numerical approximations of complex_embedding

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Complex embeddings are defined for number fields. You can for example do:

sage: e = QQbar(3^(1/2)/2)
sage: K,e1,phi = e.as_number_field_element()
sage: g = e1.galois_conjugate(QQbar)
sage: g      # these are arbitrary precision
[-0.866025403784439?, 0.866025403784439?]
sage: g[0].numerical_approx(digits=100)
-0.86602540378443864676372317075293618347140262690519

But since your example is a square root the embeddings are itself and its negative, so you can do in a more straightforward way:

sage: (-3^(1/2)/2).numerical_approx(digits=50)
-0.86602540378443864676372317075293618347140262690519

Vincent