Re: and color via PlotStyle
- To: mathgroup at smc.vnet.net
- Subject: [mg118565] Re: and color via PlotStyle
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Tue, 3 May 2011 05:45:26 -0400 (EDT)
Wrap the argument to Plot with Evaluate.
On 5/2/2011 6:50 AM, Dushan Mitrovich wrote:
> Helen Read wrote:
>> On 4/30/2011 5:51 AM, AES wrote:
>>
>>> In article<ipe7mj$r1o$1 at smc.vnet.net>,
>>> Bill Rowe<readnews at sbcglobal.net> wrote:
>>>
>>>
>>>>
>>>>> Plot[{ a x, a x^2, a x^3}/. {a -> 1},{x, 0, 2},
>>>>> PlotStyle -> {Red, Green, Blue}]
>>>>>
>>>>
>>>>> just produces blue plots.
>>>>>
>>>> Exactly as it should.
>>>>
>>> The statement "Exactly as it _should_" is open to discussion here.
>>>
>>> Consider an "ordinary user" (a user attempting to use Mathematica to do
>>> some simple but useful task) who is at a level of sophistication where
>>> he/she understands the Plot command; how to use it to plot a List of
>>> functions {f1,f2,f3}; the use of simple PlotStyles; and the use of the
>>> "\." syntax =AD=AD but has never had to encounter the concepts of Hold or
>>> Evaluate.
>>>
>>> After all, having a rudimentary understanding of Plot, PlotStyle, the \=2E
>>> syntax, and lists (which are all relatively simple, understandable,
>>> learnable commands that do familiar things) permits this user to do many
>>> useful tasks =AD=AD and to do themwithout ever having any interaction with
>>> the much more complex and arcane (and much less standard or familiar in
>>> ordinary life) concepts of Hold and Evaluate.
>>>
>>> This mythical user might then well be forgiven for thinking that the two
>>> commands
>>>
>>> a = 1;
>>> Plot[{ a x, a x^2, a x^3}, {x, 0, 2},
>>> PlotStyle -> {Red, Green, Blue}]
>>>
>>> Plot[{ a x, a x^2, a x^3}/. {a -> 1}, {x, 0, 2},
>>> PlotStyle -> {Red, Green, Blue}]
>>>
>>> _should_ do exactly the same thing, except that the first form will also
>>> obviously leave a assigned the value 1 in subsequent cells.
>>>
>>> But of course, this is not what happens, and so the user who uses the
>>> second form (perhaps doing so for compactness, or perhaps wanting to
>>> make a test Plot of their List without setting a to a fixed value)
>>> encounters another of the copious supply of puzzling Mathematica
>>> "gotchas".
>>>
>>> I'm not arguing that this outcome is in some sense "wrong", or in any
>>> way a bug. There may be -- probably are -- deep reasons, buried deep in
>>> the logic and design of Mathematica, as to why Plot has to function in
>>> this way (or maybe an unnecessary design decision was made that Plot
>>> would function in this way to simplify other aspects of Mathematica
>>> programming?).
>>>
>>> But it's still unfortunate that it does operate this way. Would you
>>> (and maybe Helen ??? in Washington) really want to argue that high
>>> school students, or freshman students in college, should have to first
>>> go through a tutorial in Hold and Evaluate (and maybe also HoldAll,
>>> HoldFirst, NHoldAll, HoldAllComplete, HoldRest, SequenceHold, Extract,
>>> and Unevaluated) before they could start plotting Lists using Plot?
>>>
>> Oh, please. Nobody needs to go through all that "before they could start
>> plotting Lists using Plot".
>>
>> My beginning students plot lists all the time. Normally they do it by
>> defining functions first, for whatever it is they are plotting.
>>
>> f[x_]:=x
>> g[x_]:=x^2
>> h[x_]:=x^3
>>
>> Plot[{f[x],g[x],h[x]},{x,0,2},PlotStyle -> {Red, Green, Blue}]
>>
>> (Although actually, most of them accept the default colors and rarely
>> bother with PlotStyle. Either way, they will get a nice plot with each
>> curve a different color.)
>> Then they might go back and edit f[x], g[x], and h[x] to make them 2x,
>> 2x^2, 2x^3, or what have you, and re-evaluate. A little later on (when
>> not exactly a newbie anymore), they might try something along these
>> lines, which also produces different colored curves.
>>
>>
>> Manipulate[
>> Plot[{a x, a x^2, a x^3}, {x, -2, 2},
>> PlotStyle -> {Red, Green, Blue}, PlotRange -> {-10, 10}], {a, -5, 5,
>> 1, Appearance -> "Labeled"}]
>>
>>
>> I have *never* seen a beginner try to use anything remotely like
>> { a x, a x^2, a x^3}/. {a -> 1} inside a Plot. But if they did, it
>> would not bother anybody. They would either ask why it came out that
>> way, or try a different way of doing it, or ignore it and move on. It's
>> just not a big deal.
>>
>> But I don't even show them the /. notation until there is a real need
>> for it. I teach them about defining functions from day one.
>>
>> --
>> Helen Read
>> University of Vermont
>>
>
> So far everybody has been talking about whether the behavior is reasonable
> or unreasonable to expect, but nobody has (AFAIK) done the obvious, namely
> stated the solution to the question: Just how does one get
> differently-colored curves when using the '/.{a->1}'?
>
> I am a near-beginner, have run into the problem myself, and have been reading
> the thread hoping to learn the solution. No luck.
>
> - Dushan
>
>
--
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