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    Generate BICs for stratum with signature orders of genus g.

    DO NOT USE!!! USE bic_alt instead!!!

    Args:
        g (int): genus
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    Returns:
        list: list of BICs
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    Construct all non-horizontal divisors in the stratum sig.

    More precisely, each BIC is LevelGraph with two levels numbered 0, -1
    and marked points 1,...,n where the i-th point corresponds to the element
    i-1 of the signature.

    Note that this is the method called by GeneralisedStratum.gen_bic.

    Args:
        sig (Signature): Signature of the stratum.

    Returns:
        list: list of 2-level non-horizontal LevelGraphs.

    EXAMPLES::

        sage: from admcycles.diffstrata import *
        sage: assert comp_list(bic_alt(Signature((1,1))),        [LevelGraph([1, 0],[[3, 4], [1, 2, 5, 6]],[(3, 5), (4, 6)],{1: 1, 2: 1, 3: 0, 4: 0, 5: -2, 6: -2},[0, -1],True),        LevelGraph([1, 1, 0],[[4], [3], [1, 2, 5, 6]],[(3, 5), (4, 6)],{1: 1, 2: 1, 3: 0, 4: 0, 5: -2, 6: -2},[0, 0, -1],True),        LevelGraph([1, 1],[[3], [1, 2, 4]],[(3, 4)],{1: 1, 2: 1, 3: 0, 4: -2},[0, -1],True),        LevelGraph([2, 0],[[3], [1, 2, 4]],[(3, 4)],{1: 1, 2: 1, 3: 2, 4: -4},[0, -1],True)])

        sage: assert comp_list(bic_alt(Signature((2,))),        [LevelGraph([1, 1],[[2], [1, 3]],[(2, 3)],{1: 2, 2: 0, 3: -2},[0, -1],True),        LevelGraph([1, 0],[[2, 3], [1, 4, 5]],[(2, 4), (3, 5)],{1: 2, 2: 0, 3: 0, 4: -2, 5: -2},[0, -1],True)])

        sage: assert comp_list(bic_alt(Signature((4,))),        [LevelGraph([1, 1, 0],[[2, 4], [3], [1, 5, 6, 7]],[(2, 5), (3, 6), (4, 7)],{1: 4, 2: 0, 3: 0, 4: 0, 5: -2, 6: -2, 7: -2},[0, 0, -1],True),        LevelGraph([1, 1, 1],[[3], [2], [1, 4, 5]],[(2, 4), (3, 5)],{1: 4, 2: 0, 3: 0, 4: -2, 5: -2},[0, 0, -1],True),        LevelGraph([2, 0],[[2, 3], [1, 4, 5]],[(2, 4), (3, 5)],{1: 4, 2: 2, 3: 0, 4: -4, 5: -2},[0, -1],True),        LevelGraph([2, 0],[[2, 3], [1, 4, 5]],[(2, 4), (3, 5)],{1: 4, 2: 1, 3: 1, 4: -3, 5: -3},[0, -1],True),        LevelGraph([1, 0],[[2, 3, 4], [1, 5, 6, 7]],[(2, 5), (3, 6), (4, 7)],{1: 4, 2: 0, 3: 0, 4: 0, 5: -2, 6: -2, 7: -2},[0, -1],True),        LevelGraph([1, 2],[[2], [1, 3]],[(2, 3)],{1: 4, 2: 0, 3: -2},[0, -1],True),        LevelGraph([2, 1],[[2], [1, 3]],[(2, 3)],{1: 4, 2: 2, 3: -4},[0, -1],True),        LevelGraph([1, 1],[[2, 3], [1, 4, 5]],[(2, 4), (3, 5)],{1: 4, 2: 0, 3: 0, 4: -2, 5: -2},[0, -1],True)])

        sage: len(bic_alt(Signature((1,1,1,1)))) # long time (2 seconds)
        102

        sage: len(bic_alt(Signature((2,2,0,-2))))
        61

        sage: len(bic_alt((2,2,0,-2)))
        61
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    The BICs of the stratum sig up to isomorphism of LevelGraphs.

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        sig (tuple): signature tuple

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    Return a list of representatives of isomorphism classes of L.

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    Compare two lists of LevelGraphs (up to isomorphism).

    Returns a tuple: (list L without H, list H without L)
    cs&g|]�t�fdd��D��s��qS)c3s|]}��|�VqdSr7r�r�r�rrr:r%�'comp_list.<locals>.<listcomp>.<genexpr>�r��r)�Hr�rrr%zcomp_list.<locals>.<listcomp>cs&g|]�t�fdd��D��s��qS)c3s|]}��|�VqdSr7r�r�r�rrr:�r%r�r�r�)r�r�rr�r%r)r�r�r)r�r�r�	comp_listys�r�csDd�fdd�	�g}g}�||||�t|�t|�koBt|�t|�kS)a�
    Check if graph given by the two sets of half edges is connected.
    We do this by depth-first search.
    Note that we assume that both ends of each edge have the same number,
    i.e. each edge is of the form (j,j).

    EXAMPLES::

        sage: from admcycles.diffstrata.bic import is_connected
        sage: is_connected([[1],[2]],[[1,2]])
        True
        sage: is_connected([[1],[2]],[[2],[1]])
        False
    rcsV|�|�||D]:}t|�D],\}}||vr||vrF�|||||�qqq||fSr7)rRr�)Z
current_edgesZother_edgesZseen_currentZ
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    Compare output of bics and bic_alt.

    EXAMPLES::

        sage: from admcycles.diffstrata import *
        sage: test_bic_algs()  # long time (45 seconds)  # skip, not really needed + long # doctest: +SKIP
        (1, 1): ([], [])
        (1, 1, 0, 0, -2): ([], [])
        (2, 0, -2): ([], [])
        (1, 0, 0, 1): ([], [])
        (1, -2, 2, 1): ([], [])
        (2, 2): ([], [])

        sage: test_bic_algs([(0,0),(2,1,1)])  # long time (50 seconds)  # doctest: +SKIP
        (0, 0): ([], [])
        (2, 1, 1): ([], [])

        sage: test_bic_algs([(1,0,-1),(2,),(4,),(1,-1)])
        WARNING! This is not the normal BIC generation algorithm!
        Only use if you know what you're doing!
        (1, 0, -1): ([], [])
        WARNING! This is not the normal BIC generation algorithm!
        Only use if you know what you're doing!
        (2,): ([], [])
        WARNING! This is not the normal BIC generation algorithm!
        Only use if you know what you're doing!
        (4,): ([], [])
        WARNING! This is not the normal BIC generation algorithm!
        Only use if you know what you're doing!
        (1, -1): ([], [])
    N))r!r!)r!r!rrr�)rJrr�)r!rrr!)r!r�rJr!)rJrJz%r: %r)r
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