GaloisGroupFactorizationUtilities(R, UP, F)

galfact.spad line 205 [edit on github]

• R : Ring
• UP : UnivariatePolynomialCategory(R)
• F : Join(FloatingPointSystem, RetractableTo(R), Field, TranscendentalFunctionCategory, ElementaryFunctionCategory)

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 -> F

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

bombieriNorm : (UP, PositiveInteger) -> F

bombieriNorm(p, n) returns the nth 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 -> 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.

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.