How are monomials used in symbolic computation?

Definition: Monomial. A monomial is a single-term algebraic expression that is the product of constants and variables, where the variables only have nonnegative ... Divide a polynomial expression by a monomial expression with rational number coefficients. Clarifications Clarification 1: Within the Algebra 1 course, ... Let J ⊂ R a monomial ideal minimally generated by monomials. µ1,...,µr . For all subset σ ⊂ {1,...,r} we define the monomial. µ(J,σ) := lcm(µi |i ∈ σ) ∈ R ... Illustrated definition of Monomial: A polynomial with just one term. Example: 3x2. May 19, 2006 ... ... monomial order γ, which is a total order on the monomials, compatible with the multiplication and such that 1 is smaller than any other monomial ... Aug 5, 2024 ... Title:The Automorphism groups of zero-dimensional monomial algebras ... Abstract:A monomial algebra B is defined as a quotient of a polynomial ... It is important to understand when G is a Cohen-Macaulay ring, that is dim G = depthG; in this case, this is equivalent to (tg1 )∗ being a non-zerodivisor. Mar 7, 2005 ... sequence of monomials. Macaulay [Ma] showed in 1927 that all Hilbert functions over B = k[x1, ··· , xn] are attained by lex ideals. Jul 24, 2014 ... 1 Answer ... A monomial is a mathematical expression which is made up of only one term. It cannot contain any addition or subtraction signs or a ... Jan 31, 2022 ... I decided to formalize this definition and make it more rigorous by defining a monomial as a polynomial such that all the coefficients except one are zero.