# GaloisGroupPolynomialUtilities(R, UP)¶

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.