Learning Target Unit Sheet Course: Algebra Chapter 8: Polynomials
I can determine the degree of a polynomial
I can write a polynomial in standard form
I can combine polynomials using addition and/or subtraction.
I can multiply a monomial by a polynomial.
I can factor a monomial from a polynomial.
I can multiply two binomials or a binomial by a trinomial.
Theory of Algorithms - Baylor University | Texas
... For Each Algorithm Find a Function f(n)
The Argument n is the Size of the Input
The Function f(n) Gives the Amount of
Time Required to Process the Input
For Any Machine there Must be a Constant
K such that Kf(n) is Close to the Real Run
Time on Machine M.
K Also Depends on the Algorithm
Factorization of polynomials over finite fields
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.The case of the factorization of univariate polynomials over a finite field, which is the subject of this article, is especially important, because all the algorithms (including the case of multivariate polynomials over the rational numbers), which are sufficiently efficient to be implemented, reduce the problem to this case (see Polynomial factorization). It is also interesting for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.