Summary: 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. As a special case, a finite presentation of the algebra of multisymmetric polynomials is obtained. Reducedness of the invariant commuting scheme is proved as a by-product. The algebra of multisymmetric polynomials over an arbitrary base ring is revisited.