Polynomials over the Integers

The functions in this section are available for univariate polynomials over the integers only.

Sign(p) : RngUPolElt -> RngIntElt

The sign of the leading coefficient of p.

AbsoluteValue(p) : RngUPolElt -> RngUPolElt

Abs(p) : RngUPolElt -> RngUPolElt

Returns either p or -p according to which one has non-negative leading coefficient.

MaxNorm(p) : RngUPolElt -> RngIntElt

The maximum of the absolute values of the coefficients of p.

SumNorm(p) : RngUPolElt -> RngIntElt

The sum of the coefficients of p.

DedekindTest(p, m) : RngUPolElt, RngIntElt -> Boolelt

Given a monic polynomial p (univariate or multivariate in one variable) and a prime number m, this returns true if p satisfies the Dedekind criterion at m, and false otherwise. The Dedekind criterion is satisfied at m if and only if the equation order corresponding to p is locally maximal at m [PZ89, p. 295].