... rank. Let S again be an orientedquadratic ring and K = S ⊗Q the corresponding quadratic Q-algebra. A rankn ideal of S is an S-submodule of Knhaving rank 2n as a Z-module. Two rankn ideals ... ∧3Z6also has a unique polynomial invariant for the action ofSL6(Z), which we call the discriminant. This discriminant again has degree 4,and one checks that the map (12) is discriminant-preserving.4Despite ... det(v3,v4,v5)Annals of Mathematics, 159 (2004), 217–250Higher composition laws I: A new view on Gauss composition,and quadratic generalizationsBy Manjul Bhargava1. IntroductionTwo centuries ago, in...