The terms in the quotient and remainder of polynomial long division are monomials. How are they obtained?

Feb 4, 2025 ... Monomial Binomial and Trinomial. A monomial expression has, only one term. For example, 3xy is a monomial. A binary expression is one which has ... Feb 29, 2000 ... monomial in its degree, nothing else can have this monomial ξ1ξ2 n−1 in its image. Hence ξn cannot be a summand of an invariant polynomial ... Jan 25, 2010 ... Given a monomial curve C: t 7→ (1 : ti1 : ... : tin ), and the surface Z: (λ, ω) 7→ (1 − λ, ωi1 − λ,...,ωin − λ) ⊂ Tn+1. Then: T (Sec1 ... ... monomial ideal of depth at most 2, to any monomial ideal in at most 3 variables, and to any monomial ideal which is generic with respect to one variable. For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik–Solomon ideal) to the set of flats of M of rank at most r. In ... 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 ... Jun 3, 2016 ... monomials with higher than generic rank. Theorem 1. Let M be a monomial in n ≥ 4 variables and let d = deg M > 1. Then r(M) < rgen(n, d) ... A monomial is in a standard form, if first there is a constant (numerical) factor, and then variable factors in alphabetical order. If there are several ... Sep 28, 2019 ... Abstract. Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor. ture on complexity issues and monomial ideals in four or more variables. 1 Introduction. A monomial ideal M is an ideal generated by monomials xi1. 1 xi2. 2 ...