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  1. A monomial is an expression in algebra that contains one term, like 3xy. Monomials include: numbers, whole numbers and variables that are multiplied together, and variables that are multiplied together. Any number, all by itself, is a monomial, like 5 or 2, A monomial can also be a variable, like m or b.
  2. A monomial is a polynomial which has only one term. Dividing a monomial by a monomial is similar to multiplying a monomial with a monomial, except a small difference. When you multiply two monomials, you multiply the coefficients together and then you multiply the variables together.
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  5. As mentioned, two common orderings for monomials are "grlex" (graded lexicographic) and "grevlex" (graded reverse lexicographic). The word "graded" in both names indicates that, for both orderings, one monomial is "less" than another if its total degree is less. Thus, for both orderings, xyz^2 is less than y^5 because a monomial of.
  6. A generalized monomial is an identity if and only if it is a trivial identity. Thus we have the criterion: A multilinear generalized polynomial is nontrivial iff one of its generalized monomials has a nonzero value. The proof of Lemma follows from Lemma by an easy induction on degree.
  7. A monomial is an algebraic expression that consists of only one term. (A term is a numerical or literal expression with its own sign.) For instance, 9 x, 4 a 2, and 3 mpx 2 are all monomials. The number in front of the variable is called the numerical coefficient. In 9 x, 9 is the coefficient.

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