# Revision history [back]

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.

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