1 | initial version |

The method you are looking for is called `lift`

:

```
sage: g = f.lift()
sage: g
7*x^9 + 9*x^8 + 9*x^7 + 7*x^6 + 8*x^5 + 8*x^4 + 8*x + 8
sage: g.parent()
Univariate Polynomial Ring in x over Ring of integers modulo 14
sage: g.discriminant()
0
```

*As a side comment:* I created `Zn = Zmod(14)`

. If you want to work in a finite field with `p`

elements, you should better use `K = GF(p)`

than `Zn = Zmod(p)`

since you are telling `Sage`

that `K`

is a field.

2 | No.2 Revision |

The method you are looking for is called `lift`

:

```
sage: g = f.lift()
sage: g
7*x^9 + 9*x^8 + 9*x^7 + 7*x^6 + 8*x^5 + 8*x^4 + 8*x + 8
sage: g.parent()
Univariate Polynomial Ring in x over Ring of integers modulo 14
sage: g.discriminant()
0
```

*As a side comment:* I created `Zn = Zmod(14)`

. If you want to work in a finite field with `p`

elements, you should better use `K = GF(p)`

than `Zn = Zmod(p)`

since you are telling `Sage`

that `K`

is a field.

**EDIT:** If you want the polynomial over $\mathbb{Z}$, you can do the following:

```
sage: h = g.change_ring(ZZ)
sage: h.discriminant()
19634094616613079744512
```

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