fixdiv - Maple Programming Help

fixdiv

compute the fixed divisor of a polynomial

 Calling Sequence fixdiv(a, x)

Parameters

 a, x - a is polynomial in x over the integers

Description

 • Compute the fixed divisor of $a\left(x\right)$ in ${Z}_{x}$.  The fixed divisor is the largest integer that divides $a\left(k\right)$ for all k in $Z$.  For primitive polynomials, the fixed divisor is no greater than $n!$ where $n=\mathrm{degree}\left(a,x\right)$.
 • The probability that the fixed divisor is greater than one for random polynomials of degree n is approximately 0.278 as n goes to infinity.

Examples

 > $\mathrm{fixdiv}\left(x\left(x+1\right)\left(x+2\right)\left(x+3\right),x\right)$
 ${24}$ (1)