Xavier-François Roblot on 01 Oct 2002 13:05:05 +0200


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Bug rnfconductor


Hi, 

with the latest CVS development version:

? bnf = bnfinit(y^4 + 4*y^3 - 49*y^2 - 106*y + 787);
? pol = x^3 + (-1/29*y^3 - 3/29*y^2 + 81/29*y - 236/29);
? setrand(1); rnfconductor(bnf, pol)
%3 = [[[2, 0, 0, 0; 0, 2, 0, 0; 0, 0, 2, 0; 0, 0, 0, 2], []], [9, [3,
3], [[0, -1, -1, -1]~, [21, 4, 0, 1; 0, 1, 0, 0; 0, 0, 3, 2; 0, 0, 0,
1]]], [3, 2; 0, 1]]
? setrand(2); rnfconductor(bnf, pol)
%4 = [[[2, 0, 0, 0; 0, 2, 0, 0; 0, 0, 2, 0; 0, 0, 0, 2], []], [9, [3,
3], [[0, -1, -1, 0]~, [21, 4, 0, 1; 0, 1, 0, 0; 0, 0, 3, 2; 0, 0, 0,
1]]], [3, 1; 0, 1]]

Note the change in the last entry of the result (congruence subgroup)
from [3, 2; 0, 1] to [3, 1; 0, 1]. The second one is the correct one, by
the way. The bug doesn't show up in the stable version.

Xavier

PS: this one really caused me trouble since I've found it while working
on the forthcoming implementation in PARI of Fieker's version of
rnfkummer and I thought during weeks that the incorrect result was due
to some errors in my code :o(