# numerical approximations of complex_embedding

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

numerical approximations of complex_embedding

add a comment

1

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

Asked: **
2014-02-14 00:14:39 -0500
**

Seen: **929 times**

Last updated: **Jul 07 '14**

Numerical approximation of coefficients in fractions

Ignoring the very small imaginary part

Difference between RealField and numerical_approx

Smallest positive numerical solution of an equation in one variable

Weird behaviour/bug with pi and rational exponents

Solving zeta function equation numerically

Getting all (complex) solutions of a non polynomial equation

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.