Re: Why does Mathematica 5.0 fail where Mathematica 4.1 works ?

• To: mathgroup at smc.vnet.net
• Subject: [mg47009] Re: Why does Mathematica 5.0 fail where Mathematica 4.1 works ?
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Sat, 20 Mar 2004 03:50:22 -0500 (EST)
• References: <c3e5b5\$qm1\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```For version 5.0.1 on a Mac

k=E;

Solve[{y==x^y, y==k}, x]

"Inverse functions are being used by Solve, so some solutions may not be found;
use Reduce for complete solution information. ..."

{{x -> (1/y)^(-y^(-1))}}

Simplify[%, y>0]

{{x -> y^(1/y)}}

Using Reduce as suggested by Solve::ifun goes off somewhere for longer than I
will wait.  However, if you limit it to the real domain, Reduce returns (albeit
slowly):

Reduce[{y==k, y==x^y}, x, Reals]

y == E && x == E^(1/E)

Bob Hanlon

In article <c3e5b5\$qm1\$1 at smc.vnet.net>, Oleksandr Pavlyk <pavlyk at phys.psu.edu>
wrote:

<< I was looking at excellent talk by Daniel Lichtblau
"Tactics for solving equations in Mathematica" from

http://library.wolfram.com/infocenter/Conferences/337/

In the "Tricky Solve problem" chapter we find the
following

k = E;
Solve[ { y == x^y , y == k }, x ]

So here are outputs in the freshly started notebooks in
two versions of Mathematica

Mathematica 4.1 on Solaris returns

E^(1/E)

and Mathematica 5.0 on Windows returns

(1/y)^(-1/y)

where y is an unknown variable.

Both versions complain that inverse functions were used and hence
some solution maybe lost. See output from 5.0 attached below.

I would not be surprised of somebody tells me this bug has been fixed
in 5.0.1. In fact this is what happened with all earlier bug reports
posted on this mailing list. >><BR><BR>

```

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