Yeah, I do favor working with Sage over, say, working with Magma,
because if I run into a bug like this (nice one, eh'?):
{{{
sage: V = span([[1/7,0,0] ,[0,1,0]], ZZ); V
Free module of degree 3 and rank 2 over Integer Ring
Echelon basis matrix:
[1/7 0 0]
[ 0 1 0]
sage: T = matrix(ZZ,3,[1,0,0,0,0,0,0,0,0]); T
[1 0 0]
[0 0 0]
[0 0 0]
sage: W = T.kernel_on(V); W.basis()
[
(0, 1, 0)
]
sage: W.is_submodule(V)
False
}}}
then I can debug it, and fix it (!), all on myself. That one hit me
during an intermediate step in some general Hecke module code, so from
the beginning, it was far from obvious where to look. (Patch is up for
review at #9425 ...)
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