I'm afraid I don't know the mathematics behind Grobner. In algsys, variables
which are not named are parameters, and any solution must be correct for all
values of the parameters (they are not solved for). Is it correct to call
poly_reduced_grobner on parameters as well as variables?
poly_reduced_grobner also seems very slow (I didn't wait 20 minutes this
time...) in other trivial cases:
poly_reduced_grobner([x=1,y=2],[x,y])
And it seems not to understand constant expressions:
eqs: [ sqrt(2)*y^2 + 2*x^2 - 1, 2*y^2 + sqrt(2)*x^2 - 1 ]
fails though
poly_reduced_grobner( eqs, [x,y,sqrt(2)])
is fine (!!). Same if you substitute %e for sqrt(2).
Is that the way it is supposed to work?
-s