Function to calculate the nullspace

[hamorabi]

The Prime has built-in functions to calculate the column and row spaces. For some reason, there's no function for the nullspace.

I'd like to share this piece of code (written in Python syntax) that calculates the nullspace of a matrix. The left nullspace can be calculate by taking the transpose of the matrix first.

Here's a 7x10 random matrix that you can try.

PHP Code:

[[13,31,27,33,77,47,77,2,95,42][95,60,98,44,84,58,64,89,37,63][9,33,18,13,68,72,34,27,3,95][7,61,12,88,55,24,62,7,37,72][53,2,20,67,33,3,82,73,40,32][71,90,46,45,14,64,95,35,67,7][69,67,9,40,93,34,64,88,25,81]] 


PHP Code:

#cas
def nullspace(mat):
    m = rowDim(mat)
    n = colDim(mat)
    mat = RREF(mat)
    pivcols = [] 
    freecols = []
    res = []
    jj:=0;
    ii:=0;
    while((jj<n) and (ii<m)):
        while (mat[ii,jj]==0 and jj<n):
            freecols.append(jj)
            jj=jj+1
        if (jj<n):    
            if ((mat[ii,jj])!=0):
                pivcols.append(jj)
            else:
                freecols.append(jj)
        jj=jj+1
        ii=ii+1
    #For fat matrices, add the columns to the right of the last pivot
    if (jj<n):
        freecols = concat(freecols,range(jj,n))
    nfree = len(freecols)
    #Return the 0 matrix
    if (nfree==0):
        return TRN([0 for x in range(0,n)])
    for kk in range(0,nfree):
        sol = [0 for x in range(0,n)]
        sol[freecols[kk]] = 1
        for ii in range(n-nfree-1,1,-1):
            sol[pivcols[ii]] = -sum(mat[ii,rr]*sol[rr],rr,pivcols[ii],n-1)
        res = concat(res,TRN(sol));    
    return res
#end