Robert Harron on Thu, 22 Aug 2019 23:33:26 +0200


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nfinit misleading documentation


Hi,

The online documentation for nfinit says that the 7th component is an integral basis for Z_K and that the first element is guaranteed to be 1. However, if you run

? nfinit(x^4 - 66*x^2 - 172*x + 54)[7]
%1 = [5, 5*x, x^3 - 2*x^2 - 57*x - 63, -x^3 + 7*x^2 + 37*x - 102]

the first element is a 5. Now, if you divide every entry by 5, you get an integral basis. The documentation implies that nf.zk is an alias for getting the 7th component, however:

nfinit(x^4 - 66*x^2 - 172*x + 54).zk
%2 = [1, x, 1/5*x^3 - 2/5*x^2 - 57/5*x - 63/5, -1/5*x^3 + 7/5*x^2 + 37/5*x - 102/5]

So, nf.zk is an integral basis where 1 is (or at least seems to be) the first element. I.e. nf.zk does what the documentation says it should, but that's not what the 7th component of a call to nfinit is. Could this be clarified in the documentation?

Thanks,

Rob