As noted in the introduction, for the basics on multivariate polynomial rings and their elements, including their creation, the user should refer to Chapter MULTIVARIATE POLYNOMIAL RINGS. For creation of polynomial rings with non-default (currently lexicographic) monomial ordering, the user should refer to Chapter GRÖBNER BASES. Similarly, the basic creation functions for ideals and additional basis options are described in Chapter GRÖBNER BASES. The commonest creation methods are the ideal constructor and the Ideal function.