The GIgcdex function returns g = GIgcd(a, b), and optionally s and/or t such that

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

$\mathrm{GIgcdex}\left(-345+515\mathrm{I}\,1574+368\mathrm{I}\,'s'\,'t'\right)$

$41+117\mathrm{I}$

$s\;$$t$

$5-2\mathrm{I}$

$-2\mathrm{I}$