Fiori, Andrew on Fri, 15 Mar 2019 23:08:17 +0100

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nfbasis with complete list of factors of field discriminant


I am unsure if I am misreading the documentation, if this is a bug in the documentation or a bug in the code. In any case the documentation for nfbasis suggests that if I call:
   nfbasis([x^4 - x^3 + 10558*x^2 - 2169592*x + 195873967, [13,73,89]])
I should obtain a global integral basis because:
     "The result is actually a global integral basis if all prime divisors of the field discriminant are included!"

However, even though the discriminant of the field in this case is (13*73*89)^3, the basis returned has index (103*499), so is not globally maximal.

For reference, I am using gp version 2.11.1.