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Re: Solutions that are not solutions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg32091] Re: Solutions that are not solutions
*From*: "PSi" <no at tee.gr>
*Date*: Sat, 22 Dec 2001 04:23:19 -0500 (EST)
*References*: <9vuth9$of2$1@smc.vnet.net> <ide62uoerv0s19vjoh6haskthif0drb7qs@4ax.com>
*Sender*: owner-wri-mathgroup at wolfram.com
I have nine such systems of equations, some of them with much more
complicated A and X, giving four or five solutions.
The actual warning message is "Equations may not give solutions for
all "solve" variables".
----- Original Message -----
From: "Tom Burton" <tburton at cts.com>
To: mathgroup at smc.vnet.net
Subject: [mg32091] Re: Solutions that are not solutions
> Hello,
>
> This system of equations contains only four nontrivial equations
(the rest being tautologies)
>
> t + a y == t + z
> u + v == v + a y
> a u + w == w + a z
> 2
> t u y - w y - u x z + v y z == 1
>
> Furthermore, only two of the first three are linearly independent,
yielding by inspection u == z == ay. Hence the warning from the
solver that not all variables are found. You need to supplement
solution 1 with the additional specification y==0.
>
> Tom Burton
>
> On Fri, 21 Dec 2001 08:57:13 +0000 (UTC), in
comp.soft-sys.math.mathematica you 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}}
>
> Tom Burton
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