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GaussInt

 GIsqrt
 Gaussian integer square root

 Calling Sequence GIsqrt(x)

Parameters

 x - Gaussian integer

Description

 • The GIsqrt function computes a Gaussian integer approximation to the square root of x. The approximation is exact for perfect squares; the distance between x and its approximation is less than or equal to $\frac{1}{2}\sqrt{2}$ otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GIsqrt}\left(-5+12I\right)$
 ${2}{+}{3}{}{I}$ (1)
 > $\mathrm{GIsqrt}\left(7+9I\right)$
 ${3}{+}{I}$ (2)