On the verification of Clark's example of a euclidean but not norm-euclidean number field

In the preceding paper 2], D. Clark proved—modulo a finite amount of computation—that the ring of integersR of admits explicit euclidean algorithms, although it is not euclidean for the norm: In fact, every completely multiplicative function ϕ:R→R _>-0 which sends the prime elements above 23 to a value larger than 25 and which agrees with the absolute norm at all other primes defines a euclidean algorithm forR. The referee had felt that an independent verification of the computer-assisted proofs of Lemmas 1 and 2 of 2] was desirable, and that it should be carried out separately from the refereeing process in the light of the public, conforming to C. Lam's eloquent suggestions 3]. F. Lemmermeyer and the present author succeeded in confirming Clark's result (independently of each other). This note gives some details of the methods employed in the verifications.