class FaceMonoid(Parent):
    def __init__(self, generators):
        Parent.__init__(self, category = FiniteMonoids())
        self._semigroup_generators = map(self._element_constructor_, generators)

    def _repr_(self):
        return "Monoïde de vecteurs de signes engendré par: %s" % (self._semigroup_generators)

    def one(self):
        length = len(self._semigroup_generators[0].value)
        return self((0,) * length)

    def semigroup_generators(self):
        return [self.one()] + [self(g) for g in self._semigroup_generators]

    def product(self, x, y):
        xv = x.value
        yv = y.value
        z = tuple([xv[i] if xv[i] != 0 else yv[i] for i in range(len(xv))])
        return self(z)

    def regions(self):
        return [x for x in self if 0 not in x.value]

    class Element(ElementWrapper):
        wrapped_class = tuple

        def _repr_(self):
            d = {0:'0', 1:'+', -1:'-'}
            return "".join([d[i] for i in self.value])