Function lagrange_coefficient 

pub fn lagrange_coefficient(i: u32, participants: &[u32]) -> Scalar

Compute the Lagrange coefficient λ_i for party i relative to the participating set S (party indices, all distinct). The coefficient is

  λ_i = ∏_{j ∈ S, j ≠ i}  j / (j - i)

evaluated in the scalar field mod ℓ. Used both during DKG (to weight per-party VSS contributions) and during signing (to weight share responses).

Panics if i is not in participants. Callers must ensure the roster is well-formed before calling.