Order theory | Polynomials

Monomial order

In mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication, i.e., * If and is any other monomial, then . Monomial orderings are most commonly used with Gröbner bases and multivariate division. In particular, the property of being a Gröbner basis is always relative to a specific monomial order. (Wikipedia).

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Related pages

Dot product | Basis (linear algebra) | Well-order | Total order | Rational dependence | Monic polynomial | Mathematics | Vector space | Field (mathematics) | Gröbner basis | Monomial | Elimination theory | Polynomial ring | Linear combination