GaussInt - Maple Programming Help

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

GaussInt

 GIfactors
 Gaussian integer factorization

 Calling Sequence GIfactors(n)

Parameters

 n - Gaussian integer

Description

 • The GIfactors function returns the Gaussian integer factorization of the Gaussian integer n.
 • The result is returned in the form $[u,[[{p}_{1},{ⅇ}_{1}],\mathrm{...},[{p}_{m},{ⅇ}_{m}]]$ where $n=u{{p}_{1}}^{{ⅇ}_{1}}...{{p}_{m}}^{{ⅇ}_{m}}$, ${p}_{i}$ is a primary prime integer, ${e}_{i}$ is its exponent (multiplicity) and u is one of four units.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GIfactors}\left(0\right)$
 $\left[{0}{,}\left[{}\right]\right]$ (1)
 > $\mathrm{GIfactors}\left(72+100I\right)$
 $\left[{-}{I}{,}\left[\left[{1}{+}{I}{,}{4}\right]{,}\left[{-}{3}{-}{2}{}{I}{,}{1}\right]{,}\left[{-}{3}{+}{8}{}{I}{,}{1}\right]\right]\right]$ (2)
 > $\mathrm{GIfactors}\left(1574+368I\right)$
 $\left[{I}{,}\left[\left[{1}{+}{I}{,}{2}\right]{,}\left[{1}{+}{2}{}{I}{,}{2}\right]{,}\left[{1}{-}{4}{}{I}{,}{1}\right]{,}\left[{5}{-}{2}{}{I}{,}{1}\right]{,}\left[{-}{7}{+}{2}{}{I}{,}{1}\right]\right]\right]$ (3)