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Multivariate polynomial rings in any number of variables may be formed
over any coefficient ring, including a polynomial ring. Multivariate
polynomials are represented in distributive form, using ordered arrays
of coefficient-monomial pairs. Different orderings are allowed on the
monomials; these become significant in the construction of Gröbner
bases of ideals.
Computations with ideals are available (since V2.8) for ideals
defined over general Euclidean rings as well as for ideals defined over fields.