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- Monomial_order abstract "In mathematics, a monomial order is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the following two properties: If u < v and w is any other monomial, then uw<vw. In other words, the ordering respects multiplication. If u is any monomial then 1<u.These conditions imply that If u and v are any monomials then u < uv.They imply also that the ordering is a well ordering, which means that every strictly decreasing sequence of monomials is finite, or equivalently that every non-empty set of monomials has a minimal element.Among the powers of any one variable x, the only ordering satisfying these conditions is the natural ordering 1<x<x2<x3... (with only the first condition, the opposite ordering would also qualify, but the set of all powers of x would fail to have a minimal element). Therefore the notion of monomial ordering is interesting only in the case of multiple variables.Monomial orderings are most commonly used with Gröbner bases and multivariate division.".
- Monomial_order wikiPageID "696408".
- Monomial_order wikiPageRevisionID "565339439".
- Monomial_order hasPhotoCollection Monomial_order.
- Monomial_order subject Category:Order_theory.
- Monomial_order subject Category:Polynomials.
- Monomial_order type Abstraction100002137.
- Monomial_order type Function113783816.
- Monomial_order type MathematicalRelation113783581.
- Monomial_order type Polynomial105861855.
- Monomial_order type Polynomials.
- Monomial_order type Relation100031921.
- Monomial_order comment "In mathematics, a monomial order is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the following two properties: If u < v and w is any other monomial, then uw<vw. In other words, the ordering respects multiplication.".
- Monomial_order label "Monomial order".
- Monomial_order label "Monomordnung".
- Monomial_order label "Orden monomial".
- Monomial_order label "Ordine monomiale".
- Monomial_order label "Порядок на мономах".
- Monomial_order label "単項式順序".
- Monomial_order sameAs Monomordnung.
- Monomial_order sameAs Orden_monomial.
- Monomial_order sameAs Ordine_monomiale.
- Monomial_order sameAs 単項式順序.
- Monomial_order sameAs m.033k2_.
- Monomial_order sameAs Q934509.
- Monomial_order sameAs Q934509.
- Monomial_order sameAs Monomial_order.
- Monomial_order wasDerivedFrom Monomial_order?oldid=565339439.
- Monomial_order isPrimaryTopicOf Monomial_order.