# GaloisGroupFactorizationUtilities(R, UP, F)ΒΆ

GaloisGroupFactorizationUtilities provides functions that will be used by the factorizer.

beauzamyBound: UP -> Integer

`beauzamyBound(p)` returns a bound on the larger coefficient of any factor of `p`.

bombieriNorm: (UP, PositiveInteger) -> F

`bombieriNorm(p, n)` returns the `n`th Bombieri`'s` norm of `p`.

bombieriNorm: UP -> F

`bombieriNorm(p)` returns quadratic Bombieri`'s` norm of `p`.

height: UP -> F

`height(p)` returns the maximal absolute value of the coefficients of the polynomial `p`.

infinityNorm: UP -> F

`infinityNorm(f)` returns the maximal absolute value of the coefficients of the polynomial `f`.

length: UP -> F

`length(p)` returns the sum of the absolute values of the coefficients of the polynomial `p`.

norm: (UP, PositiveInteger) -> F

`norm(f, p)` returns the `lp` norm of the polynomial `f`.

quadraticNorm: UP -> F

`quadraticNorm(f)` returns the `l2` norm of the polynomial `f`.

rootBound: UP -> Integer

`rootBound(p)` returns a bound on the largest norm of the complex roots of `p`.

singleFactorBound: (UP, NonNegativeInteger) -> Integer

`singleFactorBound(p, r)` returns a bound on the infinite norm of the factor of `p` with smallest Bombieri`'s` norm. `r` is a lower bound for the number of factors of `p`. `p` shall be of degree higher or equal to 2.

singleFactorBound: UP -> Integer

`singleFactorBound(p)` returns a bound on the infinite norm of the factor of `p` with smallest Bombieri`'s` norm. `p` shall be of degree higher or equal to 2.