I apologize if this question is too naive.
I need to know the irreducible components of an algebraic scheme defined over R. I can get Sage to do this if I consider the scheme is defined over Q, but this is not sufficient to answer my question over R.
Can Sage actually do this for real algebraic schemes?
and here is the code I tried: K = RealField() A9 = AffineSpace(K, 2, 'a,b') A9.coordinate_ring().inject_variables() W=A9.subscheme([a*b^2]); W.is_irreducible()