Re: and color via PlotStyle
- To: mathgroup at smc.vnet.net
- Subject: [mg118528] Re: and color via PlotStyle
- From: Helen Read <readhpr at gmail.com>
- Date: Sun, 1 May 2011 06:22:03 -0400 (EDT)
- References: <ipe7mj$r1o$1@smc.vnet.net> <ipgm2t$8op$1@smc.vnet.net>
On 4/30/2011 5:51 AM, AES wrote:
> In article<ipe7mj$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
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- From: Dushan Mitrovich <dushanm@spinn.net>
- Re: and color via PlotStyle