def polyNormalize (P):
    Q = [0] * max(len(P),1)
    for I in range(len(P)):
        if abs(P[I] - float(int(P[I]))) < 1.0E-14:
            Q[I] = int(P[I])
        else:
            Q[I] = P[I]
    while (len(Q) > 1) and (Q[-1] == 0): del Q[-1]
    return Q

def polyAdd (P0,P1):       # P0 and P1 are polynomial lists [_,_,_,_]
    Q = [0] * max(len(P0),len(P1))
    for I in range(len(P0)): Q[I] = Q[I] + P0[I]
    for I in range(len(P1)): Q[I] = Q[I] + P1[I]
    return polyNormalize(Q)
    
def polySubtract (P0,P1):       # P0 and P1 are polynomial lists [_,_,_,_]
    Q = [0] * max(len(P0),len(P1))
    for I in range(len(P0)): Q[I] = Q[I] + P0[I]
    for I in range(len(P1)): Q[I] = Q[I] - P1[I]
    return polyNormalize(Q)