1 | initial version |

You can do the following:

```
R.<x> = PolynomialRing(QQ)
f = (x^2-2)*(x^2-3)
K.<a> = f.splitting_field()
```

Note that `f.splitting_field()`

requires a name for the primitive element of the field (`a`

here), which is passed here by using the shorthand notation, as shown in the documentation.

To identify the elements of the splitting field `K`

which correspond to the roots of `f`

you can do e.g.

```
f.change_ring(K).factor()
```

or in this case also something like

```
sqrt(K(3))
```

2 | No.2 Revision |

You can do the following:

```
R.<x> = PolynomialRing(QQ)
f = (x^2-2)*(x^2-3)
K.<a> = f.splitting_field()
```

Note that `f.splitting_field()`

requires a name for the primitive element of the field (`a`

here), which is passed here by using the shorthand notation, as shown in the documentation.

To identify the elements of the splitting field `K`

which correspond to the roots of `f`

you can do e.g.

~~f.change_ring(K).factor()
~~f.change_ring(K).roots()

or in this case also something like

```
sqrt(K(3))
```

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