Jeroen Demeyer on Wed, 28 Oct 2015 12:22:25 +0100

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qfgaussred() for singular matrices


it is not clear to me if qfgaussred() is officially supported for singular matrices.

I am asking because of this unexpected output:

gp> qfgaussred([1,1;1,1])
%1 =
[1 1]

[1 0]

The problem is that the new basis vectors are (1,1) and (1,1) which are not linearly independent. It would be useful if the vectors

x_i + sum_{i != j} a_ij x_j

(where x_i is a given basis) would always form a new basis, even in the singular case.