350.sagews

def sns(a):
    """
    Determines the sns of a sign pattern matrix.
        
    INPUT:
        A square matrix, where each element should only be from the set {-1,0,1}.
        1 signifying a positive sign and -1 signifying a negative sign,
        while 0 will simply signify 0.
    
    OUTPUT:
        Outputs the sns number of the matrix.

    EXAMPLES::
        sage:a = matrix([[1,-1],[-1,1]])
        sage:a

        [ 1 -1]
        [-1  1]
        sage:sns(a)
        1
    """    
    length = a.ncols();
    new_matrix=matrix(length,[var('x%s%s'%(i,j)) for i in range(length) for j in range(length)])
    b = matrix(length,[(new_matrix[i,j] * a[i,j]) for i in range(length) for j in range(length)])
    for i in range(length,0,-1):
        for v in CartesianProduct(Subsets(range(length),i),Subsets(range(length),i)):
            for det in [b[list(v[0]),list(v[1])].det().expand()]:
                w=[[-1 in term.operands() for term in det.operands()]]
                if any([not(True in k and False in k) for k in w]):
                    return i

# Make a random -1,0,1 matrix
a=random_matrix(ZZ,5,x=-1,y=2)
a

[ 0 0 0 0 0] [ 0 1 1 -1 0] [-1 -1 -1 0 -1] [ 1 1 -1 -1 0] [-1 -1 0 -1 0]

sage_input(a)

matrix(ZZ, [[0, 0, 0, 0, 0], [0, 1, 1, -1, 0], [-1, -1, -1, 0, -1], [1, 1, -1, -1, 0], [-1, -1, 0, -1, 0]])

sns(a)

5

g=DiGraph(a)

g.plot(edge_labels=True, save_pos=True)

g.plot(color_by_label=True)

g.weighted_adjacency_matrix()

[ 0 0 0 0 0] [ 0 1 1 -1 0] [-1 -1 -1 0 -1] [ 1 1 -1 -1 0] [-1 -1 0 -1 0]