class SymmetricCone:
    def __init__(self, dimension):
        self._dimension = dimension

    def dimension(self):
        return self._dimension


class NonnegativeOrthant(SymmetricCone):
    pass

class IceCream(SymmetricCone):
    pass

class SymmetricPSD(SymmetricCone):
    pass

class CartesianProduct(SymmetricCone):
    def __init__(self, *factors):
        self._factors = factors

    def factors(self):
        return self._factors

    def cvxopt_dims(self):
        d = { 'l':0, 'q':[], 's':[] }
        d['l'] += sum([ K.dimension() for K in self.factors()
                                      if isinstance(K, NonnegativeOrthant) ])
        d['q'] = [ K.dimension() for K in self.factors()
                                 if isinstance(K, IceCream) ]
        d['s'] = [ K.dimension() for K in self.factors()
                                 if isinstance(K, SymmetricPSD) ]
        return d

    def dimension(self):
        return sum([ f.dimension() for f in self.factors() ])