from snappy import *

def prove_link_complement(filename, order = 0):

    # Load manifold as triangulation, this avoids computing
    # hyperbolic structure which is slow and not needed here
    M = Triangulation(filename)

    # Fill cusps, 20 at a time, replace manifold by filled
    # manifold.
    # Do not fill the last cusp. This would result in a triangulation
    # with no ideal vertices and SnapPy doesn't do to well on them.
    while M.num_cusps() > 1:
        n = min(20, M.num_cusps() - 1)
        M.dehn_fill(n*[(1,0)])
        M = M.filled_triangulation()

    # Mark the last cusp as filled without changing the triangulation
    M.dehn_fill((1,0))

    if order == 0:
        # We want to show trivial fundamental group.
        # It suffices to show that it has no generators
        if not M.fundamental_group().generators():
            print filename + " is a link complement"
            return True
        else:
            raise Exception, filename + " is NOT a link complement!!!"
    else:
        # We want to show cyclic fundamental group of given order.
        # It suffices to show that the fundamental group has only one
        # generator and that the homology group is isomorphic to the
        # cyclic group of given order.
        if (len(M.fundamental_group().generators()) == 1 and
            M.homology().coefficients == [order]):
            print filename + " is a link complement"
            return True
        else:
            raise Exception, filename + " is NOT a link complement!!!"
    
def main():
    tetrahedral = [
        "universal_tets_2_plus_0_zeta_0010_tets_with_meridians.trig",
        "universal_tets_2_plus_1_zeta_0028_tets_with_meridians.trig",
        "universal_tets_2_plus_2_zeta_0120_tets_with_meridians.trig",
        "universal_tets_3_plus_0_zeta_0054_tets_with_meridians.trig",
        "universal_tets_3_plus_1_zeta_0182_tets_with_meridians.trig",
        "universal_tets_3_plus_2_zeta_0570_tets_with_meridians.trig",
        "universal_tets_4_plus_0_zeta_0640_tets_with_meridians.trig",
        "universal_tets_4_plus_1_zeta_0672_tets_with_meridians.trig"]

    octahedral = [
        "universal_octahedra_2_plus_0_i_0004_octahedra_with_meridians.trig",
        "universal_octahedra_2_plus_1_i_0005_octahedra_with_meridians.trig",
        "universal_octahedra_2_plus_2_i_0016_octahedra_with_meridians.trig",
        "universal_octahedra_3_plus_0_i_0030_octahedra_with_meridians.trig",
        "universal_octahedra_3_plus_1_i_0030_octahedra_with_meridians.trig",
        "universal_octahedra_3_plus_2_i_0091_octahedra_with_meridians.trig",
        "universal_octahedra_4_plus_1_i_0204_octahedra_with_meridians.trig"]
    
    cubical = [
        "universal_cubes_1_plus_1_zeta_0006_cubes_with_meridians.trig",
        "universal_cubes_2_plus_0_zeta_0016_cubes_with_meridians.trig",
        "universal_cubes_2_plus_1_zeta_0084_cubes_with_meridians.trig"]

    dodecahedral = [
        ("universal_dodecahedra_2_plus_0_zeta_0240_dodecahedra_quotient_with_meridians.trig", 15)]

    for filename in tetrahedral + octahedral + cubical:
        prove_link_complement(filename)

    for filename, order in dodecahedral:
        prove_link_complement(filename, order)

if __name__ == "__main__":
    main()