Elements of a free module over a ring

map.py

class Map(dict):
    """Element of a free module over a ring."""

    def __add__(self, other):
        m = Map(self)
        for k, v in other.items():
            n = m.setdefault(k, v.__class__()) + v
            if not n and k in m:
                del m[k]
                continue
            m[k] = n
        return m

    def __mul__(self, other):
        m = Map(self)
        for k, v in self.items():
            n = v * other
            if not n and k in m:
                del m[k]
                continue
            m[k] = n
        return m

    def __rmul__(self, other):
        return self.__mul__(other)

    def __sub__(self, other):
        return self + (-other)

    def __neg__(self):
        m = Map(self)
        for k, v in m.items():
            m[k] = -v
        return m

    def supp(self):
        return set(self.keys())


f = Map({"a": 2, "b": 4})
g = Map({"b": 4, "c": 4})

print("f =", f)
print("g =", g)

print("f + g = ", f + g)
print("f - g = ", f - g)
print("supp(f - g) = ", (f - g).supp())
print("f * 2 =", f * 2)
print("2 * f =", 2 * f)