Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: FindInstance puzzler

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83712] Re: FindInstance puzzler
  • From: m.r at inbox.ru
  • Date: Wed, 28 Nov 2007 05:50:25 -0500 (EST)
  • References: <figur5$fpn$1@smc.vnet.net>

On Nov 27, 5:25 am, Tom Burton <n... at brahea.com> wrote:
> A diagnosis seems easy enough, but so far a cure eludes me. Observe  
> that your conditions contain the radical Sqrt[z1^2+4z2]. Your  
> invocation of FindInstance asks it to assume that, not only the  
> variables but also all function values are real, in particular Sqrt,  
> implying that z1^2+4z2>0. Indeed, all points found satisfy this  
> condition. No puzzler here. Unfortunately, when I try the suggested  
> variation to relax this assumption,
>
> RegionPlot[conds,{z1,-.75,2.25},{z2,-1.25,1.25},PlotPoints->90,
> Epilog->Point[{z1,z2}/.
> FindInstance[conds&&Element[{z1,z2},Reals],{z1,z2},10^3]
> ]]
>
> the kernel goes out to lunch.  I hope someone has a better idea.
>
> Tom
>
> When responding, please replace news with my first initial and full  
> last name, as one word.
>
> Tom Burton
>
> > ...
> > RegionPlot[conds, {z1, -.75, 2.25}, {z2, -1.25, 1.25}, PlotPoints -
> > > 90,
> >  Epilog ->  Point[{z1, z2} /. FindInstance[conds, {z1, z2}, Reals,  
> > 10^3]]]
> > ...

Hitting conds a couple of times with a hammer helps:

In[2]:= Reduce[ComplexExpand[conds /. Sqrt[z1^2 + 4 z2] -> r, r] &&
    Element[{z1, z2}, Reals] /.
   a_/z2^2 >= b_ :> a >= b z2^2 && z2 != 0  /.
  r -> Sqrt[z1^2 + 4 z2],
 {z1, z2}]

Out[2]= (z1 == -1/2 && z2 == 1/2) || (-1/2 < z1 < 0 && -z1 <= z2 <= 1
+ z1) || (0 <= z1 < 1 && 0 < z2 <= 1 - z1) || (0 < z1 <= 1 && (-z1^2/4
< z2 < 0 || -z1 <= z2 <= -z1^2/4)) || (1 < z1 < 2 && (-z1^2/4 < z2 <=
1 - z1 || -1 <= z2 <= -z1^2/4)) || (z1 == 2 && z2 == -1)

RegionPlot[conds, {z1, -.75, 2.25}, {z2, -1.25, 1.25},
 PlotPoints -> 90,
 Epilog -> Point[{z1, z2} /. FindInstance[%, {z1, z2}, 10^3]]]

Maxim Rytin
m.r at inbox.ru


  • Prev by Date: Re: Create random binary images
  • Next by Date: Re: Mathematica 6.0 Desperation
  • Previous by thread: Re: FindInstance puzzler
  • Next by thread: Re: FindInstance puzzler