fq_mat_reduce_row

Reduces row $m$ of $A$ against the earlier rows, which must already be in reduced form (pivot entries 1, not necessarily in order), and returns the column of the new pivot, or $-1$ if row $m$ becomes zero. P[i] is the row with its pivot in column $i$, or $-1$; it is updated when a new pivot is found, and the new pivot row is scaled to make the pivot 1. L[i] is the number of possibly nonzero columns of row $i$, which allows faster reduction of matrices that are zero on the right; the entries of L must be nondecreasing, and can all be set to the number of columns. The arithmetic is done without intermediate reductions modulo the defining polynomial.