PARI Groups

See pari:polgalois for the PARI documentation of these objects.

class sage.groups.pari_group.PariGroup(x, degree)

Bases: object

EXAMPLES:

sage: PariGroup([6, -1, 2, "S3"], 3)
PARI group [6, -1, 2, S3] of degree 3
sage: R.<x> = PolynomialRing(QQ)
sage: f = x^4 - 17*x^3 - 2*x + 1
sage: G = f.galois_group(pari_group=True); G
PARI group [24, -1, 5, "S4"] of degree 4
cardinality()

Return the order of self.

EXAMPLES:

sage: R.<x> = PolynomialRing(QQ)
sage: f1 = x^4 - 17*x^3 - 2*x + 1
sage: G1 = f1.galois_group(pari_group=True)
sage: G1.order()
24
degree()

Return the degree of self.

EXAMPLES:

sage: R.<x> = PolynomialRing(QQ)
sage: f1 = x^4 - 17*x^3 - 2*x + 1
sage: G1 = f1.galois_group(pari_group=True)
sage: G1.degree()
4
order()

Return the order of self.

EXAMPLES:

sage: R.<x> = PolynomialRing(QQ)
sage: f1 = x^4 - 17*x^3 - 2*x + 1
sage: G1 = f1.galois_group(pari_group=True)
sage: G1.order()
24
permutation_group()