Square roots that create extensions (extend=True as for integers) for rational number field

[DavidAyotte]

We are implementing square roots that create extensions for elements in rational number field. The code should return the equivalent of the element b in the code below :

sage: P.<x> = QQ[]
sage: K.<a> = NumberField(x^2 - 7)
sage: Q.<y> = K[]
sage: E.<b> = K.extension(y^2 - a)
sage: b^2
a

CC: @kevinywlui

Component: number fields

Keywords: square roots, sd87

Branch/Commit: u/davidayotte/square_roots_that_create_extensions__extend_true_as_for_integers__for_rational_number_field @ 740fd54

Issue created by migration from https://trac.sagemath.org/ticket/23462

[DavidAyotte]

Branch: u/davidayotte/square_roots_that_create_extensions__extend_true_as_for_integers__for_rational_number_field

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a5d2d40

added some doctest

[sagetrac-git]

Commit: a5d2d40

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2d98ff3

the user can now specify the name of the square root

[sagetrac-git]

Changed commit from a5d2d40 to 2d98ff3

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

92b1057

nth root that create extension but it does not work

[sagetrac-git]

Changed commit from 2d98ff3 to 92b1057

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1779b63

implemented nth root that create extension and add doctest

[sagetrac-git]

Changed commit from 92b1057 to 1779b63

[DavidAyotte]

comment:9

I don't think it's the best algorithm, because it's kind of slow.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

740fd54

Square roots and nth roots working

[sagetrac-git]

Changed commit from 1779b63 to 740fd54