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].