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Re: What's going on here (Table-generated lists)?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98092] Re: What's going on here (Table-generated lists)?
  • From: Albert Retey <awnl at gmx-topmail.de>
  • Date: Mon, 30 Mar 2009 04:41:38 -0500 (EST)
  • References: <gqfl2e$ksp$1@smc.vnet.net> <gqiaag$op5$1@smc.vnet.net> <gqkuvv$4bt$1@smc.vnet.net>

Erik Max Francis wrote:
Hi,

> Thanks to you and everyone who responded.  I do understand the HoldAll
> attribute and why Plot is doing what it's doing.
> 
> I fully understand why the HoldAll attribute is generally useful and why
> it's used here, but I still don't see why it doesn't make sense for Plot
> to recognize a list as an actual list and plot each with a different
> color.  Shouldn't it be manually evaluating its argument, then plotting
> with different colors if it ends up with a list?
> 
> Is there any particular situation where you'd want the current behavior
> -- not the HoldAll, but rather the plotting what ends up being a list of
> functions with the same color?

I think it is a general problem: how many colors would you expect for this:

Plot[Table[x^n, {n, 0, Floor[x]}], {x, 1, 10}, PlotRange -> All]

or for this:

f[x_] := (Pause[120]; Exp[x])

f[x_?NumericQ] := {Exp[x], Log[x]}

Plot[f[x], {x, 0, 1}]

Of course Plot could be programmed so that it detects more unambiguous
cases and not only explicit Lists, but it also need to be reasonably
fast, so there always is a limit on what it can handle "as intended". I
think the current behaviour is not too bad and there is a very simple
workaround with which you can control exactly what it will do...

albert


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