monomial

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monomial

adj. made of one term; of a monomial (Algebra)

n. one term or letter (Algebra)

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Monomial

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

For the first definition, a monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. The constant 1 is a monomial, being equal to the empty product and ⁰ for any variable . If only a single variable is considered, this means that a monomial is either 1 or a power of , with a positive integer. If several variables are considered, say, then each can be given an exponent, so that any monomial is of the form with non-negative integers (taking note that any exponent 0 makes the corresponding factor equal to 1).
For the second definition, a monomial is a monomial in the first sense multiplied by a nonzero constant, called the coefficient of the monomial. A monomial in the first sense is also a monomial in the second sense, because the multiplication by 1 is allowed. For example, in this interpretation and are monomials (in the second example, the variables are and the coefficient is a complex number).