Jinyue Luo on Wed, 25 Oct 2023 00:46:09 +0200


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bnfinit in different versions of pari


?  f=x^16 - 8*x^13 - 756*x^12 + 24*x^10 + 3240*x^9 + 568620*x^8 - 32*x^7 - 3888*x^6 - 314928*x^5 - 2204480*x^4 + 864*x^3 + 34992*x^2 + 629856*x + 8503056;
?  F=bnfinit(f,1);
? F[8][5]
%3 = [;]

When I did it in pari 2.15.3 & pari 2.13.3, I will get the output [;]. But in pari 2.11.2, the output is the fundamental units I want.

bnf=bnfinit(x^6+x-1,1);
? bnf[8][5]
%5 = [-x^5 - 1, -x^5 - x^4 + x - 1, -x^5 - x^3 - 1]

This will also work for smaller fields in pari 2.15.3 & pari 2.13.3 as the codes above.

How could I fix it?

Best,
Jinyue