The ChangeBasis(p, P1, .., Pk) calling sequence creates a series expanded in terms of the polynomials P1, .., Pk that is equal to the polynomial p. The polynomials P1, .., Pk must have distinct indices and variables, and be in the OrthogonalSeries database.

The ChangeBasis(S, P1, .., Pk) calling sequence replaces each polynomial in S  by the polynomial Pi that depends on the same variable if it exists. If multiple polynomials Pi, .., Pj share the same variable, the last one is used.

If the series S is infinite, the change of polynomial is not necessarily possible for every Pi. For infinite  series, the ChangeBasis routine attempts an iterated derivative representation transform to perform the change of polynomials. If the process fails for some Pi, it is ignored and a warning message is printed.