The function GImcmbine computes a Gaussian integer $x$ such that $x=\mathrm{ra}\mathbf{mod}a$ and $x=\mathrm{rb}\mathbf{mod}b$. If no Gaussian integer $x$ exists, it returns FAIL.

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

$a≔4+14\mathrm{I}\:$$b≔10+35\mathrm{I}\:$$\mathrm{ra}≔7-11\mathrm{I}\:$$\mathrm{rb}≔1-32\mathrm{I}\:$

$\mathrm{GImcmbine}\left(a\,\mathrm{ra}\,b\,\mathrm{rb}\right)$

$11+3\mathrm{I}$

$\mathrm{ra}≔7-11\mathrm{I}\:$$\mathrm{rb}≔1-23\mathrm{I}\:$$a≔-16+8\mathrm{I}\:$$b≔-24+12\mathrm{I}\:$

$\mathrm{GImcmbine}\left(a\,\mathrm{ra}\,b\,\mathrm{rb}\right)$

$\mathrm{FAIL}$