Re: Functions, plotting, and other questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg19966] Re: Functions, plotting, and other questions*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Thu, 23 Sep 1999 23:26:17 -0400*Organization*: Universitaet Leipzig*References*: <7sa3vq$mb3@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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