Lesson plan
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 u \leq v and w is any other monomial, then uw \leq vw . 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.
Article summary
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 u \leq v and w is any other monomial, then uw \leq vw . 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.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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