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
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