This is definitely a bug in RootFinding:-Isolate. Could you please post the system which produces this error ? As an alternative, you might try the fsolve command. If you post the system I may be able to give you other suggestions as well.

This is the system as rendered by my cut and paste and plain text conversion of sb572's post.

sys:=
{
x[1]^2+y[1]^2-1 ,
x[2]^2+y[2]^2-1 ,
x[3]^2+y[3]^2-1 ,
x[4]^2+y[4]^2-1 ,
x[5]^2+y[5]^2-1 ,

x[1]*x[2]+x[1]*x[3]+y[1]*y[3]+y[1]*y[5]+x[2]*x[5]+x[1]*x[5]+x[3]*x[4]
+y[3]*y[5]+y[2]*y[3]+x[3]+x[4]+x[1]*x[4]+x[3]*x[5]+y[1]*y[4]
+y[1]*y[2]+x[4]*x[5]+x[5]+y[3]*y[4]+y[2]*y[4]+x[1]+x[2]*x[4]+x[2]+
x[2]*x[3]+y[2]*y[5]+y[4]*y[5],

-y[3]*sqrt(3)*x[4]+2*x[1]*y[3]*sqrt(3)-2*y[1]*x[3]*sqrt(3)+x[3]*y[4]*sqrt(3)
+y[1]*x[5]*sqrt(3)-2*y[2]*sqrt(3)*x[5]+y[4]*sqrt(3)*x[5]+y[2]*sqrt(3)*x[3]
-x[2]*y[3]*sqrt(3)+y[1]*sqrt(3)+3*y[1]*y[5]+3*x[1]*x[5]
-x[4]*y[5]*sqrt(3)+3*x[3]*x[4]+3*y[2]*y[3]+2*x[2]*y[5]*sqrt(3)
-2*y[4]*sqrt(3)+3*x[4]*x[5]+3*y[3]*y[4]+3*x[1]-x[1]*y[5]*sqrt(3)
+3*x[2]+y[2]*sqrt(3)+3*x[2]*x[3]+3*y[4]*y[5],

-y[3]*sqrt(3)*x[4]+x[3]*y[4]*sqrt(3)+y[1]*x[5]*sqrt(3)-y[2]*sqrt(3)*x[5]
-y[4]*sqrt(3)*x[5]+y[2]*sqrt(3)*x[3]-y[1]*x[2]*sqrt(3)-x[3]*y[5]*sqrt(3)
+x[1]*y[2]*sqrt(3)-x[2]*y[3]*sqrt(3)+y[1]*sqrt(3)+x[4]*y[5]*sqrt(3)
-3*x[1]*x[3]+x[2]*y[5]*sqrt(3)-y[4]*sqrt(3)+y[3]*sqrt(3)-3*x[5]-3*y[1]*y[3]
-3*y[2]*y[4]+x[1]*y[4]*sqrt(3)-x[1]*y[5]*sqrt(3)-y[2]*sqrt(3)-3*x[2]*x[4]
+y[3]*sqrt(3)*x[5]-y[1]*x[4]*sqrt(3),

y[2]*sqrt(3)*x[4]-x[1]*y[3]*sqrt(3)+y[1]*x[3]*sqrt(3)-y[4]*sqrt(3)*x[5]
+y[2]*sqrt(3)*x[3]-2*x[3]*y[5]*sqrt(3)-x[2]*y[3]*sqrt(3)+y[1]*sqrt(3)
+y[5]*sqrt(3)+x[4]*y[5]*sqrt(3)-3*y[2]*y[3]-3*y[4]*y[5]-3*x[1]*x[3]
-3*x[2]*x[3]-x[2]*y[4]*sqrt(3)-3*x[5]-3*y[1]*y[3]-3*x[1]-3*y[2]*y[4]
+2*x[1]*y[4]*sqrt(3)-2*y[2]*sqrt(3)-3*x[4]*x[5]-3*x[2]*x[4]
+2*y[3]*sqrt(3)*x[5]-2*y[1]*x[4]*sqrt(3),

y[2]*sqrt(3)*x[4]+x[1]*y[3]*sqrt(3)-y[1]*x[3]*sqrt(3)+2*y[4]*sqrt(3)*x[5]
+y[5]*sqrt(3)-2*x[4]*y[5]*sqrt(3)-3*y[2]*y[3]-3*y[4]*y[5]-3*y[3]*y[5]
-3*y[2]*y[5]-3*x[3]-2*y[3]*sqrt(3)-3*x[4]-3*x[2]*x[3]-x[2]*y[4]*sqrt(3)
-2*x[1]*y[2]*sqrt(3)-3*y[1]*y[4]-3*x[1]-3*x[1]*x[2]+2*y[1]*x[2]*sqrt(3)
+y[3]*sqrt(3)*x[4]-3*x[3]*x[5]+y[2]*sqrt(3)-3*x[1]*x[4]-3*x[4]*x[5]
-3*x[2]*x[5]+x[1]*y[5]*sqrt(3)-y[1]*x[5]*sqrt(3)-x[3]*y[4]*sqrt(3)-3*y[1]*y[2]
};

Maple 12's solve throws FGb at this system and it runs out of memory trying to get a tdeg Gröbner basis.  Maple 11's solve uses different techniques and hasn't crashed on it after about an hour and looks doomed to churn for as long as I let it.   So, the obvious things don't work...

John

To me it looks as a system of quadrics and generically they intersect
discrete due to dim = #equations. But the only thing I can 'see' or
guess is that the first 5 are equivalent to "Mittelpunktsflächen"
(= "centered hypersurfaces" ?) and the others seem parabolic. Not sure,
but if one would have the normal form for them, then it may be clearer.

The reason for the question might certainly help ... sqrt(3) smells
a bit like something based on Algebra or Number Theory.

And if the solution is not a discrete set, then it might matter over
which ring this is considered (not that I want to solve it ... never
used that corner of Maple).

Thanks for your comments,

replacing the sqrt(3) by the variable s3 and adding the equation s3^2-3 worked using the function Isolate. So thanks for that suggestion.

Does anyone know why this might be the case? i.e. why the computation is easier if we add an extra equation and variable but make all of the coefficients integers?

Also, I'm interested in exactly how the "Isolate" function works - in particular how would I use the Groebner bases functions to reproduce the results? For example if I call Groebner[bases] and use the tdeg ordering Maple doesn't finish the computation even after 24 hours (compared to the 1min it takes using the Isolate function).

Steve