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MathGroup Archive 1993

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Re: ParametricPlot

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: ParametricPlot
  • From: twj
  • Date: Fri, 19 Feb 93 08:41:20 CST

>I have a function of one argument that returns a point in a plane,
>that is a list {a,b}. I would like to get a plot of this function
>and I have used ParametricPlot
>but this is what I get:
>
>In[34]:= ParametricPlot[Td,{theta,-Pi,Pi}]
>
>ParametricPlot::ppcom: 

>   Function Td cannot be compiled; plotting will proceed with the  
>uncompiled
>     function.
>
>ParametricPlot::pptr: 

>   Td does not evaluate to a pair of real numbers at theta = -3.14159.

There are two problems here as shown by the two error messages.  The
second message arrives because ParametricPlot has set theta to a value
and then evaluated the first argument Td.    It is expecting the first
argument to evaluate to a pair of real numbers and since it has not
an error results.  I presume the problem here is that Td is set up to
be a function of one argument and hence the error results.  To make it
work we must supply the argument...

In[4]:=  Td[ t_] := {Sin[t], Cos[t]}

In[5]:= ParametricPlot[ Td[ t], {t,0,Pi}]

ParametricPlot::ppcom: 

   Function Td[t] cannot be compiled; plotting will proceed with the
     uncompiled function.

Out[5]= -Graphics-

ParametricPlot cannot do this automatically since it is possible that
instead Td may have been set to return an expression...

In[8]:= Td := {Sin[2 t], Cos[t]}

In[9]:=  ParametricPlot[ Td, {t,0,Pi}]

ParametricPlot::ppcom: 

   Function Td cannot be compiled; plotting will proceed with the uncompiled
     function.

Out[9]= -Graphics-


The other problem which is demonstrated by the ParametricPlot::ppcom message
is from the Mathematica compiler.  At the moment this can only return 

numbers.   The example here is trying to return a list of numbers which 

cannot be done and the compiler cannot be used.  ParametricPlot then 

continues with the uncompiled function and the result is EXACTLY the same
as if the command

In[10]:=  ParametricPlot[ Td, {t,0,Pi}, Compiled -> False]

Out[10]= -Graphics-

was entered which does not use the internal compiler.

Tom Wickham-Jones
WRI










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