       solving with inverse functions/inexact coefficients

• To: mathgroup at smc.vnet.net
• Subject: [mg67397] solving with inverse functions/inexact coefficients
• From: Dave Spence <dspence at ics.mq.edu.au>
• Date: Wed, 21 Jun 2006 02:13:39 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I'm trying to solve a set of simultaneous equations describing a laser cavity. A much simplified set of equations in Real unknowns F1, F2 and NU looks like this:

F2  == Exp[0.76 NU] F1, F1 == 0.5 F2 Exp[0.76 NU], 0.5 F2 + NU == 15

They can be solved by hand very easily with two solutions, {F1=F2=0 && NU = 15} and {NU=0.46, F1=14.5,  F2=29.1}

Now Solve cannot solve these equations unless I change both instances of 0.76 to integers. Reduce seems to hang (or at least take too long to return and answer). Reduce can solve the problem quickly if I change both instances of 0.76 to 0.75! Reduce gives the message "Reduce::ratnz: Reduce was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result"

I guess this is just a difficulty with the way mathematica attempts to solve problem. There are references in the manuals to difficulties solving multiple simultaneous equations that all invoke inverse functions. Are there any options I can set to enable mathematica to quickly solve these equations?

I note that while these equations can be manipulated by hand into a form that can be solved by mathematica, by full set of equations are far more complex and can't easily be edited by hand.

```

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