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Finding minimal linearly dependent vectors

I have a matrix whose rows are linearly dependent. Showing that with sage is straightforward. Is there a reasonably fast algorithm to find the smallest set of rows that form such a linear dependence and would it be simple to implement in sage?

Finding minimal linearly dependent vectors

I have a matrix whose rows are linearly dependent. Showing that with sage is straightforward. Is there a reasonably fast algorithm to find the a smallest set of rows that form such a linear dependence and would it be simple to implement in sage?