Polynomial Norm

For a polynomial

(1)

several classes of norms are commonly defined. The -norm is defined as

(2)

for , giving the special cases

			(3)
			(4)
			(5)

Here, is called the polynomial height. Note that some authors (especially in the area of Diophantine analysis) use as a shorthand for and as a shorthand for , while others (especially in the area of computational complexity) used to denote the -norm and (Zippel 1993, p. 174).

Another class of norms is the -norms, defined by

(6)

for , giving the special cases

			(7)
			(8)
			(9)

(Borwein and Erdélyi 1995, p. 6).