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 ?
As is noted in section 2, energy consumption in any time slot is a convex monomial function depending on the size of transmission data and the wireless channel gain, which is constant during a time slot.
Van Tuyl Resolutions of square-free monomial ideals via facet ideals: a survey arxiv: math/0604301v2.
According to the results of monomial potential ecological risk indices (Eir), arsenic posed moderate and considerable ecological risk at F2 and F3 stations.
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||.
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 longing melancholy of monomial artist Sabzi's fluid figurative paintings evoke memories of experiences past and an existential present.
The resultant of two polynomials is a monomial multiple of a polynomial in their coefficients which has the property that it is equal to zero if and only if the polynomials have a common root.
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.
Here m is any monomial in F[X] containing neither [x.
c) For any integer p, q [member of] Z satisfying k := p + q [not equal to] 0, the monomial [x.