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Re: A riddle: Functions that return unevaluated when they

• To: mathgroup at smc.vnet.net
• Subject: [mg82449] Re: [mg82394] A riddle: Functions that return unevaluated when they
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Sat, 20 Oct 2007 05:58:26 -0400 (EDT)
• References: <200710190859.EAA04845@smc.vnet.net>

Dear Szabolcs,

I am not getting this timing behavior in another instance,
using a fresh kernel:

e.g.,
In[1] = FindInstance[a > b && b > c, {a, b}] // Timing
returns an FindInstance::exvar error, and the result
Out[1]= {0.036232, FindInstance[a > b && b > c, {a, b}]}

But,
In[2] = FindInstance[a > b && b > c, {a, b}] // Timing
also returns an FindInstance::exvar error, but the result
Out[2] = {0.002348, FindInstance[a > b && b > c, {a, b}]}
Craig

> Date: Fri, 19 Oct 2007 04:59:08 -0400 (EDT)
> From: Szabolcs Horv=E1t <szhorvat at gmail.com>
> In[1]:=
> FindInstance[
>     x^3+y^3==z^3 && x>0 && y>0 && z>0,
>     {x,y,z}, Integers] // Timing
>
> During evaluation of In[1]:= FindInstance::nsmet: The methods available
> to FindInstance are insufficient to find the requested instances or
> prove they do not exist. >>
>
> Out[1]=
> {1.156, FindInstance[x^3+y^3==z^3&&x>0&&y>0&&z>0,{x,y,z},Integers]}
>
> Evaluating this expression takes a relatively long time on my system (~1
> sec).  If FindInstance cached its result the way I described above, then
> subsequent evaluations should be instantaneous.  But they aren't!
>
> In[2]:=
> FindInstance[x^3+y^3==z^3&&x>0&&y>0&&z>0,{x,y,z},Integers]//Timing
>
> During evaluation of In[2]:= FindInstance::nsmet: The methods available
> to FindInstance are insufficient to find the requested instances or
> prove they do not exist. >>
>
> Out[2]= {1.063,FindInstance[x^3+y^3==z^3&&x>0&&y>0&&z>0,{x,y,z},Int=
egers]}
>

• References:
  • A riddle: Functions that return unevaluated when they cannot solve
    • From: Szabolcs Horvát <szhorvat@gmail.com>