> It is highly likely that this system was solved by an earlier version of algsys.
(1) Maxima 5.9.0 (circa 2003) is unable to solve this equation:
(C2) algsys([x^2 + y^2 = 1, (x - 0.5)^2 + (y - 0.5)^2 = 1],[x,y]);
(D2) []
(C3) build_info();
Maxima version: 5.9.0
Maxima build date: 19:10 2/9/2003
The sourceforge download page has Maxima back to 5.0 -- these are tar.gz files ( I was too lazy to try them).
(2) The source code documentation for algsys says
"It solves systems of polynomial equations by straight-forward resultant hackery."
Although I don't know how algsys expunges spurious roots, the source code comment and code
;;note if $algepsilon is too large you may lose some roots.
(defmvar $algdelta 1e-5 )
is a bit sketchy, I think. The variable algdelta is undocumented.
(3) Since 2000, algsys has been modified about 15 times. Mostly of these changes seem fairly minor: change $algdelta from 1e-4 to 1d-4, for example.
Of course, changes to other files might have introduced the bug algsys([x^2 + y^2 = 1, (x - 0.5)^2 + (y - 0.5)^2 = 1],[x,y]) --> [] bug.
--Barton