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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