       Re: System for which Solve and NSolve both fail

• To: mathgroup at smc.vnet.net
• Subject: [mg30650] Re: System for which Solve and NSolve both fail
• From: Ben Langton <ben at quickmath.com>
• Date: Sun, 2 Sep 2001 03:58:56 -0400 (EDT)
• References: <9mi1rt\$54r\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thanks for your helpful replies, everyone.

Would I be correct in concluding that Solve (or NSolve for higher degree
systems) will always produce at least a numerical approximation of the
complete solution set for a system of polynomial equations, but is not
guaranteed to do so for non-polynomial systems? Also, is there any reliable
predictor of which non-polynomial systems these commands will fail on (I'm
guessing not, since otherwise WRI would use such a predictor to extend their
software to deal with these cases)? I know this is probably getting a bit
esoteric, but if anyone could shed some light on why these commands work for
some non-polynomial systems but not others, I would be very interested to
find out more.

Regards,

Ben Langton, QuickMath

> From: Ben Langton <ben at spam.bugs.me.quickmath.com>
To: mathgroup at smc.vnet.net
> Organization: OzEmail Ltd, Australia
> Newsgroups: comp.soft-sys.math.mathematica
> Date: Wed, 29 Aug 2001 06:25:01 +0000 (UTC)
> Subject: [mg30650] System for which Solve and NSolve both fail
>
> Hi,
>
> I noticed that Mathematica seems unable to solve this system of equations :
>
> 3^x + 3^y = 90
>
> x + y = 6
>
> With a bit of thought, you can see by inspection that the solutions are
>
> {x , y} = {2 , 4} or {4 , 2}
>
> However, when I use the commands
>
> Solve[{3^x+3^y==90,x+y==6},{x,y}]
>
> or
>
> NSolve[{3^x+3^y==90,x+y==6},{x,y}]
>
> I get a warning message starting with
>
> Solve::incnst: Inconsistent or redundant transcendental equation
>
> Can anyone shed some light on what is going on here? Any way to get around
> this problem?
>
> (I am using Mathematica v 3.0.0.0 under Mac OS 9.2.1, although I believe a
> similar thing occurs under v 4.x)
>
> Regards,
>
> Ben Langton
>
> http://www.quickmath.com/
>

```

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