human
Complete the below
def homomorphism(domain, codomain, matrix):

    ''''Create a homomorphism object.
    This function tries to build a homomorphism from ``domain`` to ``codomain``
    via the matrix ``matrix``.
    Examples
    >>> from sympy import QQ
    >>> from sympy.abc import x
    >>> from sympy.polys.agca import homomorphism
    >>> R = QQ.old_poly_ring(x)
    >>> T = R.free_module(2)
    If ``domain`` is a free module generated by `e_1, \ldots, e_n`, then
    ``matrix`` should be an n-element iterable `(b_1, \ldots, b_n)` where
    the `b_i` are elements of ``codomain``. The constructed homomorphism is the
    unique homomorphism sending `e_i` to `b_i`.
    >>> F = R.free_module(2)
    >>> h = homomorphism(F, T, [[1, x], [x**2, 0]])
    >>> h
    Matrix([
    [1, x**2], : QQ[x]**2 -> QQ[x]**2
    [x,    0]])
    >>> h([1, 0])
    [1, x]
    >>> h([0, 1])
    [x**2, 0]
    >>> h([1, 1])
    [x**2 + 1, x]
    If ``domain`` is a submodule of a free module, them ``matrix`` determines
    a homomoprhism from the containing free module to ``codomain``, and the
    homomorphism returned is obtained by restriction to ``domain``.
    >>> S = F.submodule([1, 0], [0, x])
    >>> homomorphism(S, T, [[1, x], [x**2, 0]])
    Matrix([
    [1, x**2], : <[1, 0], [0, x]> -> QQ[x]**2
    [x,    0]])
    If ``domain`` is a (sub)quotient `N/K`, then ``matrix`` determines a
    homomorphism from `N` to ``codomain``. If the kernel contains `K`, this
    homomorphism descends to ``domain`` and is returned.
otherwise an exception
    is raised.
    >>> homomorphism(S/[(1, 0)], T, [0, [x**2, 0]])
    Matrix([
    [0, x**2], : <[1, 0] + <[1, 0]>, [0, x] + <[1, 0]>, [1, 0] + <[1, 0]>> -> QQ[x]**2
    [0,    0]])
    >>> homomorphism(S/[(0, x)], T, [0, [x**2, 0]])
    Traceback (most recent call last):
    ValueError: kernel <[1, 0], [0, 0]> must contain sm, got <[0,x]>'
    '''
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#Here is the Python code you requested.
    def freepres(module):
        '\n                                Return    a    tuple    ``(F,    S,    Q,    c)``    where    ``F``    is    a    free    module,    ``S``    is    a\n                                submodule    of    ``F``,    and    ``Q``    a    submodule    of    ``S``,    such    that\n                                ``module    =    S/Q``,    and    ``c``    is    a    conversion    function.\n                                '
        if isinstance(module, FreeModule):
            return (module, module, module.submodule(), (lambda x: module.convert(x)))
        if isinstance(module, QuotientModule):
            return (module.base, module.base, module.killed_module, (lambda x: module.convert(x).data))
        if isinstance(module, SubQuotientModule):
            return (module.base.container, module.base, module.killed_module, (lambda x: module.container.convert(x).data))
        return (module.container, module, module.submodule(), (lambda x: module.container.convert(x)))
    (SF, SS, SQ, _) = freepres(domain)
    (TF, TS, TQ, c) = freepres(codomain)
    return FreeModuleHomomorphism(SF, TF, [c(x) for x in matrix]).restrict_domain(SS).restrict_codomain(TS).quotient_codomain(TQ).quotient_domain(SQ)