Compute the greatest common divisor of two ideals in ZZ[sqrt(-5)]

Compute the greatest common divisor of the ideals (1-2\sqrt{-5}) and (2) in \mathbb{Z}[\sqrt{-5}].


Recall that ((1-2\sqrt{-5}),(2)) = (1-2\sqrt{-5},2). Since 1 = 1-2\sqrt{-5} + 2\cdot \sqrt{-5}, this ideal contains 1, and so ((1-2\sqrt{-5}),(2)) = (1).

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