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Oct 29, 2013 at 17:20 comment added Jean Raimbault Thanks! I guess this answer the question pretty well; I'll wait to see if anybody has anything else to contribute before accepting it since the formulation of my question was pretty open. A few remarks on the algorithm for those who don't want to have to go to the likned paper: it computes a basis for the class-group, and then computes the order of each of its elements. It uses the order generated by the powers of a root (if this is the whole integer ring then it is OK, otherwise they rely on some other work by Pohst and H. Zassenhaus).
Oct 29, 2013 at 14:16 history answered Igor Rivin CC BY-SA 3.0