Ask Your Question

numerical approximations of complex_embedding

asked 2014-02-14 07:14:39 +0200

cjsh gravatar image

updated 2014-06-29 15:00:50 +0200

vdelecroix gravatar image

How can I get a numerical approximation of an expression like 3^(1/2)/2 which is not 0.866025403784439?

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted

answered 2014-06-29 14:59:01 +0200

vdelecroix gravatar image

updated 2014-06-29 15:01:15 +0200

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)

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)


edit flag offensive delete link more


thank you very much!

cjsh gravatar imagecjsh ( 2014-07-07 11:19:41 +0200 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools



Asked: 2014-02-14 07:14:39 +0200

Seen: 1,091 times

Last updated: Jul 07 '14