# GaloisGroupFactorizationUtilities(R, UP, F)¶

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 nth 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(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.