John Jones on Thu, 12 Jul 2012 22:19:38 +0200
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Possible improvements for bnfcertify and documentation
The documentation for bnfinit says that the computation of both the class group and fundamental units assumes GRH. In bnfcertify there is a flag to only certify that the class group is a quotient of the one which is computed. It would be good if the documentation would clarify whether or not this affects certification of the units.
Also, there are fields where pari spends much longer than magma in certifying class group/unit data. I don't know the internal algorithms in detail, but have the impression that they are doing very similar things, but with different bounds. If so and you can find out what bounds magma uses, then maybe pari could use the minimum of its current bound and whatever magma is using?