monomial


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Related to monomial: degree of a polynomial, monomial factor

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 ?
3, we compare convergence for the model problem using D-CG and CAD-CG with the monomial, Newton, and Chebyshev polynomial basis, respectively, each for a few representative s values.
A well known basis for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] consists of the descent monomials.
Reading meters to households and businesses monomial rate for SC Enel Distribution Muntenia SA (leading association) in combination with SC Enel Distribution Banat SA in association with SC Enel Dobrogea SA Distribution.
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||.
For fixed N and m, we call a solution of (5) optimal if its maximum and total degrees are minimal, and its number of monomial terms is minimal among all solutions.
The monomial will enter other neurons with a weight equal to its coefficient c.
The greedy add method is slower than the methods described in [3, 14], but this is due to the use of a more general basis than the monomial basis.
Intersections of Leray complexes and regularity of monomial ideals.
In the most extensive paper from the May 2008 workshop, three Japanese mathematicians classify squarefree monomial ideals of deviation two in a polynomial ring S in terms of hypergraphs, and prove that the arithmetical rank of an ideal I is equal to the projective dimension of S/I.
then one of the two functions [alpha](z) or [delta](z) must be a monomial.
N]p, where the coefficient of the leading monomial was assumed to be one without loss of generality.
13 that every Laurent monomial in a Laurent expansion of a type A cluster variable corresponds to a vertex of the Newton polytope.