e/Multivariate division algorithm

Information
has gloss	eng: Given a polynomial g, polynomials (f1, ..., fm) and an order on the monomials in k[x1, ..., xn], we construct the reduction of g modulo f1, ..., fm by the following algorithm. Let ai denote the leading term of fi with respect to the monomial order. Repeatedly apply the following until no monomial term of g is divisible by any of the ai :
lexicalization	eng: Multivariate division algorithm
instance of	(noun) a mathematical function that is the sum of a number of terms multinomial, polynomial