A Laurent polynomial in x (over a field k)
is an expression of the form
a-nx-n+...+a0+a1x+...+amxm
where the coefficients ai lie in k. (You can take
k to be the real numbers or complex numbers.)
For example, 10+5x, x-1, and x-2+3x2
are all Laurent polynomials.
They can be added and multiplied in just the way you expect (so that x.x-1=1)
and the collection k[x,x-1] of all Laurent polynomials
forms a commutative ring. | 
