GaussInt/GImod - Maple Help

GaussInt

 GImod
 Gaussian integer modular arithmetic

 Calling Sequence GImod(a, m)

Parameters

 a - Gaussian integer or polynomial with Gaussian integer coefficients, or a set or list of these m - Gaussian integer

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GImod}\left(17+32I,5+4I\right)$
 ${2}{}{I}$ (1)
 > $\mathrm{GImod}\left(\left(12+13I\right){z}^{2}-\left(27-22I\right)z+17+14I,3+4I\right)$
 ${-}{3}{}{I}{}{{z}}^{{2}}{+}\left({1}{+}{I}\right){}{z}{+}{1}{+}{I}$ (2)
 > $\mathrm{GImod}\left(\left(17+32I\right)&^12345,5+5I\right)$
 ${-3}{+}{2}{}{I}$ (3)
 > $\mathrm{GImod}\left(\mathrm{inv}\left(17+32I\right),5+5I\right)$
 ${-1}{-}{4}{}{I}$ (4)
 > $\mathrm{GImod}\left(\left\{17+32I,\mathrm{inv}\left(17+32I\right)\right\},3+7I\right)$
 $\left\{{-1}{+}{2}{}{I}{,}{2}{-}{3}{}{I}\right\}$ (5)