica" does not evaluate  
>> the
>> arguments before Plot is applied and leaves any evaluating to  
>> Plot.) Of
>> course, you are right that Plot does evaluate its arguments in some  
>> way
>> (this sort of behavior is also referred in the often used phrase:   
>> "Plot
>> evaluates its arguments in a non-standard way"). The fact that this
>> "non-standard" evaluation results in a plot of a function is actually
>> new in version 6; in all previous versions all you will get is an  
>> error
>> message about the values of the function being plotted not being  
>> numeric.
>> Anyway, my point was that this has been a normal (non quirky)  
>> behavior
>> of Mathematica since version 1 and has been discussed here a number  
>> of
>> times.  (It must be at least the fourth of fifth time in 10 years  
>> that I
>> am addressing this issue on this forum). It is also fully documented
>> (with examples) in the Mathematica online documentation, all past
>> printed documentation and a vast number of books dealing with
>> Mathematica.
>>
>> Andrzej Kozlowski
>>
>>
>> On 31 Jul 2008, at 20:15, DrMajorBob wrote:
>>
>>> But Plot DOES evaluate its arguments, of course, and DOES  
>>> (eventually)
>>> see that multiple functions are being plotted. (Else they couldn't  
>>> be
>>> plotted.)
>>>
>>> It's just not happening before colors are assigned.
>>>
>>> Nonetheless, it's prudent to take note of what functions actually  
>>> do,
>>> and get used to it. Calling everything in sight a quirk serves no
>>> purpose.
>>>
>>> (Paraphrasing Andrzej, perhaps.)
>>>
>>> Bobby
>>>
>>> On Thu, 31 Jul 2008 05:04:10 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl
>>>> wrote:
>>>
>>>> There is nothing at all quirky about this. Yes, FullForm[Table[g[x,
>>>> n], {n, 1, 2}]] and FullForm[{g[x, 1], g[x, 2]}] are indeed  
>>>> identical,
>>>> but that is because FullForm evaluates its argument. But Plot has
>>>> attribute:
>>>>
>>>> In[2]:= Attributes[Plot]
>>>> Out[2]= {HoldAll, Protected}
>>>>
>>>> so, unlike FullForm, it does not evaluate its argument. In your  
>>>> first
>>>> example,  Plot[{g[x, 1], g[x, 2]}, {x, 0, 1}, PlotStyle -> {Red,
>>>> Blue}], the first argument of Plot has an explicit List bracket, so
>>>> Plot can see that it supposed to treat the argument as two  
>>>> different
>>>> functions, without evaluating the argument. But in the second  
>>>> case, it
>>>> does not see an explicit bracket, so it treats the entire  
>>>> expression
>>>> as the graph of a single function (in versions of Mathematica  
>>>> before 6
>>>> you would not have got any plot at all in this case).
>>>>
>>>> If you use Evaluate in the second code you will get the same  
>>>> result as
>>>> you get form the first:
>>>>
>>>> Plot[Evaluate[Table[g[x, n], {n, 1, 2}]], {x, 0, 1}, PlotStyle ->
>>>> {Red, Blue}]
>>>>
>>>> Finally, since you have given ample proof that, in spite of many  
>>>> years
>>>> of using Mathematica, you have not mastered its basics (this
>>>> particular issue has been raised and answered a countless number of
>>>> times on this forum), why do you keep assuming that the problems  
>>>> that
>>>> you keep coming across are Mathematica's "quirks" rather than (as  
>>>> is
>>>> much more likely) gaps in your won understanding? What do you  
>>>> think of
>>>> first year undergraduate students who whenever they do not  
>>>> understand
>>>> something in their introductory lectures claim that it is wrong, or
>>>> blame their textbook or their lecture rather then themselves?
>>>>
>>>> Andrzej Kozlowski
>>>>
>>>>
>>>>
>>>> On 31 Jul 2008, at 08:56, AES wrote:
>>>>
>>>>> g[x_, n_] := x^n
>>>>> FullForm[Table[g[x, n], {n, 1, 2}]]
>>>>> FullForm[{g[x, 1], g[x, 2]}]
>>>>> Plot[{g[x, 1], g[x, 2]}, {x, 0, 1}, PlotStyle -> {Red, Blue}]
>>>>> Plot[Table[g[x, n], {n, 1, 2}], {x, 0, 1}, PlotStyle -> {Red,  
>>>>> Blue}]
>>>>>
>>>>> The FullForm[]s are identical.  One Plot[] has red and blue  
>>>>> curves;
>>>>> the
>>>>> other has two blue curves.
>>>>>
>>>>> Quirky!
>>>>>
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>> --DrMajorBob at longhorns.com
>>
>>
>
>
>
> -- 
> DrMajorBob at longhorns.com
>



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