       Re: Solutions that are not solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg32087] Re: Solutions that are not solutions
• From: "M.Weber" <matweber at indiana.edu>
• Date: Sat, 22 Dec 2001 04:23:07 -0500 (EST)
• Organization: Indiana University, Bloomington
• References: <9vuth9\$of2\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```PSi wrote:

> I'm trying to solve a system as follows:
> X={{0,y,z},{y,x,t},{u,v,w}}
> A={{1,1,a},{0,1,0},{0,0,1}}
> Solve[{X.A==Transpose[A].X, Det[X]==1},
> {x,y,z,t,u,v,w}]
>
> Mathematica 4.1 gives two solutions:
> X1={{0,y,0},{y,x,t},{0,v,-1/y^2}}
> and
> X2={{0,y,a*y},{y,(a*t*y^2-1+a*v*y^2-w*y^2)/(a*y)^2,t},
> {a*y,v,w}}
>
> However, X1 is not a solution:
> X1.A-Transpose[A].X1={{0,0,0},{0,0,a*y},{0,-a*y,0}}
>
> Could anybody explain this behaviour?
> Thanks
> PSi

You might want to include 'a' as a variable. However, this is clearly a
bug. I have found similar problems in Version 3 and 4.1 where Mathematica
returns more 'solutions' than exist or where reduce returns an inequivalent
system. Very annoying. But we all think of
course that better graphics has the priority, right?

Matthias

```

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