Re: How can I plot the region satisfying an inequality?

• To: mathgroup at smc.vnet.net
• Subject: [mg18892] Re: How can I plot the region satisfying an inequality?
• From: phbrf at t-online.de (Peter Breitfeld)
• Date: Sun, 25 Jul 1999 03:30:21 -0400
• Organization: das ist ein breites Feld ...
• References: <7mp3dn\$l99@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```ELodger <elodger at my-deja.com> schrieb:
> Hi There,
>
> Is there a way to plot the region satisfying a set of inequalities,
> such as:
>
> x - y > 0 and
> x + y < 0
>
> on [-10, 10]
>

I have a Function to do this. It requires Algebra`InequalitySolve` and
Graphics`FilledPlot` to work. Sorry for the german usage, but I just
copied it :-)
----------------8<----------------8<----------------
InequalityPlot::usage=
"InequalityPlot[ungl,{x,xmin,xmax},{y,ymin,ymax},(opts)] zeichnet das
Loesungsgebiet der Ungleichung `ungl' in den beiden Variablen `x' und `y'
innerhalb des angegebenen Gebiets. Die Ungleichungen mussen der Syntax
von `InequalitySolve' gehorchen. Moegliche Optionen sind die fur
`FilledPlot' erlaubten."

InequalityPlot[ungl_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_},opts___] :=
Module[{lsg, ur, plots, i, a, b},
lsg = InequalitySolve[(ungl) && (xmin <= x <= xmax) &&
(ymin <= y <= ymax),{x, y}];
ur = ((List @@ lsg) /. LessEqual -> Less);
ur = ur //.
{Inequality[a_, Less, x, Less, b_] -> {x, a, b},
Inequality[a_, Less, y, Less, b_] -> {a, b},
And[a_, b__] -> {a, b},
{a_, HoldPattern[Or[b__]]} :> ({a, #} &) /@ {b} };
b = Position[{ur}, {{_, _, _}, {_, _}}];
a = Table[Extract[{ur}, b[[i]] ], {i, 1, Length[b]}];
plots =
Table[
FilledPlot[a[[i]][[2]], a[[i]][[1]],
DisplayFunction -> Identity, opts],
{i, 1, Length[a]}];
Show[plots, DisplayFunction -> \$DisplayFunction];
]

Protect[InequalityPlot]
----------------8<----------------8<----------------

In:= InequalityPlot[x-y>0 && x+y<0, {x,-10,10},{y,-10,10}];

I don't know if there are still some bugs in it, but it works for your
example and a lot of others I used it for.
I used `Extract' in the code wich is new to Mathematica 4 IIRC, but you can use
`Part' instead with slightly change of the syntax to make it work on Mathematica 3
as well.

When testing this function, I realized, that InequalitySolve returns only
Inequalities in Less and LessEqual. Can the gurus in this group confirm
this observation?

Gruss, Peter
--
=--=--=--=--=--=--=--=--=--=--=--=--= http://home.t-online.de/home/phbrf
Peter Breitfeld, Saulgau, Germany        PGP public key:  08548045

```

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