David Loeffler on Wed, 03 Dec 2008 13:06:52 +0100 |
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nfsnf problems |
Dear PARI/GP people, I'm having some trouble with the "nfsnf" function. Firstly, in quite a lot of cases -- particularly where the matrix is close to being in Smith form already -- I get the error message "bug2 in nfsmith". This happens in both 2.3.3 and 2.4.2alpha. Secondly, when I do get an answer I'm not convinced it's the right one. Here's an example: E = nfinit(x^2 - x + 2); M = [1, 0, x; 0, x, 0; 0,0,2+x]; MM = nfalgtobasis(E, M); N = [[1, 0; 0, 1], [1, 0; 0, 1], [1, 0; 0, 1]]; nfsnf(E, [MM, N, N]) If I've understood everything correctly, that should calculate the SNF of the matrix [1,0,w; 0,w,0; 0,0,2+w] where w^2 - w + 2 = 0. But it returns [[8, 3; 0, 1], [1, 0; 0, 1], [1, 0; 0, 1]] Converting these back to polmods, that's saying that the matrix has elementary factors 1, 1, and the ideal generated by 8 and w + 2 (since E.zk[1] = 1, E.zk[2] = x-1.) But it's clear just by looking at the matrix that its elementary factors are 1, w and 2 + w. If I change the [1,3] entry of M to 0 instead of x, it gives me the bug2 in nfsmith error message. Any suggestions what's going on here? Yours, David Loeffler