The GIfactors function returns the Gaussian integer factorization of the Gaussian integer n.

The result is returned in the form $\[u,\[\[p_1,{\ⅇ}_1\],\mathrm{...},\[p_m,{\ⅇ}_m\]\]$ where $n=u{p_1}^{{\ⅇ}_1}...{p_m}^{{\ⅇ}_m}$, $p_i$ is a primary prime integer, $e_i$ is its exponent (multiplicity) and u is one of four units.

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

$\mathrm{GIfactors}\left(0\right)$

$\left[0\,\left[\right]\right]$

$\mathrm{GIfactors}\left(72+100\mathrm{I}\right)$

$\left[\mathrm{-I}\,\left[\left[1+\mathrm{I}\,4\right]\,\left[\mathrm{-3}-2\mathrm{I}\,1\right]\,\left[\mathrm{-3}+8\mathrm{I}\,1\right]\right]\right]$

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

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