How are monomials used in the theory of toric varieties?

Sep 20, 2024 ... The main contribution of this paper is the introduction of a novel invariant of a monomial ideal, termed its signature. 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 ... Sep 28, 2019 ... Abstract. Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor. a reduced monomial of degree P since we only multiply P − 1 monomials from ... This monomial is then not an extended S-box monomial. Heuristically, the. Definition An ideal is a monomial ideal if it is generated by a set of monomials. , where . In this case, we write . Properties of Monomial Ideals. 1. If. , ... 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. A monomial is a polynomial with just one term. A monomial has a coefficient, a variable or variables, and exponents for each variable. 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 ... what is a Groebner basis? ... A Groebner basis is a specific generating set of an ideal or submodule over a polynomial ring. It is not minimal in general, but has ... Monomials and polynomials ... are not since these numbers don't fulfill all criteria. The degree of the monomial is the sum of the exponents of all included ...