# polynomial

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Related to monic polynomial: monic equation, Irreducible polynomial

## polynomial

(pŏl′ē-nō′mē-əl)
Of, relating to, or consisting of more than two names or terms.
n.
1. A taxonomic designation consisting of more than two terms.
2. Mathematics
a. An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to nonnegative integral powers. For example, x2 - 5x + 6 and 2p3q + y are polynomials. Also called multinomial.
b. An expression of two or more terms.
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Proposition 4 For a monic polynomial f(x) = [[summation].sup.r.sub.j=0][c.sub.j][x.sup.j] of degree r in Z[x], one has an isomorphism of abelian groups
Finally, in section 5, as an example, we study the class of the linear functional w when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is a particular Laguerre-Hahn sequence of monic polynomials of class zero.
By [F.sub.q][z] we denote the set of monic polynomials with coefficients in [F.sub.q].
between the polynomial p(x) = [ax.sup.2] + bx + c, with a [not equal to] 0, and the monic polynomial p(-[alpha]y)/(a[[alpha].sup.2]) = q(y) = [y.sup.2] - 2[beta]y + e defined by the forward and backward relations
For example, one can compute and use as interpolation points in [S.sub.N] the zeros of the monic polynomial [p.sub.n] [member of] [P.sub.n] such that the ratio [p.sub.n]/[[pi].sub.m] has the smallest possible max-norm (a min-max approach like that leading to Chebyshev polynomials and Chebyshev points for polynomial interpolation).
If [L.sub.R-1] given as in (1.7), is a quasi-definite linear functional, then [[PSI].sub.n](z), the nth monic polynomial orthogonal with respect to [L.sub.R-1], is
So let there be given a real monic polynomial [[pi].sub.m] (x) of strict degree m, whose zeros {[[alpha].sub.1], ..., [[alpha].sub.m]} are all outside [-1,1].
In other words we want to estimate the norm of [q.sub.n] provided that the norm of its product with a monic polynomial is given.
The minimal polynomial of A for V is the nonzero monic polynomial of lowest degree such that P(A)V = 0.
In the sequel [[??].sub.n] (z) will be the monic polynomial and [[??].sub.n] (z) will be the normalized polynomial.

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