Concepts inFactoring Polynomials Over Algebraic Number Fields
Factorization of polynomials
In mathematics and computer algebra, polynomial factorization refers to factoring a polynomial into irreducible polynomials over a given field.
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Algebraic number field
In mathematics, an algebraic number field (or simply number field) F is a finite field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
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Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x ¿ x/4 + 7 is a polynomial, but x ¿ 4/x + 7x is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2).
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