Repository: sympy/sympy
File: sympy/combinatorics/free_groups.py (Python)

Code before:
        Examples
        ========

        >>> from sympy.combinatorics import free_group
        >>> f, x, y, z = free_group("x y z")
        >>> x*y**2*y**-4
        x*y**-2
        >>> z*y**-2
        z*y**-2
        >>> x**2*y*y**-1*x**-2
        <identity>

        """
        group = self.group
        if not isinstance(other, group.dtype):
            raise TypeError("only FreeGroup elements of same FreeGroup can "
                    "be multiplied")
        if self.is_identity:
            return other
        if other.is_identity:
            return self
        r = self.array_form + other.array_form
        return group.dtype._new_reduce_at_boundary(r, len(self.array_form) - 1)

    @classmethod
    def prod(cls, words):
        """Return the product of an iterable of words from the same free group.

        Examples
        ========

        >>> from sympy.combinatorics import free_group
        >>> F, x, y = free_group("x y")
        >>> F.dtype.prod([x, y, x**-1])
        x*y*x**-1
        """
        parts = []
        for word in words:
            if not isinstance(word, cls):
                raise TypeError("only FreeGroup elements of same FreeGroup can "
                        "be multiplied")
            if word:
                parts.append(word.array_form)
        if not parts:
            return cls.group.identity
        return cls._new(_concat_reduced_array_forms(*parts))

    def __truediv__(self, other):
        group = self.group
        if not isinstance(other, group.dtype):
            raise TypeError("only FreeGroup elements of same FreeGroup can "

Review comment (suggestion):
Use static analysis here, words must be at least an Iterable[C].
```python
def prod(cls: Type[C], words: Iterable[C]) -> C:
```
Where C is a TypeVar of course.

Code after:
        rep = (head,) + (middle + bridge)*(n - 1) + middle + (tail,)
        return group.dtype._new(rep)

    def __mul__(self, other):
        """Returns the product of elements belonging to the same ``FreeGroup``.

        Examples
        ========

        >>> from sympy.combinatorics import free_group
        >>> f, x, y, z = free_group("x y z")
        >>> x*y**2*y**-4
        x*y**-2
        >>> z*y**-2
        z*y**-2
        >>> x**2*y*y**-1*x**-2
        <identity>

        """
        group = self.group
        if not isinstance(other, group.dtype):
            raise TypeError("only FreeGroup elements of same FreeGroup can "
                    "be multiplied")
        if self.is_identity:
            return other
        if other.is_identity:
            return self
        r = self.array_form + other.array_form
        return group.dtype._new_reduce_at_boundary(r, len(self.array_form) - 1)

    @classmethod
    def prod(cls: type[C], words: Iterable[C]) -> C:
        """Return the product of an iterable of words from the same free group.

        Examples
        ========

        >>> from sympy.combinatorics import free_group
        >>> F, x, y = free_group("x y")
        >>> F.dtype.prod([x, y, x**-1])
        x*y*x**-1
        """
        parts = []
        for word in words:
            if not isinstance(word, cls):
                raise TypeError("only FreeGroup elements of same FreeGroup can "
                        "be multiplied")
            if word:
                parts.append(word.array_form)
        if not parts:
            return cls._new(())