In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols.

In algebra, a term is a product of the form x^n (in the univariate case), or more generally of the form x_1^(a_1)...x_n^(a_n) (in the multivariate case) in a polynomial (Becker and Weispfenning 1993, p. 188).

The word "term" is also used commonly to mean a summand of a polynomial including its coefficient (more properly called a monomial), or the corresponding quantity in a series (i.e., a series term).

One term is said to divide another if the powers of its variables are no greater than the corresponding powers in the second monomial. For example, x^2y divides x^3y but does not divide xy^3. A term m is said to reduce with respect to a polynomial if the leading term of that polynomial divides m. For example, x^2y reduces with respect to 2xy+x+3 because xy divides x^2y, and the result of this reduction is x^2y-x(2xy+x+3)/2, or -x^2/2-3x/2. A polynomial can therefore be reduced by reducing its terms beginning with the greatest and proceeding downward. Similarly, a polynomial can be reduced with respect to a set of polynomials by reducing in turn with respect to each element in that set. A polynomial is fully reduced if none of its terms can be reduced (Lichtblau 1996).

See also

Coefficient, Monomial, Polynomial, Series Term, String Rewriting System

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Becker, T. and Weispfenning, V. Gröbner Bases: A Computational Approach to Commutative Algebra. New York: Springer-Verlag, 1993.Lichtblau, D. "Gröbner Bases in Mathematica 3.0." Mathematica J. 6, 81-88, 1996.

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Cite this as:

Weisstein, Eric W. "Term." From MathWorld--A Wolfram Web Resource.

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