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

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  • Subject: [mg91000] Re: [mg90973] Re: [mg90956] Re: [mg90947] When is a List not a List?
  • From: Peter Lindsay <peter.lindsay at>
  • Date: Sat, 2 Aug 2008 03:27:59 -0400 (EDT)
  • References: <>

just a crazy off-the-top-of-my-head idea here: Why don't Wolfram  
publish a manual for Mathematica ?

Peter Lindsay

On 1 Aug 2008, at 08:00, AES wrote:

> At 7:44 PM -0500 7/31/08, DrMajorBob wrote:
>> 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.)
> If the above is true -- and I'd suppose it is -- then I'd say it's
> also very much an unfortunate, not to say flat-out *bad* design
> choice or artifact.
> An innocent novice-level user creates a Plot[ ] with three curves
> using the {f1, f2, f3} List form of the first argument, and discovers
> that M by default assigns a different color to each curve -- a good
> and helpful default design choice on M's part, I'd say.
> Maybe this novice user wants to go a bit further: Thicken certain
> curves, change the Dashing, and so on.  He or she discovers the
> PlotStyle option (or equivalent); learns how to do this; is happy.
> And then this user also realizes: Hey, I could plot 8 or 10 curves
> this way, without having to type in f1 thru f8 by just using a Table[
> ] command for the first argument and iterating over some appropriate
> parameter.  A Table[ ] creates a List, right?
> So he/she does this; the 8 or 10 curves appear exactly as desired;
> except the styling behavior is suddenly all screwed up.  Once again,
> a classic M-style Gotcha!!! -- and a particularly nasty Gotcha:  Am I
> getting this unwanted result because of the way I structured the
> PlotStyle commands I used? -- or because of something mysterious with
> using Table[ ]?  The coloring and so on in the default  {f1, f2, f3}
> case has the nice default cycling behavior for the styling -- Why am
> I not getting it now?
> Andrzej says this unfortunate result _has_ to be the case because
> Plot[ ]  doesn't "pre-Evaluate" the first argument.
> Well, somehow, if the first argument is {f1, f2, f3, f4, f5, f6, f7,
> f8}, Plot[ ] somehow "pre-evaluates" (lower-case pre-evaluate) this
> argument at least enough to know that it's not only a List, but how
> many elements that List has.  Is it somehow impossible for Plot[ ] to
> know that Table will also produce a List, and to similarly
> pre-evaluate how many elements that List will have?  I suspect it's
> not impossible.
> And if that is indeed impossible with the PlotStyle option in Plot[ ]
> then can Andrzej  explain how it _is _ possible for Plot[ ] to
> somehow handle the PlotRange->All option correctly (i.e.,
> identically) with either form of the first argument -- even though
> that option needs to determine not only the number of curves in the
> first argument, but the maximum and minimum values over all those
> curves, in order to set the axes and axis Tick locations and values
> for the plot.  Is just getting the number of curves and picking the
> colors for them really harder than that?
> I very much like DrMajorBob's wording here:  I'll bet the coloring
> problem with List vs Table is precisely "an [accidental] design
> choice/artifact, not a necessity preordained by fate" -- and an
> unfortunately unfortunate "design choice/artifact".
> The only things more unfortunate are (a) that M has a fair (and
> increasing?) number of these Gotchas; (b) M's documentation is
> substantially less helpful than it could or should be either in
> diagnosing or in warning about them; and (c) it's far from clear that
> anyone at WRI really recognizes these points.

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