(12:28) gp > id=idealprimedec(nf,3)[1];id
%5 = [3, [-1, 1]~, 1, 1, [1, -5; 1, 1]]
(12:28) gp > idealfactor(nf,id)
%6 =
[[3, [-1, 1]~, 1, 1, [1, -5; 1, 1]] 1]
(12:29) gp > idtwo=idealtwoelt(nf,id);idtwo
%7 = [3, [-1, 1]~]
(12:29) gp > idealfactor(nf,idtwo)
%8 =
[ [3, [-1, 1]~, 1, 1, [1, -5; 1, 1]] 1]
[[3, [1, 1]~, 1, 1, [-1, -5; 1, -1]] 1]
What I expected is that %6 and %9 are the same.
GP/PARI CALCULATOR Version 2.9.4 (released)
amd64 running mingw (x86-64/GMP-6.1.2 kernel) 64-bit version
compiled: Dec 20 2017, gcc version 4.9.1 (GCC)
threading engine: single
(readline v6.2 enabled, extended help enabled)
Sincerely.