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MathGroup Archive 2004

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AW: Re: NSolve freezes on two polynomial equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48394] AW: [mg48379] Re: [mg48332] NSolve freezes on two polynomial equations
  • From: Matthias.Bode at oppenheim.de
  • Date: Fri, 28 May 2004 00:50:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Gentlemen:

I made my Mathematica Solve the "innocent looking system of 2 quadratic
equations". It worked with Mathematica 4.2, Windows XP, Dell Latitude D 600,
512 MB:

In[11]:=
(ClearAll[x, y]; )*
  (eqs = {(37.5*(-0.005707305713190276 + 
         12.52471957392599*I + x)*
        (4.672373972379857 + 
         12.52471957392599*I + x))/
       ((100. + 939.3539680444492*I)*x + 
        37.5*x^2 - 487.5*
         (0.4594268481272286 + 
          8.967155112255348*I + y)*
         (1.1815987928984124 + 
          16.08228403559663*I + y)) == 
      -0.03653043382891893, 
     (-487.5*(-1.0444224854481148 + 
         12.524719573925989*I + y)*
        (0.6854481264737559 + 
         12.524719573925989*I + y))/
       ((100. + 939.3539680444492*I)*x + 
        37.5*x^2 - 487.5*
         (0.4594268481272286 + 
          8.967155112255348*I + y)*
         (1.1815987928984124 + 
          16.08228403559663*I + y)) == 
      -0.8852848076704578}; )*
  (sol = Solve[eqs, {x, y}]; Print[sol]; )

From In[11]:=
{{x -> -4.756099422616801 - 
     12.524719573971973*I, 
   y -> 0.24947810152228808 - 
     12.524719573922921*I}, 
  {x -> -4.647002719987395 - 
     12.52471957397541*I, 
   y -> -0.8044685244186461 - 
     12.524719573929334*I}, 
  {x -> 0.0729009975315758 - 
     12.550214172446713*I, 
   y -> -0.28483107133237673 - 
     12.771014333465603*I}, 
  {x -> 0.07290099753245932 - 
     12.49922497531001*I, 
   y -> -0.2848310713460754 - 
     12.278424814386105*I}}

I plugged in the results; equation II:

In[13]:=
(-487.5*(-1.0444224854481148 + 
      12.524719573925989*I + y)*
     (0.6854481264737559 + 
      12.524719573925989*I + y))/
    ((100. + 939.3539680444492*I)*x + 
     37.5*x^2 - 487.5*(0.4594268481272286 + 
       8.967155112255348*I + y)*
      (1.1815987928984124 + 
       16.08228403559663*I + y)) + 
   0.8852848076704578 /. 
  {{x -> -4.756099422616801 - 
      12.524719573971973*I, 
    y -> 0.24947810152228808 - 
      12.524719573922921*I}, 
   {x -> -4.647002719987395 - 
      12.52471957397541*I, 
    y -> -0.8044685244186461 - 
      12.524719573929334*I}, 
   {x -> 0.0729009975315758 - 
      12.550214172446713*I, 
    y -> -0.28483107133237673 - 
      12.771014333465603*I}, 
   {x -> 0.07290099753245932 - 
      12.49922497531001*I, 
    y -> -0.2848310713460754 - 
      12.278424814386105*I}}

Out[13]=
{2.7965885163183657*^-10 - 
   1.80979573072997*^-11*I, 
  -9.459135696943122*^-10 + 
   6.363585730395986*^-11*I, 
  3.1304736580750614*^-10 + 
   9.781465722569389*^-11*I, 
  2.970678147917738*^-10 - 
   1.3786237375214977*^-10*I}

The result is fine but it took some time: 1470 s.

Best regards,
Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Untermainanlage 1
D-60329 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 95 380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de



-----Ursprüngliche Nachricht-----
Von: Daniel Lichtblau [mailto:danl at wolfram.com] 
Gesendet: Mittwoch, 26. Mai 2004 08:42
An: mathgroup at smc.vnet.net
Betreff: [mg48379] Re: [mg48332] NSolve freezes on two polynomial equations


Carlos Felippa wrote:
> This innocent looking system of 2 quadratic equations (extracted with
> InputForm from the guts of a large code) freezes Mathematica 4.2 on my
> Mac.  Same if NSolve is replaced by Solve. I wonder why, and how to
> fix it.  Thanks.
> 
> ClearAll[x,y];
> eqs=
> {(37.5*(-0.005707305713190276 + 12.52471957392599*I + 
>               x)*(4.672373972379857 + 12.52471957392599*I + 
>               x))/((100. + 939.3539680444492*I)*x + 
>           37.5*x^2 - 487.5*(0.4594268481272286 + 8.967155112255348*I +
>                 y)*(1.1815987928984124 + 16.08228403559663*I + 
>                 y)) == -0.03653043382891893,
> (-487.5*(-1.0444224854481148 + 12.524719573925989*I + 
>               y)*(0.6854481264737559 + 12.524719573925989*I + 
>               y))/((100. + 939.3539680444492*I)*x + 
>           37.5*x^2 - 487.5*(0.4594268481272286 + 8.967155112255348*I +
>                 y)*(1.1815987928984124 + 16.08228403559663*I + 
>                 y)) == -0.8852848076704578};
> sol=NSolve[eqs,{x,y}]; Print[sol];
> 

I believe this is a bug in NSolve handling of rational functions (I need 
to look into this further). A work around would be to remove them with 
Numerator[Together[...]].

exprs = {
   (37.5*(-0.005707305713190276 + 12.52471957392599*I + x)*
     (4.672373972379857 + 12.52471957392599*I + x))/
	((100. + 939.3539680444492*I)*x + 37.5*x^2 -
	487.5*(0.4594268481272286 + 8.967155112255348*I + y)*
	(1.1815987928984124 + 16.08228403559663*I + y)) +
-0.03653043382891893,
   (-487.5*(-1.0444224854481148 + 12.524719573925989*I + y)*
     (0.6854481264737559 + 12.524719573925989*I + y))/
	((100. + 939.3539680444492*I)*x + 37.5*x^2 -
	487.5*(0.4594268481272286 + 8.967155112255348*I + y)*
	(1.1815987928984124 + 16.08228403559663*I + y)) +
0.8852848076704578};

Out[24]//InputForm=
{0.04*Second, {{x -> -4.585064233464287 - 12.524719573926033*I,
    y -> 0.20980857814216422 - 12.524719573926097*I},
   {x -> -4.700243789960978 - 12.524719573926033*I,
    y -> -0.8168089849056585 - 12.524719573925948*I},
   {x -> -0.06353162442403039 - 12.49422903643516*I,
    y -> -0.29523493134015644 - 12.79648760504943*I},
   {x -> -0.0635316244240563 - 12.555210111416677*I,
    y -> -0.29523493134014506 - 12.25295154280242*I}}}


Daniel Lichtblau
Wolfram Research


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