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Substituting a complex embedding for a number field element

asked 2017-12-08 06:34:33 +0200

jaebond gravatar image

Is there a way to take an element of a number field (or a polynomial or a number field) and replace the generator of the field by one of its complex embeddings? For example, something like

sage: K.<a> = NumberField(x^2 - 3)
sage: (3*a + 5).substitute(a=a.complex_embeddings()[1])

It's feasible to do this with sage_eval, but hopefully there is a better way.

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answered 2017-12-08 08:36:37 +0200

FrédéricC gravatar image

Like that

sage: K.<a> = NumberField(x^2 - 3)
sage: z=K.complex_embeddings()[1]
sage: z(3*a+1)
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Asked: 2017-12-08 06:34:33 +0200

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Last updated: Dec 08 '17