4th edition and still hasn't bothered to disambiguate between polynomial and polynomial function.
Still a good example of mathematical writing. But, as Einstein supposedly said, "as simple as possible but not simpler". Why is it always American authors that forget that last part?
I do not know what the previous poster has meant to say, but polynomials can be defined in a more abstract way as just elements of certain vector spaces on which an additional operation of multiplication between polynomials is defined, which obeys special rules (the "carry-less multiplication", which is implemented in hardware by most modern CPUs, is an example of polynomial multiplication).
In computers there are many applications of such abstract polynomials, e.g. for error detecting or correcting codes, pseudo-random number generation, authenticated encryption and others, which depend only on the rules for addition, internal multiplication and multiplication with scalars, and which have nothing to do with the polynomial functions associated with the polynomials.
Still a good example of mathematical writing. But, as Einstein supposedly said, "as simple as possible but not simpler". Why is it always American authors that forget that last part?