Re: qfgaussred() for singular matrices

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Oct 28, 2015 at 12:22:18PM +0100, Jeroen Demeyer wrote:
> Hello,
> 
> 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.

Note that this does not seem to contradict the documentation.

> 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.

You can extract the linear forms associated to non-zero diagonal terms
and use matsupplement to get a basis.

Cheers,
Bill.