A Laurent polynomial with Coefficients in the Field is an algebraic object
that is typically expressed in the form
where the are elements of , and only finitely many of the are Nonzero. A Laurent polynomial is an
algebraic object in the sense that it is treated as a Polynomial except that the indeterminant ``'' can also
have Negative Powers.
Expressed more precisely, the collection of Laurent polynomials with Coefficients in a Field
form a Ring, denoted
, with Ring operations given by componentwise addition and
multiplication according to the relation
for all and in the Integers. Formally, this is equivalent to saying that
the Group Ring of the Integers and the Field . This corresponds to
(the Polynomial ring in one variable for ) being the Group Ring or Monoid ring for the
Monoid of natural numbers and the Field .
See also Polynomial
Lang, S. Undergraduate Algebra, 2nd ed. New York: Springer-Verlag, 1990.
© 1996-9 Eric W. Weisstein