2018-09-23 12:55:03 +0200 received badge ● Nice Question (source) 2018-09-19 22:51:33 +0200 received badge ● Student (source) 2018-09-19 22:39:03 +0200 asked a question Real Algebraic Scheme question I apologize if this question is too naive. I need to know the irreducible components of an algebraic scheme defined over $\mathbb{R}$. I can get Sage to do this if I consider the scheme is defined over $\mathbb{Q}$, but this is not sufficient to answer my question over $\mathbb{R}$. 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()