The GIbasis function returns a value of true if x and y form a basis of the Gaussian integer domain, and false otherwise.

Any two Gaussian integers (x and y) form a basis if every Gaussian integer can be represented in the form $ax+by$ where a and b are integers.

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

$\mathrm{GIbasis}\left(1+\mathrm{I}\,3+2\mathrm{I}\right)$

$\mathrm{true}$

$\mathrm{GIbasis}\left(5+11\mathrm{I}\,9+2\mathrm{I}\right)$

$\mathrm{false}$