Factorisation (copy)

elementary algebra

elementary algebra

In ________, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors.

Matrices

________ possess many kinds of matrix factorizations.

efficient computer algorithms

There are ________ for computing (complete) factorizations within the ring of polynomials with rational number coefficients (see factorization of polynomials)

mathematical object

Factorization may also refer to more general decompositions of a(n) ________ into the product of smaller or simpler objects.

commutative ring

A(n) ________ possessing the unique factorization property is called a unique factorization domain.

Factorization

________ was first considered by ancient Greek mathematicians in the case of integers.

In particular, a univariate polynomial with complex coefficients admits a unique (up to ordering) factorization into linear polynomials

this is a version of the fundamental theorem of algebra

However, rings of algebraic integers satisfy the weaker property of Dedekind domains

ideals factor uniquely into prime ideals