Computing with differential-difference operators

Computer algebra can be used to prove identities in the algebra of operator s on polynomials which is generated by multiplication by coordinate functio ns, and the group translations and Dunkl operators associated with a reflec tion group. This technique is illustrated by a conceptual proof of a comple te orthogonal decomposition of the harmonic polynomials associated with the abelian reflection groups. (C) 1999 Academic Press.