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FindInstance question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg55736] FindInstance question
*From*: János <janos.lobb at yale.edu>
*Date*: Tue, 5 Apr 2005 03:20:55 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
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
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