# 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

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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

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

Seen: **1,053 times**

Last updated: **Jul 07 '14**

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