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 ?
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.
n](0), for any field F, by constructing another basis for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which consists of certain polynomials whose leading terms are the descent monomials.
Wolna, The stability of monomials on a restricted domain, Aequationes Math.
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:
Alge-Blaster 3's Challenger activity is an interactive tutorial that covers 27 algebraic subjects including systems of equations, quadratic equations, monomials and polynomials, integers, radical expressions, and factoring.
The Newton polytope of a Laurent polynomial is the convex hull of all the exponent vectors of the monomials, i.
Roots of unity are beautifully convenient: the basis of monomials [z.
n+r] (as many as the monomials of degree [less than or equal to] r in n undeterminates).
Thus, the number of packed monomials of degree n is [2.