Univariate Polynomials With Coefficients in A Field
The case of univariate polynomials over a field is specially important for several reasons. Firstly, it is the most elementary case and therefore appear in most first courses in algebra. Secondly, it is very similar to the case of the integers, and this analogy is the source of of the notion of Euclidean domain. A third reason is that the theory and the algorithms for the multivariate case and for coefficients in a unique factorization domain are strongly based on this particular case. Last but not least, polynomial GCD algorithms and derived algorithms allow one to get useful information on the roots of a polynomial, without computing them.
Read more about this topic: Greatest Common Divisor Of Two Polynomials
Famous quotes containing the word field:
“I don’t like comparisons with football. Baseball is an entirely different game. You can watch a tight, well-played football game, but it isn’t exciting if half the stadium is empty. The violence on the field must bounce off a lot of people. But you can go to a ball park on a quiet Tuesday afternoon with only a few thousand people in the place and thoroughly enjoy a one-sided game. Baseball has an aesthetic, intellectual appeal found in no other team sport.”
—Bowie Kuhn (b. 1926)