# monomial

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## monomial

1. Maths an expression consisting of a single term, such as 5ax
2. consisting of a single algebraic term
3. Biology of, relating to, or denoting a taxonomic name that consists of a single term

## Monomial

the simplest type of algebraic expression considered in elementary algebra. A product consisting of a numerical coefficient and one or several variables, each with some integral positive exponent, is called a monomial. An individual numeral without literal factors is also called a monomial. Examples of monomials are –5ax3, + a3c3xy, –7, + x3 and –a. In these examples, the coefficient +1 is implicit for the monomials +a3c3xy and +x3 and the coefficient –1 is implicit for the monomial –a.

In older algebra textbooks, an algebraic expression in which the last operation in the order of operations is not addition or subtraction is sometimes called a monomial. In this case, for example, the expressions 2(a + b) and x/(y + 1) are called monomials. However, even textbooks that start out by using this definition usually subsequently treat monomials in the narrower sense given above.

## monomial

[mə′nō·mē·əl]
(mathematics)
A polynomial of degree one.
References in periodicals archive ?
General equations for exact integration of trivariate monomials over a three-dimensional domain can be derived when the integration limits a, b, r, s, p, and q in (22) are [0, 1].
j], j) of the pivot elements follow from the monomial order and can be determined at a negligible cost.
n]] is a free F[[THETA]]-module on the basis of descent monomials
t]} be a set of polynomials and let < be any monomial ordering.
Kaiser in (14) proved the stability of monomial functional equation where the functions map a normed space over a field with valuation to a Banach space over a field with valuation and the control function is of the form [epsilon]([||x||.
The monomial terms of P, which are not divisible by any of the monomials [x.
Wu, Multiple exponential sums with monomials and their applications in number theory, Acta Math.
A special case is the purely boolean where the monomials are composed with variables [X.
The key property of leading monomials in this proof is this lemma:
The logical optional argument USER_F_DF specifies that the user is supplying hand-crafted code for function and Jacobian matrix evaluation--this option is recommended if efficiency is a concern, or if the original formulation of the system is other than a linear combination of monomials.
Mathematical Expression Omitted] + sum of monomials with higher order
These classes include (a) disjunctions of two monomials, (b) Boolean threshold functions, and (c) Boolean formulas in which each variable occurs at most once.

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