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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()

 2 None tmonteil 20888 ●25 ●150 ●387 http://wiki.sagemath.o...

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: tried:

K = RealField()
A9 = AffineSpace(K, 2, 'a,b')
A9.coordinate_ring().inject_variables()
W=A9.subscheme([a*b^2]);
W.is_irreducible()W.is_irreducible()