GIsqrfree - Maple Help

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GaussInt

 GIsqrfree
 Gaussian integer square-free factorization

 Calling Sequence GIsqrfree(n)

Parameters

 n - Gaussian integer

Description

 • The GIsqrfree function returns the square-free Gaussian integer factorization of the Gaussian integer n.
 • The function returns the result in the form $[u,[[{p}_{1},{ⅇ}_{1}],\mathrm{...},[{p}_{m},{ⅇ}_{m}]]$ where ${p}_{i}$ is a primary factor of n, ${e}_{i}$ is its multiplicity, $\mathrm{gcd}\left({p}_{i},{p}_{j}\right)=1$ for all $i\ne j$, and u is a unit in Gaussian integer ring. The square-free factorization of n is: $n=u{{p}_{1}}^{{ⅇ}_{1}}...{{p}_{m}}^{{ⅇ}_{m}}$.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GIsqrfree}\left(1574+368I\right)$
 $\left[{I}{,}\left[\left[{65}{+}{148}{}{I}{,}{1}\right]{,}\left[{-1}{+}{3}{}{I}{,}{2}\right]\right]\right]$ (1)
 > $\mathrm{GIsqrfree}\left(3369067456+16670818364I\right)$
 $\left[{I}{,}\left[\left[{-3}{-}{2}{}{I}{,}{1}\right]{,}\left[{-7}{+}{2}{}{I}{,}{2}\right]{,}\left[{1}{+}{I}{,}{4}\right]{,}\left[{5}{-}{2}{}{I}{,}{5}\right]{,}\left[{1}{+}{4}{}{I}{,}{6}\right]\right]\right]$ (2)

 See Also