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Re: Solutions that are not solutions


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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