Example of the project fnx.Demo.BigInts for Lazarus

Extended GCD over the quadratic ring Z[Sqrt(2)] using the TEuclideanQuadRing object of the fnx.BigInts.QuadInts unit.

//////////////////////////////////////////////////////////////////////////////// The ring used is Z[Sqrt(2)] Random quadratic integer A -------------------------- U=-826451900113318504126853363824103227304 V=-10360592979228788180599853266450408523880708389690494876328345 Random quadratic integer B -------------------------- U=4641 V=2540742992571 Bezout coefficient X -------------------- U=-2601262381893 V=1846369240757 Bezout coefficient Y -------------------- U=-10607377796462405878493317323248353485939949826220117416111939 V=7529089039465614961958497162726006169775959224107165362896526 D = GCD(A,B) ------------ U=-65 V=-46 D is not a unit Check ((A mod D) = 0) : OK Check ((B mod D) = 0) : OK Check ((AX + BY) = D) : OK XGCD running time = 0.477 ms ////////////////////////////////////////////////////////////////////////////////