  First and second fundamental theorems are given for polynomial invariants of
a class of pseudo-reflection groups (including the Weyl groups of type $B_n$),
under the assumption that the order of the group is invertible in the base
field. Special case of the result is a finite presentation of the algebra of
multisymmetric polynomials. Reducedness of the invariant commuting scheme is
proved as a by-product. The algebra of multisymmetric polynomials over an
arbitrary base ring is revisited.
