GImod(a, m), where a is a Gaussian integer, computes the Gaussian integer remainder of a divided by m.

GImod(a, m), where a is a polynomial with Gaussian integer coefficients, reduces the coefficients mod m.

To compute GImod(a^n, m), where a is a Gaussian integer and n is a positive integer, without first computing a^n, use the inert powering operator, &^: GImod(a &^ n, m).

To compute GImod(a^(-1), m), where a is a Gaussian integer, use the form GImod(inv(a), m).

GImod(a, m) = GImod~(a, m) if a is a set or list, where ~ is the elementwise operator.

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

$\mathrm{GImod}\left(17+32\mathrm{I}\,5+4\mathrm{I}\right)$

$2\mathrm{I}$

$\mathrm{GImod}\left(\left(12+13\mathrm{I}\right)z^2-\left(27-22\mathrm{I}\right)z+\left(17+14\mathrm{I}\right)\,3+4\mathrm{I}\right)$

$-3\mathrm{I}{z}^2+\left(1+\mathrm{I}\right)z+1+\mathrm{I}$

$\mathrm{GImod}\left(\left(17+32\mathrm{I}\right)\&ˆ12345\,5+5\mathrm{I}\right)$

$\mathrm{-3}+2\mathrm{I}$

$\mathrm{GImod}\left(\mathrm{inv}\left(17+32\mathrm{I}\right)\,5+5\mathrm{I}\right)$

$\mathrm{-1}-4\mathrm{I}$

$\mathrm{GImod}\left(\left\{17+32\mathrm{I}\,\mathrm{inv}\left(17+32\mathrm{I}\right)\right\}\,3+7\mathrm{I}\right)$

$\left\{\mathrm{-1}+2\mathrm{I}\,2-3\mathrm{I}\right\}$