Minkowski-Siegel Mass Constants

Let X denote either a vector space over the real numbers R or a module over the integers Z . A symmetric positive definite bilinear form f on X is an inner product if, for any linear form g on X, there exists a unique x ∈ X such that g(y) = f(x, y) for all y ∈ X. This nondegeneracy condition is superfluous whenX is a finite-dimensional vector space [1, 2]. The pair (X, f) is called an inner product space or an inner product module, respectively. Two pairs (X, f) and (X 0, f 0) are isomorphic if there is a bijective linear transformation h : X → X 0 satisfying