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Re: Functions, plotting, and other questions


Hi Michael,


> I'm running Mathematica 3.0.x on Winduh NT, and have a couple of general
> questions concerning functions, 3D plots, and logical statements.
> 
> First, is there a way to tell Mathematica that I want to have a variable
> treated as being strictly real (or positive real, or imaginary, etc)?
> Specifically, I'm thinking that being able to do so might result in
> 'better' Simplify results, for instance.

No, in Mathematica 4.0 you can give Simplify[], FullSimplify[] 
the additional assumptions, in Mathematica 3.x not.

> 
> Also, I noticed that there is an If statement, but no Elseif.  I guess
> that the Which statement essentially replicates If ... Elseif statements?

You can nest the If[] statements 

If[someTest1,
  makeSomething[],
(* Else *)
  If[someTest2,
    makeSomething1[]
   ]
 ]

    > 
> My final (and more pressing) question concerns 3d graphing of functions in
> Mathematica.  My problem arises from the fact that I want to do a *surface*
> plot of the following parametric equations:

SNIP SNAPP SNIP

> (Essentially, I want to do a surface parametric plot, with varying
> simulation times depending on what g is ... kind of like double integrals,
> with on limit (x) from 0 to 1, and another limit (y) from 0 to x.)
> 
> Is there a way to do this?  I've been struggling with this for a while,
> and don't see anyway to do this.

I don't know if I understand your explanation right. You want a
ParametricPlot3D[]
with a non rectanglular area in the parameter space ?

a) You can do it by your self and creating the Polygon[] primitives
b) You can use a construct like

ParametricPlot3D[
    Catch[
      If[x > y, Throw[{x, x, x^2}], {x, y, x*y}]],
    {x, 0, 1}, {y, 0, 1}, 
    Compiled -> False, 
    ViewPoint -> {-1.604, -2.208, 2.000}
  ]

it will draw the function z= x*y for x in [0,1] and y in [0,x]

Hope that helps
  Jens


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