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The PSLQ algorithm computes integer relations for real numbers and Gaussianinteger relations for complex numbers. We endeavour to extend PSLQ to findinteger relations consisting of algebraic integers from some quadraticextension fields (in both the real and complex cases). We outline thealgorithm, discuss the required modifications for handling algebraic integers,problems that have arisen, experimental results, and challenges to furtherwork.

Extending the PSLQ Algorithm to Algebraic Integer Relations