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GaussInt

 GIchrem
 Chinese remainder algorithm for Gaussian integers

 Calling Sequence GIchrem(a, u)

Parameters

 a - list [a_0,a_1,...,a_n] of Gaussian integers u - list of Gaussian moduli [u_0,u_1,...,u_n]

Description

 • The chrem(a, u) calling sequence computes the unique integer e such that $e\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{u}_{0}={a}_{0}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{u}_{0},e\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{u}_{1}={a}_{1}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{u}_{1}$, ..., $e\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{u}_{n}={a}_{n}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{u}_{n}$. The moduli ${u}_{0},{u}_{1},...,{u}_{n}$ must be pairwise relatively prime.
 • For a definition, see Chinese remainder theorem.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GIchrem}\left(\left[5+13I,15-9I\right],\left[3+4I,7-11I\right]\right)$
 ${-}{17}{+}{17}{}{I}$ (1)