Algsys Not Solving A Simultaneous Polynomial I Would Expect It To

Hi Everyone,

I am a big fan of Maxima, but I have stumbled across a simultaneous 
polynomial which algsys (and hence solve) doesn't seem to be able to 
resolve, and I'm wondering if anyone can tell me what the problem is, 
please. Here's the original command:

(%i7) assume (s>0)$
(%i8) algsys([x^2+y^2=4,(s-x)^2+y^2=16,x^2+(s-y)^2=25],[s,x,y]);
(%o8) []

I then tried rewriting the 3 polynomials with their factors expanded:

(%i9) e1: y^2+x^2-4$
(%i10) e2: y^2+x^2-2*s*x+s^2-16$
(%i11) e3: y^2-2*s*y+x^2+s^2-25$
(%i12) algsys([e1, e2, e3], [s,x,y]);
(%o12) []

This would imply that there are no solutions. However - this is not true - 
these simultaneous polynomials can be solved. If I set values for s, x and 
y, and then calculate the expressions, I can obtain the correct results:

(%i57) s: sqrt(sqrt(511)/2+41/2)$
(%i58) x: sqrt(33*sqrt(511)/520+857/520)$
(%i59) y: sqrt(1223/520-33*sqrt(511)/520)$

(%i61) x^2 + y^2;
(%o61) 4

(%i63) y^2+x^2-2*s*x+s^2,numer;
(%o63) 16.0

(%i70) y^2-2*s*y+x^2+s^2,numer;
(%o70) 25.0

I'm not sure if this is related to the algsys problem, but I noticed just 
now that to calculate those expressions, line %i61 above was fine, wheras 
for each of the lines %i63 and %i70, I had to append "numer" to get Maxima 
to calculate the value.

Thanks for any advice!

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