numtheory/GIgcd(deprecated) - Help

numtheory

 GIgcd
 gcd of Gaussian integers

 Calling Sequence GIgcd(x1, x2,..., xn)

Parameters

 x1, x2, ..., xn - Gaussian integers

Description

 • Important: The numtheory[GIgcd] command 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.

Examples

 > $\mathrm{with}\left(\mathrm{numtheory}\right):$
 > $\mathrm{GIgcd}\left(24,12\right)$
 ${12}$ (1)
 > $\mathrm{GIgcd}\left(-345+515I,1574+368I\right)$
 ${41}{+}{117}{}{I}$ (2)