Important: The numtheory package has been deprecated.  Use the superseding command GaussInt[GIgcd] instead.

This function computes and returns the first quadrant associate of a gcd of the Gaussian integers $\mathrm{x1}=\mathrm{a1}+\mathrm{b1}I,...,\mathrm{xn}=\mathrm{an}+\mathrm{bn}I$, where the ais and the bis are integers.  The first quadrant associate of a Gaussian integer is defined as I^(5-j)*x where x is a Gaussian integer and $j\left(1..4\right)$ is the quadrant containing x (see GaussInt[GInormal]).

The command with(numtheory,GIgcd) allows the use of the abbreviated form of this command.

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

$\mathrm{GIgcd}\left(24\,12\right)$

$12$

$\mathrm{GIgcd}\left(-345+515\mathrm{I}\,1574+368\mathrm{I}\right)$

$41+117\mathrm{I}$