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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97993] Re: What's going on here (Table-generated lists)?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 27 Mar 2009 05:36:32 -0500 (EST)
  • References: <gqfl2e$ksp$1@smc.vnet.net>

Hi,

consider the function myTest[]

defined as follows

SetAttributes[myTest, HoldAll]
myTest[funs : {__}, {x_Symbol, x0_?NumericQ,
    x1_?NumericQ}] := "List of functions."

myTest[fun_, {x_Symbol, x0_?NumericQ,
    x1_?NumericQ}] := "Single function."

and what may come out from

{myTest[{x, Sin[x], Cos[x]}, {x, 0, Pi}],
  myTest[Table[Cos[k*x], {k, 3}], {x, 0, Pi}],
  myTest[Evaluate[Table[Cos[k*x], {k, 3}]], {x, 0, Pi}]}

as expected you get

{"List of functions.", "Single function", "List of functions."}

and this is so, because the patterns are defined in that way.
And as you have noticed, the myTest[] function behave in the
same way as Plot[] does.

Regards
   Jens


Erik Max Francis wrote:
> I'm seeing a difference in behavior with Plot in conjunction with Table, 
>   and I'm rather confused at the reason.  If I use Plot to plot a list 
> of functions, it works as expected, and I get a plot with each function 
> in its own color:
> 
> Plot[{x, 2 x, 3 x, 4 x, 5 x}, {x, -1, 1}]
> 
> If I use Table, then this doesn't work the same way -- the five lines 
> are all plotted with the same color:
> 
> Plot[Table[k x, {k, 1, 5}], {x, -1, 1}]
> 
> I verified that the both objects created have a Head of List, so I don't 
> see anything obviously different about them.
> 
> Here's what confuses me more:  If I generate the table separately and 
> then use that as a result in a later evaluation in the Plot, then I get 
> the colors back:
> 
> In[25]:= Table[k x, {k, 1, 5}]
> 
> Out[25]= {x, 2 x, 3 x, 4 x, 5 x}
> 
> In[26]:= Plot[%, {x, -1, 1}]
> 
> What is going on here?  Is it something like Plot does a special scan of 
> its first argument before Evaluating it, and if it doesn't start out as 
> a List, it concludes that it's all one thing and plots it with the same 
> color, as opposed to an explicitly provided list of separate colors?
> 


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