The order of a univariate polynomial is its highest power (or, more properly, its polynomial degree). For example, the polynomial
 |
is of order 
, denoted 
. The order of a polynomial
is implemented in the Wolfram Language
as Exponent[poly,
x].
It is preferable to use the word "degree" for the highest exponent in a polynomial, since a completely different meaning is given to the word "order"
in polynomials taken modulo some integer (where this meaning is the one used in the
multiplicative order of a modulus). In particular,
the order of a polynomial 
over a finite field with
is the smallest positive
integer 
for which 
divides 
(Lidl and Niederreiter 1994). For example, in the finite
field GF(2), the order of 
is 31, since
 |
This concept is closely related to that of the multiplicative order.
If 
is an irreducible polynomial of degree
, then its order has to divide the order of the multiplicative
group in the corresponding field extension, i.e., 
for modulus 
.
