What is the graded lexicographical order for monomials?

Sep 20, 2024 ... The main contribution of this paper is the introduction of a novel invariant of a monomial ideal, termed its signature. A monomial is a product of positive integer powers of a fixed set of variables (possibly) together with a coefficient, eg, x, 3xy^2, or -2x^2y^3z. Feb 13, 2025 ... In essence, the method approximates the nonlinear dynamics in a linear form by moving the nonlinearity from dynamics and state constraints to ... Aug 12, 2024 ... There's no such thing as a bare 'monomial' or 'polynomial'; that refers to the relationship between two variables. monomial ideals. Proposition 56.1. (Gasharov-Hibi-Peeva, Miller) Let u ∈ M be a monomial, and consider the monomial ideal (M≤u) generated by the monomials ... Three of the most important words to learn are monomial, binomial, and polynomial. In this article, we'll define all three to deepen our understanding of ... Nov 21, 2023 ... If does define an exponential, then is externally definable in any model of with a monomial group that is compatible with the exponential. We ... Feb 6, 2024 ... When it comes to multiplying the fraction in the polynomial by the monomial ( which is one part of the original binomial) I always come up with the answer 0 to ... monomial of the form a/∆ for some a ∈ A. And it is further possible to ... weight-over-grevlex monomial ordering with wt(z) = 5 and wt(y) = 3 corre ... Jun 10, 2012 ... Thank you very much, don't know how long I'd be looking for it without your help. However, I have to do `list((x*y^3).factor())`. For some ...