# Compute common number field of algebraic numbers

Suppose we have a list of algebraic numbers, e.g., `a1,a2,a3`

in `QQbar`

. I want to compute the minimal number field `K`

which contains all these algebraic numbers and I want to get the minimal polynomial of `a1,a2,a3`

in `K`

. How can I do this?

I know how to convert one element from `QQbar`

to a number field element, e.g.,

```
sage: a = [QQbar(sqrt(3)), QQbar(sqrt(17)), QQbar(sqrt(5))]
sage: Ka, aK, emb = a[0].as_number_field_element()
sage: aK.absolute_minpoly()
x^2 - 3
```

I can also define the common number field

```
sage: K.<u> = NumberField([ai.minpoly() for ai in a])
```

But now I have no idea how to convert for instance `a[0]`

to an element of `K`

.

Did you check what is

`K`

? It does not look like a common number field. Resultants may come handy for this problem: https://en.wikipedia.org/wiki/Resulta...