<< . . . [O]ne of the many ways in which mathematicians conventionally complicate their lives is by defining polynomials over finite fields in an avoidably clumsy fashion. Restricting oneself to linear combinations of powers excludes a lot of functions which ought to be polynomial, but fail to do so on account of the Fermat little theorem x^p = x mod p.
I'm not aware of mathematicians who define polynomials over finite fields with respect to Fermat's Little Theorem. I thought the ring of polynomials over any field F is defined as all expressions of the form P(X) = c_n X^n + . . . + c_1 X + c_0, where all the c_k belong to F, and n is some nonnegative integer. With the natural addition and multiplication. (And such that two polynomials are equal precisely when all their coefficients c_k are equal.) No? Or am I misunderstanding something here? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele