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20201215 11:44:22 +0200  asked a question  Inconsistentency in parent of specialization of a polynomial? I have a family of polynomials and I want to consider special members of this family. In other words I'm considering polynomials in a ring $R = K[x]$ where $K = \mathbb{Q}[t]$. In sage I do the following: This works fine and as expected $f_1$ is a polynomial only in $x$: Now I want to do exactly the same but over $\overline{\mathbb{Q}}$ instead: I would expect $g_1$ to be a polynomial only in $x$ as above, i.e. I would expect $g_1 \in \overline{\mathbb{Q}}[x]$. However, I get: Is this a bug? Or am I misunderstanding something? 
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20190712 17:57:11 +0200  commented answer  Constructing a number field with complex embedding Thanks! I am a bit confused though: Why can we not choose the solution with positive imaginary part for 
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20190712 08:05:18 +0200  asked a question  Constructing a number field with complex embedding I am using the function sage: number_field_elements_from_algebraics([1 + sqrt(7)], embedded=True) (Number Field in a with defining polynomial y^2  7 with a = 2.645751311064591?, [a + 1], Ring morphism: From: Number Field in a with defining polynomial y^2  7 with a = 2.645751311064591? To: Algebraic Real Field Defn: a > 2.645751311064591?) sage: number_field_elements_from_algebraics([1 + sqrt(7)], embedded=True)  NotImplementedError Traceback (most recent call last) <ipythoninput1ac220615ad5b> in <module>() > 1 number_field_elements_from_algebraics([Integer(1) + sqrt(Integer(7))], embedded=True) /usr/lib/python2.7/sitepackages/sage/rings/qqbar.pyc in number_field_elements_from_algebraics( numbers, minimal, same_field, embedded, prec) 2242 real_case = False 2243 if embedded: > 2244 raise NotImplementedError 2245 # Make the numbers algebraic 2246 numbers = [mk_algebraic(_) for _ in numbers] NotImplementedError: What is the reason for why only embeddings of real numbers are supported? I modified the code in The relevant code in
