import re
from sage.all import *

def discrim(p,x):
    """
    Takes a polynomial in arbitrary variables as the first argument.
    All variables except the one specified by the second argument are treated as constants.
    Returns the discriminant of the polynomial.
    """
    vars = var_weights(p,x)
    R = singular.ring(0, '('+ ",".join(vars.keys()) +')', 'Wp(' + ",".join(vars.values())  + ')')
    singular.set_ring(R)
    d=singular.deg(p)
    l=singular.lead(p)/(singular(x)**d)
    return singular.eval('(' + repr((-1)**(d*(d-1)/2)*singular.resultant(p,singular.diff(p,x),x)) + ')/' + repr(l))

def var_weights(p,x):
    Rvar_rex = re.compile('([a-zA-Z_]+\w*)($|\+|\-|\s|\*|\/|\^|(|))')
    p_parse = Rvar_rex.findall(repr(p))
    Rvars = dict([(var,'0') for (var,d1,d2) in p_parse])
    Rvars[x]='1'
    return Rvars