Obtaining a permutation associated to a matrix

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Thank you! Is there a problem in your code to calculate the value of the permtuation at i=1? For the matrix A=matrix([[0,-1],[1,-1]]) , I get the "wrong" permutation [1,1] using your code and my code to get the complete permutation:

def permutationofmatrix(A):
    n=A.nrows()
    W=[pAi(A,i) for i in [1..n]]
    return W

I think p(A,1) should be the smallest j such that $a_{1,j} \neq 0$. In the example we should have p(A,1)=2, but your code gives $p(A,1)=1$.

I've added this condition to the code

Now it seems to return a constant number for each i. A=matrix([[0,0,0,-1],[0,0,1,-1],[0,1,0,-1],[-1,1,1,-1]]) gives [4,4,4,4] as permutation.

I think it is better to just modify the first entry in the definition. I did this and here is the code to get the permutation:

def riAj(A,i,j):
return A.row(i-1)[:j]

def pAi(A,i):
    for j in (1..A.ncols()):
        if riAj(A,i,j) not in span(A.base_ring(),(riAj(A,k,j) for k in (1..i-1))):
            return j
    raise ValueError



def permutationofmatrix(A):
    n=A.nrows()
    U=[t for t in [0..n-1] if A[0,t]!=0]
    t=min(U)+1
    W1=[t]
    W2=[pAi(A,i) for i in [2..n]]
    return W1+W2

It seems it works fine now. Thanks again!