The GIsqrfree function returns the square-free Gaussian integer factorization of the Gaussian integer n.

The function returns the result in the form $\[u,\[\[p_1,{\ⅇ}_1\],\mathrm{...},\[p_m,{\ⅇ}_m\]\]$ where $p_i$ is a primary factor of n, $e_i$ is its multiplicity, $\gcd \left(p_i\,p_j\right)=1$ for all $i\ne j$, and u is a unit in Gaussian integer ring. The square-free factorization of n is: $n=u{p_1}^{{\ⅇ}_1}...{p_m}^{{\ⅇ}_m}$.

$\mathrm{with}\left(\mathrm{GaussInt}\right)\:$

$\mathrm{GIsqrfree}\left(1574+368\mathrm{I}\right)$

$\left[\mathrm{I}\,\left[\left[65+148\mathrm{I}\,1\right]\,\left[\mathrm{-1}+3\mathrm{I}\,2\right]\right]\right]$

$\mathrm{GIsqrfree}\left(3369067456+16670818364\mathrm{I}\right)$

$\left[\mathrm{I}\,\left[\left[\mathrm{-3}-2\mathrm{I}\,1\right]\,\left[\mathrm{-7}+2\mathrm{I}\,2\right]\,\left[1+\mathrm{I}\,4\right]\,\left[5-2\mathrm{I}\,5\right]\,\left[1+4\mathrm{I}\,6\right]\right]\right]$