# AlgFactor UP¶

Factorization of univariate polynomials with coefficients in AlgebraicNumber.

- doublyTransitive?: UP -> Boolean
`doublyTransitive?(p)`

is`true`

if`p`

is irreducible over over the field`K`

generated by its coefficients, and if`p(X) / (X - a)`

is irreducible over`K(a)`

where`p(a) = 0`

.

- factor: (UP, List AlgebraicNumber) -> Factored UP
`factor(p, [a1, ..., an])`

returns a prime factorisation of`p`

over the field generated by its coefficients and`a1`

, …, an.

- factor: UP -> Factored UP
`factor(p)`

returns a prime factorisation of`p`

over the field generated by its coefficients.

- split: UP -> Factored UP
`split(p)`

returns a prime factorisation of`p`

over its splitting field.