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...

mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: A monomial, also called...

number of variables, every monomial order is thus the restriction to N n {\displaystyle \mathbb {N} ^{n}} of a monomial order of Z n {\displaystyle \mathbb...

sequence of monomials is finite. Although Gröbner basis theory does not depend on a particular choice of an admissible monomial ordering, three monomial orderings...

consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an...

In abstract algebra, a monomial ideal is an ideal generated by monomials in a multivariate polynomial ring over a field. A toric ideal is an ideal generated...

extends to monomials; thus, sin 3x = sin(3x) and even sin ⁠1/2⁠xy = sin(xy/2), but sin x + y = sin(x) + y, because x + y is not a monomial. However, this...

monomial order is generally fixed. In this case, a polynomial may be said to be monic, if it has 1 as its leading coefficient (for the monomial order)...

multivariate polynomials with respect to a monomial order, see Gröbner basis § Leading term, coefficient and monomial. In linear algebra, a system of linear...

terms of each factor (this is true whenever one uses a monomial order, like the lexicographic order used here), and the leading term of the factor ei (X1...