       Functions, plotting, and other questions

• To: mathgroup at smc.vnet.net
• Subject: [mg19947] Functions, plotting, and other questions
• From: bt585 at FreeNet.Carleton.CA (Michael Chang)
• Date: Wed, 22 Sep 1999 04:11:23 -0400
• Organization: The National Capital FreeNet
• Sender: owner-wri-mathgroup at wolfram.com

Hallo everyone!

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.

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

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:

x=(10^(1-g)-(1-g)t)^(1/(1-g))
z=-(10^(1-g)+(g-1)t)^(g/(1-g))

I'd like to start my simulation from time t=0, and simulate until time t_f
since for times>t_f, my equation 'blows up'.  I'd like the axis of my
surface plot to be x,g,z, but with each 'line' of my surface plot
generated with a variable t_f(g) so that my equations still yield
real-valued results.

(t_f(g)=10^(1-g)/(1-g) and g>1/2 and <1 (say))

Now, I can generate a (2D) ParametricPlot of this for a fixed g *and* a
fixed t_f(g).  What I'd now like to do is generate a set of such (2D)
plots for varying g *AND* therefore varying t_f, and then plot out these
results in *3D*, with z my height, and x and g my length and width.

(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.

Thanks very much in advance!

Mike

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