Re: FindInstance question

*To*: mathgroup at smc.vnet.net*Subject*: [mg55770] Re: [mg55736] FindInstance question*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Wed, 6 Apr 2005 03:10:59 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

Needs["Graphics`"]; FilledPlot[{x,x^2},{x,-1,2}]; FilledPlot[{0,Boole[x<x^2]}, {x, -1, 2}]; ListPlot[x/.FindInstance[{x<x^2,x>-1,x<2}, x,Reals,100]]; Bob Hanlon > > From: János <janos.lobb at yale.edu> To: mathgroup at smc.vnet.net > Date: 2005/04/05 Tue AM 03:20:55 EDT > To: mathgroup at smc.vnet.net > Subject: [mg55770] [mg55736] FindInstance question > > If I am looking for the solution set of x < x^2, Reduce gives me the > answer: > > In[14]:= > Reduce[x < x^2, x] > Out[14]= > x < 0 || x > 1 > > I tried to use FindInstance and ListPlot to visualize it for my 7th > grade son, based upon the example on the Book Section 3.4.8. > > In[15]:= > FindInstance[x < x^2, x, > Reals, 50] > Out[15]= > {{x -> -4375}, {x -> -4304}, > {x -> -4089}, {x -> -3945}, > {x -> -3707}, {x -> -3682}, > {x -> -3486}, {x -> -3414}, > {x -> -3331}, {x -> -3286}, > {x -> -3248}, {x -> -3018}, > {x -> -2974}, {x -> -2953}, > {x -> -2941}, {x -> -2877}, > {x -> -2864}, {x -> -2687}, > {x -> -2525}, {x -> -2373}, > {x -> -2108}, {x -> -2074}, > {x -> -1773}, {x -> -1403}, > {x -> -1402}, {x -> -1348}, > {x -> -1092}, {x -> -566}, > {x -> -51}, {x -> 77}, > {x -> 195}, {x -> 1181}, > {x -> 1216}, {x -> 1547}, > {x -> 1687}, {x -> 1765}, > {x -> 1876}, {x -> 2040}, > {x -> 2713}, {x -> 2734}, > {x -> 3018}, {x -> 3312}, > {x -> 3455}, {x -> 3503}, > {x -> 3704}, {x -> 3927}, > {x -> 3974}, {x -> 3985}, > {x -> 4349}, {x -> 4944}} > > Well, the closest values to 0 and 1 are -51 and 77. It is not > terrible useful to ListPlot them. If I select 500 points instead of > 50 it just gets worse. > > My question is: > > 1, Is it possible to suggest FindInstance to use values "much > closer" to the boundaries of 0 and 1 or > > 2 If it is not possible, what methods others would use for this > situation to visualize ? > > I tried > > In[18]:= > FindInstance[x < x^2 && > x > -2 && x < 2, x, Reals, > 50] > > but that is not the original inequality :) > I also tried to replace the Reals domain with something - logical > looking - else, but Mathematica really wants a built in domain there. > > In[32]:= > FindInstance[x < x^2, x, > x > -2 && x < 2, 50] > > or > > In[37]:= > FindInstance[x < x^2, x, > {-2, 2}, 50] > > and it complained: > > FindInstance::"bddom":"Value \!\(\(\(x > \(\(-2\)\)\)\) && \(\(x < 2\) > \)\) of \ > the domain argument should be Complexes, Reals, Algebraics, Rationals, \ > Integers, Primes, Booleans, or Automatic. \ > \!\(\*ButtonBox[\"More\[Ellipsis]\", ButtonStyle->\"RefGuideLinkText > \", \ > ButtonFrame->None, ButtonData:>\"FindInstance::bddom\"]\)" > > > A non existent "user defined Domain" would be handy here. I am > thinking of a > > myDomain[x_Real]:=UserDefinedDomain[x > -2 && x < 3] > > or similar construction to put into FindInstance. Is that too much > to ask ? > > Thanks ahead, > > János > > > >