PARI Groups¶
See pari:polgalois for the PARI documentation of these objects.
-
class
sage.groups.pari_group.
PariGroup
(x, degree=None)¶ Bases:
sage.groups.old.Group
EXAMPLES:
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 sage: G.category() Category of finite groups
Caveat: fix those tests and/or document precisely that this is an abstract group without explicit elements:
sage: TestSuite(G).run(skip = ["_test_an_element", ....: "_test_associativity", ....: "_test_elements", ....: "_test_elements_eq_reflexive", ....: "_test_elements_eq_symmetric", ....: "_test_elements_eq_transitive", ....: "_test_elements_neq", ....: "_test_enumerated_set_contains", ....: "_test_enumerated_set_iter_cardinality", ....: "_test_enumerated_set_iter_list", ....: "_test_inverse", ....: "_test_one", ....: "_test_prod", ....: "_test_some_elements"])
-
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
()¶
-