This is (has been for some time) marked as a known bug in the
rtest_to_poly_solver.mac.
Barton
-----Robert Dodier <robert.dodier at gmail.com> wrote: -----
>>?$?./maxima-local
>>?Maxima?5.18post?http://maxima.sourceforge.net
>>
>>?(%i2)?load("to_poly_solver.mac")$
>>?(%i3)?display2d?:?false$
>>
>>?(%i4)?to_poly_solve(q*sqrt(q^2+2)-1,q);
>>?(%o4)?%union([q?=?-1/sqrt(1-sqrt(2))],[q?=?1/sqrt(1-sqrt(2))],[q?=
>1/sqrt
>>?(sqrt(2)+1)])
>
>Unfortunately?this?isn't?right?either.?The?first?solution?is?spurious,
>isn't?it?
>float(subst(q?=?-1/sqrt(1-sqrt(2)),?q*sqrt(q^2+2)-1))?=>?-
>1.999999999999999
>
>Thanks?for?your?help
>
>Robert?Dodier