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MathGroup Archive 2005

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Re: Kernel Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54943] Re: Kernel Problem
  • From: Peter Pein <petsie at arcor.de>
  • Date: Mon, 7 Mar 2005 02:10:27 -0500 (EST)
  • References: <d0denl$lfr$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dana DeLouis wrote:

> Hello.  I'd like to ask a question.  The function below shuts down my
> Kernel.  Is it just me, or is this reproducible on other Windows machines.
> Thanks for any feedback.
> 
> Needs["NumberTheory`NumberTheoryFunctions`"]
> 
> Information[QuadraticRepresentation]
> 
>  "QuadraticRepresentation[d, n] gives {x, y}, where x^2 + d y^2 = n for \
> positive d and odd n."
> 
> QuadraticRepresentation[12, 9]
> 
> (Problem, and the Kernel shuts down!)
> 
> TIA
> Dana DeLouis
> 
Simply define your own function:

In[1]:=
QuadRep[d_, n_, sel_:{First, #1 & }] :=
If[Length[#]<2,{},#]&@
  Flatten[
  Extract[#1, (Position[#1, sel[[1]][#1], 1, 1] & )[sel[[2]] /@ #1]] &
   [Block[{x, y, Null}, {x, y} /.
      {ToRules[Reduce[{x^2 + d*y^2 == n && x>=0&&y>=0},
                      {x, y},Integers]]}]],
  1]
In[2]:= QuadRep[12,9]
Out[2]= {3,0}

from the Mathematica documentation:
In[3]:= QuadRep[3,13*31*61*Prime[10^7]]
Out[3]= {778,1212545}

or select the solution with the smaller of {x,y} becoming maximal:
In[4]:= QuadRep[3,13*31*61*Prime[10^7],{Max,Min}]
Out[4]= {1118614,1026239}

This is just a quick hack and might need further verification.

-- 
Peter Pein
Berlin


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