GIfacpoly - Maple Help

GaussInt

 GIfacpoly
 factor a multivariate polynomial over Gaussian ring

 Calling Sequence GIfacpoly(z)

Parameters

 z - multivariate polynomial over Gaussian ring

Description

 • The function GIfacpoly computes the factorization of a multivariate polynomial with Gaussian integer coefficients.
 • The result is returned in the form $[u,[[{p}_{1},{ⅇ}_{1}],\mathrm{...},[{p}_{m},{ⅇ}_{m}]]$ where $z=u{{p}_{1}}^{{ⅇ}_{1}}...{{p}_{m}}^{{ⅇ}_{m}}$, ${p}_{i}$ is an irreducible polynomial over Gaussian ring with the gcd of its coefficients being 1, ${e}_{i}$ is its exponent (multiplicity) and u is a Gaussian integer.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{expr1}≔{x}^{4}-17{x}^{3}-29I{x}^{3}-188{x}^{2}+339I{x}^{2}+1682x-86Ix-1178-1244I$
 ${\mathrm{expr1}}{≔}{{x}}^{{4}}{-}{17}{}{{x}}^{{3}}{-}{29}{}{I}{}{{x}}^{{3}}{-}{188}{}{{x}}^{{2}}{+}{339}{}{I}{}{{x}}^{{2}}{+}{1682}{}{x}{-}{86}{}{I}{}{x}{-}{1178}{-}{1244}{}{I}$ (1)
 > $\mathrm{GIfacpoly}\left(\mathrm{expr1}\right)$
 $\left[{1}{,}\left[\left[{-}{x}{+}{1}{+}{I}{,}{1}\right]{,}\left[{-}{x}{+}{7}{+}{11}{}{I}{,}{1}\right]{,}\left[{-}{x}{+}{4}{+}{9}{}{I}{,}{1}\right]{,}\left[{-}{x}{+}{5}{+}{8}{}{I}{,}{1}\right]\right]\right]$ (2)
 > $\mathrm{expr2}≔\left(2+I\right){x}^{2}+\left(3+7I\right)x+\left(6-14I\right)$
 ${\mathrm{expr2}}{≔}\left({2}{+}{I}\right){}{{x}}^{{2}}{+}\left({3}{+}{7}{}{I}\right){}{x}{+}{6}{-}{14}{}{I}$ (3)
 > $\mathrm{GIfacpoly}\left(\mathrm{expr2}\right)$
 $\left[{-I}{,}\left[\left[{-}{x}{+}{1}{+}{I}{,}{1}\right]{,}\left[{x}{-}{2}{}{I}{}{x}{+}{10}{-}{4}{}{I}{,}{1}\right]\right]\right]$ (4)