  The most fundamental model of a molecule is a cloud of unordered atoms, even
without chemical bonds that can depend on thresholds for distances and angles.
The strongest equivalence between clouds of atoms is rigid motion, which is a
composition of translations and rotations. The existing datasets of
experimental and simulated molecules require a continuous quantification of
similarity in terms of a distance metric. While clouds of m ordered points were
continuously classified by Lagrange's quadratic forms (distance matrices or
Gram matrices), their extensions to m unordered points are impractical due to
the exponential number of m! permutations. We propose new metrics that are
continuous in general position and are computable in a polynomial time in the
number m of unordered points in any Euclidean space of a fixed dimension n.
