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GaussInt

 GIroots
 roots of a univariate polynomial

 Calling Sequence GIroots(a)

Parameters

 a - univariate polynomial with Gaussian integer coefficients

Description

 • The GIroots function computes the Gaussian integer roots of a univariate polynomial over the Gaussian integer domain. The roots are returned as a list of pairs of the form $[[{r}_{1},{m}_{1}],\dots ,[{r}_{n},{m}_{n}]]$ where ${r}_{i}$ is a root of the polynomial a with multiplicity ${m}_{i}$, that is, ${\left(x-{r}_{i}\right)}^{{m}_{i}}$ divides a.

Examples

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

 See Also

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