Selmer groups of finite flat algebras¶
Selmer groups of finite flat algebras
- dual_pairs.selmer_group.selmer_group(A, S, n)¶
Return the n-Selmer group of A relative to S.
This is a version for étale algebras of the method
NumberField.selmer_space()
.EXAMPLES:
sage: from dual_pairs import FiniteFlatAlgebra sage: from dual_pairs.selmer_group import selmer_group sage: R.<x> = QQ[] sage: A = FiniteFlatAlgebra(QQ, [x, x^3 - x - 1]) sage: S = [2, 23] sage: Sel, gens, exp_Sel, log_Sel = selmer_group(A, S, 2) sage: v = Sel.random_element() sage: log_Sel(exp_Sel(v)) == v True sage: A = FiniteFlatAlgebra(QQ, x^2 - x + 6) sage: Sel, gens, exp_Sel, log_Sel = selmer_group(A, [], 6) sage: Sel Multiplicative Abelian group isomorphic to C6 sage: gens [3/64*a + 1/32] sage: log_Sel(gens[0]) f sage: exp_Sel(Sel.gen(0)) 3/64*a + 1/32