GaussInt - Maple Programming Help

Home : Support : Online Help : Mathematics : Group Theory : Numbers : Integer Functions : Gaussian Integers : GaussInt/GIrem

GaussInt

 GIrem
 Gaussian integer remainder
 GIquo
 Gaussian integer quotient

 Calling Sequence GIrem(m, n)  GIrem(m, n, 'q') GIquo(m, n)  GIquo(m,n, 'r')

Parameters

 m, n - Gaussian integers q, r - (optional) names

Description

 • GIrem computes the Gaussian integer remainder of m divided by n.  If the third argument is present, it is assigned the quotient. Likewise, GIquo computes the integer quotient of m divided by n; and if the third argument is present, assigns it the remainder. In special cases when there is more than one possible value for the quotient, the one with the smallest norm is chosen.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GIquo}\left(6+12I,-8+4I,'r'\right)$
 ${-}{I}$ (1)
 > $r$
 ${2}{+}{4}{}{I}$ (2)
 > $\mathrm{GIrem}\left(6+12I,-8+4I,'q'\right)$
 ${2}{+}{4}{}{I}$ (3)
 > $q$
 ${-}{I}$ (4)
 > $\mathrm{GIquo}\left(-19+33I,6+14I,'r'\right)$
 ${1}{+}{2}{}{I}$ (5)
 > $r$
 ${3}{+}{7}{}{I}$ (6)
 > $\mathrm{GIrem}\left(-19+33I,6+14I,'q'\right)$
 ${3}{+}{7}{}{I}$ (7)
 > $q$
 ${1}{+}{2}{}{I}$ (8)