Extended gcd of quadratic integers

Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.

💡 Research Summary

The paper addresses the problem of computing the extended greatest common divisor (Extended GCD) for two quadratic integers in rings of algebraic integers that are principal ideal rings (PIRs). While the classical Euclidean algorithm works efficiently in Euclidean domains, many quadratic integer rings—such as ℤ