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

• To: mathgroup at smc.vnet.net
• Subject: [mg90988] Re: [mg90956] Re: [mg90947] When is a List not a List?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 2 Aug 2008 03:25:41 -0400 (EDT)
• References: <200807310656.CAA07700@smc.vnet.net> <16711231.1217501820078.JavaMail.root@m08> <op.ue54zeqq2c6ksp@bobbys-imac> <21465667.1217530845998.JavaMail.root@m08> <op.ue6m0tdk2c6ksp@bobbys-imac> <32926975.1217563920588.JavaMail.root@m08> <op.ue7o67wi2c6ksp@bobbys-imac> <97345FCA-2165-4054-A869-BA4F30AA8450@mimuw.edu.pl>

```Just in case I have not made my point clearly enough, I suggest
pondering over the difference between:

Plot[x /. Solve[x^3 + x - 1/Sqrt[x + a] == 1, x], {a, -1, 3}]

and

Plot[Evaluate[x /. Solve[x^3 + x - 1/Sqrt[x + a] == 1, x]], {a, -1, 3}]

The second graph uses three colors, just as you and AES would have
wished, but unfortunately there is a slight problem with it :it is
quite wrong.

Understanding a bit of mathematics often helps to understand
Mathematica.

Andrzej Kozlowski

On 1 Aug 2008, at 17:30, Andrzej Kozlowski wrote:

> Because there are lots of plots of the kind which I just sent
> (Plot[x /. Solve[x^3 - 3 x^2 + a == 0, x], {a, -3, 5}]) but where
> you have FindRoot or NMaximize etc., instead of Solve and the first
> argument can't be evaluated until the value of the parameter a has
> been supplied. There have been lots of post of this kind on this
> forum so its kind if weird you managed to miss them all.
>
> Andrzej Kozlowski
>
>
>
>
> On 1 Aug 2008, at 16:29, DrMajorBob wrote:
>
>> Agreed.
>>
>> And I'm wondering what advantage HoldAll has, in the case of Plot,
>> since a plot can't result without evaluating the arguments?
>>
>> Why NOT evaluate the first argument, at least, before making style
>> decisions/assignments?
>>
>> The defense that "everybody already knows this" is irrelevant to
>> the question of how we'd LIKE Plot to behave.
>>
>> Naturally, we won't necessarily GET what we want... but we're
>> entitled to say what that is.
>>
>> I'm trying to think how David Park's Presentations package handles
>> such things.
>>
>> Bobby
>>
>> On Thu, 31 Jul 2008 22:33:50 -0500, AES <siegman at stanford.edu> 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.
>>>
>>>
>>>
>>>
>>
>>
>>
>> --
>> DrMajorBob at longhorns.com
>

```

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