Re: Ploting a transformation of a set
- To: mathgroup at smc.vnet.net
- Subject: [mg123323] Re: Ploting a transformation of a set
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Thu, 1 Dec 2011 05:53:24 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201111300819.DAA17061@smc.vnet.net>
t = (x + y < 2 && 0 < x < 2 && 0 < y < 2) /.
Solve[{xp == Sqrt[x + y/2], yp == Sqrt[y + x/2]},
{x, y}][[1]] // Simplify
xp^2 + yp^2 < 3 && 0 < 2*xp^2 - yp^2 < 3 && -3 < xp^2 - 2*yp^2 < 0
Manipulate[
Module[{
aps = AbsolutePointSize[4],
ap = (Appearance -> "Labeled")},
Row[{
RegionPlot[x + y < 2 && 0 < x < 2 && 0 < y < 2,
{x, 0, 2}, {y, 0, 2},
ImageSize -> 200,
Epilog -> {Red, aps, Point[{h, v}]}],
RegionPlot[t, {xp, 0, 2}, {yp, 0, 2},
ImageSize -> 200,
Epilog -> {Red, aps,
Point[{Sqrt[h + v/2], Sqrt[v + h/2]}]}]}]],
{{h, .5, "x"}, 0, 2, .01, ap},
{{v, .5, "y"}, 0, 2, .01, ap}]
Bob Hanlon
On Wed, Nov 30, 2011 at 3:19 AM, Justin <justin.valasek at gmail.com> wrote:
> Hello,
> I would like to plot the following transformation of the set {x,y; x+y<2 & x>0 & y> 0} => {(x+.5y)^.5, (y+.5x)^.5}.
> Is there any way to do this in mathematica?
> thanks
>