# GaloisGroupPolynomialUtilities(R, UP)ΒΆ

- R: Ring
- UP: UnivariatePolynomialCategory R

GaloisGroupPolynomialUtilities provides useful functions for univariate polynomials which should be added to UnivariatePolynomialCategory or to Factored (July 1994).

- degreePartition: Factored UP -> Multiset NonNegativeInteger
`degreePartition(f)`

returns the degree partition (i.e. the multiset of the degrees of the irreducible factors) of the polynomial`f`

.

- factorOfDegree: (PositiveInteger, Factored UP) -> UP
`factorOfDegree(d, f)`

returns a factor of degree`d`

of the factored polynomial`f`

. Such a factor shall exist.

- factorsOfDegree: (PositiveInteger, Factored UP) -> List UP
`factorsOfDegree(d, f)`

returns the factors of degree`d`

of the factored polynomial`f`

.

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

tests if`p`

is monic (i.e. leading coefficient equal to 1).

- reverse: UP -> UP
`reverse(p)`

returns the reverse polynomial of`p`

.

- scaleRoots: (UP, R) -> UP
`scaleRoots(p, c)`

returns the polynomial which has`c`

times the roots of`p`

.

- shiftRoots: (UP, R) -> UP
`shiftRoots(p, c)`

returns the polynomial which has for roots`c`

added to the roots of`p`

.