The number field code in Pari relies on factoring the discriminant
often using MPQS. In particular if you turn debugging mode on, you get
warnings like this:
*** bnfclassunit: Warning: IFAC: untested integer declared prime.
10762727634633706239259776012492757340083
So basically the number field code is no more reliable than a probable
prime test.
This is bad news if you only want unconditional results from Pari. It
may not be trivial to get unconditional results from all Pari
functions.
Bill.
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