# 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 $m$ [[Pohst and Zassenhaus, 1989](../../references.md#cite-pohst1), p. 295].