GaloisGroupPolynomialUtilities(R, UP)ΒΆ

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`.