GaussInt - Maple Programming Help

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

GaussInt

 GImcmbine
 Chinese remaindering

 Calling Sequence GImcmbine(a, ra, b, rb)

Parameters

 a, ra, b, rb - Gaussian integers

Description

 • The function GImcmbine computes a Gaussian integer $x$ such that $x=\mathrm{ra}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}a$ and $x=\mathrm{rb}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}b$. If no Gaussian integer $x$ exists, it returns FAIL.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $a≔4+14I:$$b≔10+35I:$$\mathrm{ra}≔7-11I:$$\mathrm{rb}≔1-32I:$
 > $\mathrm{GImcmbine}\left(a,\mathrm{ra},b,\mathrm{rb}\right)$
 ${11}{+}{3}{}{I}$ (1)
 > $\mathrm{ra}≔7-11I:$$\mathrm{rb}≔1-23I:$$a≔-16+8I:$$b≔-24+12I:$
 > $\mathrm{GImcmbine}\left(a,\mathrm{ra},b,\mathrm{rb}\right)$
 ${\mathrm{FAIL}}$ (2)