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Polynomial Term

In algebra, a term is a product of the form (in the univariate case), or more generally of the form (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, divides but does not divide . A term is said to reduce with respect to a polynomial if the leading term of that polynomial divides . For example, reduces with respect to because divides , and the result of this reduction is , or . 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).

Polynomial, Term

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References

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.

Cite this as:

Weisstein, Eric W. "Polynomial Term." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolynomialTerm.html