check_nabla_g3.py

from support_functions import add_maps_mod_2, expand_map_all, chain_map_mod, factorize_cycles, expand_tuple_list, \
    list_mod, generate_f_integral, derivative, chain_integrate
from Coalgebra import Coalgebra
from formatting import *

BR_C = Coalgebra(
    {0: ['v_{1}', 'v_{2}', 'v_{3}', 'v_{4}', 'v_{5}', 'v_{6}', 'v_{7}', 'v_{8}', 'v_{9}', 'v_{10}', 'v_{11}'], 1: ['m_{1}', 'm_{2}', 'm_{3}', 'm_{4}', 'm_{5}', 'm_{6}', 'm_{7}', 'm_{8}', 'm_{9}', 'm_{10}', 'm_{11}', 'm_{12}', 'm_{13}', 'm_{14}', 'c_{1}', 'c_{2}', 'c_{3}', 'c_{4}', 'c_{5}', 'c_{6}', 'c_{7}', 'c_{8}', 'c_{9}', 'c_{10}', 'c_{11}', 'c_{12}', 'c_{13}', 'c_{14}', 'c_{15}', 'c_{16}', 'c_{17}', 'c_{18}'], 2: ['a_{1}', 'a_{2}', 'a_{3}', 'a_{4}', 'e_{1}', 'e_{2}', 's_{1}', 's_{2}', 's_{3}', 's_{4}', 's_{5}', 's_{6}', 's_{7}', 's_{8}', 's_{9}', 's_{10}', 's_{11}', 's_{12}', 't_{1}', 't_{2}', 't_{3}', 't_{4}', 't_{5}', 't_{6}', 't_{7}', 't_{8}'], 3: ['D', 'q_{1}', 'q_{2}', 'q_{3}', 'q_{4}']},
    {'m_{1}': {'v_{11}': 1, 'v_{1}': 1}, 'c_{5}': {'v_{7}': 1, 'v_{8}': 1}, 'm_{3}': {'v_{11}': 1, 'v_{8}': 1}, 'c_{13}': {'v_{11}': 1, 'v_{10}': 1}, 'c_{7}': {'v_{2}': 1, 'v_{3}': 1}, 'c_{3}': {'v_{2}': 1, 'v_{3}': 1}, 't_{6}': {'m_{7}': 1, 'c_{2}': 1, 'm_{6}': 1, 'c_{5}': 1, 'c_{6}': 1}, 't_{2}': {'c_{3}': 1, 'm_{5}': 1, 'c_{4}': 1, 'c_{1}': 1, 'm_{4}': 1}, 's_{4}': {'m_{9}': 1, 'c_{16}': 1, 'm_{12}': 1, 'c_{9}': 1}, 'c_{1}': {'v_{5}': 1, 'v_{1}': 1}, 'm_{9}': {'v_{7}': 1, 'v_{6}': 1}, 't_{4}': {'c_{7}': 1, 'c_{8}': 1, 'm_{5}': 1, 'c_{11}': 1, 'm_{4}': 1}, 's_{6}': {'c_{10}': 1, 'm_{7}': 1, 'c_{14}': 1, 'm_{3}': 1}, 'e_{2}': {'c_{18}': 1, 'c_{16}': 1, 'c_{14}': 1, 'c_{11}': 1, 'c_{12}': 1}, 'a_{3}': {'m_{1}': 1, 'c_{17}': 1}, 't_{7}': {'m_{9}': 1, 'c_{10}': 1, 'm_{8}': 1, 'c_{9}': 1, 'c_{12}': 1}, 'm_{12}': {'v_{5}': 1, 'v_{8}': 1}, 'c_{11}': {'v_{5}': 1, 'v_{1}': 1}, 'c_{15}': {'v_{5}': 1, 'v_{6}': 1}, 'a_{1}': {'c_{17}': 1, 'm_{14}': 1}, 'q_{3}': {'a_{3}': 1, 's_{1}': 1, 'e_{1}': 1, 's_{5}': 1, 't_{2}': 1, 's_{11}': 1, 't_{6}': 1}, 'c_{9}': {'v_{7}': 1, 'v_{8}': 1}, 't_{8}': {'c_{10}': 1, 'm_{7}': 1, 'm_{6}': 1, 'c_{9}': 1, 'c_{12}': 1}, 'c_{17}': {'v_{11}': 1, 'v_{1}': 1}, 's_{8}': {'c_{8}': 1, 'm_{13}': 1, 'm_{10}': 1, 'm_{12}': 1, 'c_{10}': 1}, 'c_{16}': {'v_{5}': 1, 'v_{6}': 1}, 'm_{10}': {'v_{4}': 1, 'v_{5}': 1}, 's_{11}': {'m_{2}': 1, 'c_{15}': 1, 'm_{5}': 1, 'c_{4}': 1}, 'm_{2}': {'v_{3}': 1, 'v_{6}': 1}, 'm_{14}': {'v_{11}': 1, 'v_{1}': 1}, 'm_{6}': {'v_{7}': 1, 'v_{6}': 1}, 'q_{2}': {'e_{2}': 1, 'a_{2}': 1, 's_{10}': 1, 's_{8}': 1, 's_{4}': 1, 't_{3}': 1, 't_{7}': 1}, 's_{3}': {'m_{9}': 1, 'c_{5}': 1, 'c_{15}': 1, 'm_{12}': 1}, 'q_{4}': {'e_{2}': 1, 's_{2}': 1, 't_{8}': 1, 'a_{4}': 1, 's_{6}': 1, 't_{4}': 1, 's_{12}': 1}, 'D': {'a_{3}': 1, 'a_{4}': 1, 'a_{1}': 1, 'a_{2}': 1}, 'c_{10}': {'v_{8}': 1, 'v_{9}': 1}, 't_{1}': {'m_{11}': 1, 'c_{3}': 1, 'm_{10}': 1, 'c_{4}': 1, 'c_{1}': 1}, 'c_{6}': {'v_{8}': 1, 'v_{9}': 1}, 't_{5}': {'m_{9}': 1, 'c_{5}': 1, 'm_{8}': 1, 'c_{2}': 1, 'c_{6}': 1}, 's_{5}': {'m_{7}': 1, 'c_{13}': 1, 'm_{3}': 1, 'c_{6}': 1}, 's_{2}': {'m_{1}': 1, 'm_{3}': 1, 'c_{7}': 1, 'c_{9}': 1, 'm_{6}': 1, 'm_{2}': 1, 'm_{4}': 1}, 't_{3}': {'m_{11}': 1, 'c_{8}': 1, 'm_{10}': 1, 'c_{7}': 1, 'c_{11}': 1}, 'm_{13}': {'v_{3}': 1, 'v_{9}': 1}, 'm_{8}': {'v_{10}': 1, 'v_{9}': 1}, 's_{7}': {'m_{13}': 1, 'm_{10}': 1, 'm_{12}': 1, 'c_{6}': 1, 'c_{4}': 1}, 'm_{11}': {'v_{2}': 1, 'v_{1}': 1}, 'c_{8}': {'v_{4}': 1, 'v_{3}': 1}, 'c_{4}': {'v_{4}': 1, 'v_{3}': 1}, 'a_{2}': {'c_{18}': 1, 'm_{14}': 1}, 's_{1}': {'m_{1}': 1, 'c_{5}': 1, 'm_{3}': 1, 'c_{3}': 1, 'm_{6}': 1, 'm_{2}': 1, 'm_{4}': 1}, 'e_{1}': {'c_{17}': 1, 'c_{15}': 1, 'c_{2}': 1, 'c_{13}': 1, 'c_{1}': 1}, 'q_{1}': {'s_{3}': 1, 'e_{1}': 1, 'a_{1}': 1, 't_{1}': 1, 't_{5}': 1, 's_{7}': 1, 's_{9}': 1}, 'c_{2}': {'v_{10}': 1, 'v_{6}': 1}, 'c_{12}': {'v_{10}': 1, 'v_{6}': 1}, 's_{10}': {'m_{11}': 1, 'c_{7}': 1, 'c_{14}': 1, 'm_{13}': 1, 'm_{8}': 1, 'm_{14}': 1}, 'm_{7}': {'v_{10}': 1, 'v_{9}': 1}, 'a_{4}': {'m_{1}': 1, 'c_{18}': 1}, 'c_{14}': {'v_{11}': 1, 'v_{10}': 1}, 'c_{18}': {'v_{11}': 1, 'v_{1}': 1}, 'm_{4}': {'v_{2}': 1, 'v_{1}': 1}, 'm_{5}': {'v_{4}': 1, 'v_{5}': 1}, 's_{9}': {'m_{11}': 1, 'c_{13}': 1, 'c_{3}': 1, 'm_{13}': 1, 'm_{8}': 1, 'm_{14}': 1}, 's_{12}': {'m_{2}': 1, 'c_{16}': 1, 'm_{5}': 1, 'c_{8}': 1}},
    {}  # don't really care about coproduct definition
)

nabla_g3 = {'h0_0': [],
            'h2_1': [('m_{6}', 'm_{6}', 'c_{7}'), ('m_{9}', 'm_{9}', 'c_{3}'), ('m_{4}', 'c_{7}', 'm_{6}'), ('m_{9}', 'm_{9}', 'c_{7}'), ('m_{4}', 'c_{7}', 'm_{9}'), ('m_{6}', 'm_{9}', 'c_{3}'), ('m_{11}', 'c_{3}', 'm_{9}'), ('m_{11}', 'c_{3}', 'm_{6}'), ('m_{4}', 'c_{3}', 'm_{6}'), ('m_{9}', 'm_{6}', 'c_{3}'), ('m_{6}', 'm_{9}', 'c_{7}'), ('m_{6}', 'm_{6}', 'c_{3}'), ('m_{9}', 'm_{6}', 'c_{7}'), ('m_{4}', 'c_{3}', 'm_{9}'), ('m_{11}', 'c_{7}', 'm_{6}'), ('m_{11}', 'c_{7}', 'm_{9}'), ('m_{6}', 'c_{9}', 'm_{3}'), ('m_{2}', 'm_{9}', 'c_{5}'), ('t_{7}', 'm_{4}', 'v_{2}'), ('m_{6}', 'c_{5}', 'c_{3}'), ('s_{6}', 'v_{9}', 'm_{8}'), ('v_{8}', 's_{6}', 'm_{7}'), ('t_{6}', 'm_{7}', 'v_{1}'), ('v_{6}', 't_{5}', 'm_{7}'), ('t_{7}', 'c_{3}', 'v_{1}'), ('m_{4}', 't_{8}', 'v_{10}'), ('m_{9}', 'm_{6}', 'c_{5}'), ('c_{3}', 'c_{6}', 'm_{7}'), ('t_{6}', 'v_{10}', 'm_{13}'), ('m_{6}', 'c_{3}', 'c_{5}'), ('c_{6}', 'm_{8}', 'm_{4}'), ('m_{2}', 'm_{9}', 'c_{9}'), ('m_{6}', 's_{1}', 'v_{11}'), ('m_{6}', 's_{5}', 'v_{11}'), ('m_{9}', 'c_{7}', 'm_{8}'), ('c_{6}', 'm_{7}', 'm_{13}'), ('m_{9}', 'm_{6}', 'c_{9}'), ('m_{11}', 'c_{13}', 'm_{7}'), ('c_{6}', 'm_{7}', 'm_{8}'), ('m_{6}', 's_{10}', 'v_{1}'), ('m_{6}', 'v_{7}', 's_{5}'), ('m_{13}', 'c_{14}', 'm_{8}'), ('m_{4}', 't_{8}', 'v_{1}'), ('m_{6}', 'c_{3}', 'm_{2}'), ('m_{6}', 'v_{7}', 's_{10}'), ('c_{10}', 'm_{7}', 'm_{13}'), ('m_{9}', 'c_{3}', 'c_{13}'), ('v_{6}', 'm_{6}', 's_{6}'), ('m_{8}', 'c_{13}', 'm_{7}'), ('m_{9}', 's_{6}', 'v_{11}'), ('m_{6}', 'c_{6}', 'm_{13}'), ('m_{4}', 'm_{6}', 'c_{6}'), ('v_{6}', 'm_{9}', 's_{9}'), ('v_{1}', 't_{7}', 'm_{4}'), ('t_{7}', 'v_{1}', 'm_{4}'), ('c_{6}', 'm_{7}', 'm_{4}'), ('m_{13}', 'c_{14}', 'm_{7}'), ('m_{6}', 'v_{8}', 's_{5}'), ('t_{5}', 'm_{13}', 'v_{9}'), ('c_{9}', 'm_{7}', 'm_{7}'), ('v_{1}', 't_{5}', 'm_{4}'), ('c_{5}', 'm_{7}', 'c_{3}'), ('c_{5}', 'm_{3}', 'm_{7}'), ('s_{5}', 'v_{11}', 'm_{8}'), ('m_{11}', 'c_{3}', 'm_{8}'), ('c_{7}', 'c_{14}', 'm_{7}'), ('m_{9}', 'v_{7}', 's_{6}'), ('v_{1}', 'm_{9}', 's_{5}'), ('c_{3}', 'm_{6}', 'c_{10}'), ('m_{4}', 'c_{6}', 'm_{8}'), ('c_{3}', 'v_{3}', 't_{6}'), ('s_{6}', 'm_{8}', 'v_{1}'), ('t_{7}', 'm_{13}', 'v_{9}'), ('m_{2}', 'c_{6}', 'm_{8}'), ('c_{6}', 'c_{13}', 'm_{7}'), ('c_{6}', 'm_{8}', 'c_{3}'), ('m_{6}', 's_{2}', 'v_{11}'), ('m_{11}', 'c_{3}', 'm_{7}'), ('t_{5}', 'v_{10}', 'c_{3}'), ('m_{9}', 'm_{11}', 'c_{13}'), ('m_{9}', 'c_{9}', 'c_{3}'), ('v_{1}', 'c_{3}', 't_{6}'), ('m_{9}', 'm_{7}', 'c_{13}'), ('s_{10}', 'm_{7}', 'v_{10}'), ('c_{3}', 'm_{9}', 'c_{9}'), ('c_{9}', 'm_{3}', 'm_{7}'), ('m_{9}', 'c_{5}', 'm_{13}'), ('s_{10}', 'm_{8}', 'v_{10}'), ('c_{6}', 'c_{13}', 'm_{8}'), ('v_{1}', 'm_{6}', 's_{1}'), ('c_{3}', 't_{6}', 'v_{1}'), ('m_{6}', 'c_{3}', 'm_{3}'), ('m_{4}', 'v_{6}', 't_{5}'), ('s_{9}', 'v_{11}', 'm_{7}'), ('c_{7}', 'm_{2}', 'm_{8}'), ('m_{4}', 'c_{7}', 'm_{7}'), ('m_{7}', 'c_{14}', 'm_{7}'), ('m_{9}', 'v_{1}', 's_{1}'), ('c_{5}', 'm_{8}', 'm_{4}'), ('t_{8}', 'c_{3}', 'v_{3}'), ('m_{9}', 's_{9}', 'v_{11}'), ('m_{4}', 'v_{2}', 't_{5}'), ('v_{2}', 'c_{3}', 't_{5}'), ('v_{6}', 't_{7}', 'm_{13}'), ('c_{7}', 'm_{3}', 'm_{7}'), ('m_{9}', 'v_{8}', 's_{5}'), ('m_{4}', 'm_{6}', 'c_{10}'), ('m_{6}', 'c_{7}', 'c_{9}'), ('s_{1}', 'm_{8}', 'v_{10}'), ('c_{3}', 'm_{6}', 'm_{8}'), ('m_{6}', 'v_{1}', 's_{10}'), ('m_{9}', 'v_{1}', 's_{9}'), ('s_{5}', 'v_{9}', 'm_{7}'), ('m_{2}', 'c_{6}', 'm_{7}'), ('s_{6}', 'm_{7}', 'v_{10}'), ('m_{9}', 'm_{13}', 'c_{14}'), ('t_{5}', 'v_{3}', 'm_{13}'), ('m_{9}', 'c_{3}', 'm_{2}'), ('s_{2}', 'v_{11}', 'm_{7}'), ('t_{7}', 'c_{3}', 'v_{3}'), ('m_{2}', 'm_{9}', 'c_{6}'), ('c_{10}', 'm_{8}', 'c_{3}'), ('c_{5}', 'm_{3}', 'm_{8}'), ('c_{3}', 'c_{13}', 'm_{7}'), ('t_{8}', 'm_{7}', 'v_{10}'), ('v_{6}', 'm_{6}', 's_{1}'), ('t_{6}', 'm_{13}', 'v_{1}'), ('v_{1}', 'm_{6}', 's_{10}'), ('v_{3}', 'm_{2}', 't_{5}'), ('m_{4}', 't_{7}', 'v_{1}'), ('m_{6}', 'm_{7}', 'c_{14}'), ('v_{6}', 't_{6}', 'm_{13}'), ('c_{3}', 'm_{6}', 'c_{9}'), ('m_{6}', 'v_{1}', 's_{1}'), ('m_{9}', 'c_{10}', 'c_{14}'), ('t_{6}', 'v_{10}', 'm_{7}'), ('s_{10}', 'v_{11}', 'm_{7}'), ('m_{9}', 's_{10}', 'v_{11}'), ('m_{4}', 't_{6}', 'v_{1}'), ('v_{2}', 'c_{3}', 't_{8}'), ('c_{3}', 'm_{6}', 'c_{5}'), ('m_{11}', 'c_{13}', 'm_{8}'), ('c_{10}', 'm_{8}', 'm_{7}'), ('m_{9}', 'v_{7}', 's_{1}'), ('t_{6}', 'm_{4}', 'v_{1}'), ('m_{6}', 'm_{13}', 'c_{13}'), ('m_{6}', 's_{1}', 'v_{1}'), ('m_{6}', 'v_{7}', 's_{1}'), ('m_{9}', 'c_{7}', 'm_{13}'), ('m_{6}', 'c_{7}', 'm_{2}'), ('c_{9}', 'm_{7}', 'm_{4}'), ('s_{9}', 'v_{9}', 'm_{8}'), ('m_{4}', 'v_{2}', 't_{7}'), ('v_{3}', 'm_{2}', 't_{6}'), ('s_{10}', 'v_{11}', 'm_{8}'), ('c_{5}', 'm_{7}', 'm_{7}'), ('t_{8}', 'v_{10}', 'm_{4}'), ('m_{4}', 'm_{6}', 'c_{5}'), ('c_{7}', 'm_{8}', 'm_{7}'), ('c_{10}', 'm_{7}', 'm_{4}'), ('c_{7}', 'c_{9}', 'm_{7}'), ('m_{6}', 'c_{6}', 'm_{4}'), ('s_{10}', 'm_{7}', 'v_{1}'), ('v_{6}', 'm_{9}', 's_{2}'), ('c_{9}', 'm_{7}', 'c_{3}'), ('c_{10}', 'm_{8}', 'm_{13}'), ('c_{3}', 'm_{2}', 'm_{7}'), ('m_{8}', 'c_{14}', 'm_{8}'), ('c_{3}', 'c_{10}', 'm_{7}'), ('v_{6}', 't_{5}', 'c_{3}'), ('c_{6}', 'm_{8}', 'm_{13}'), ('m_{6}', 'c_{5}', 'm_{13}'), ('c_{10}', 'm_{7}', 'm_{8}'), ('m_{9}', 'v_{7}', 's_{10}'), ('t_{6}', 'c_{3}', 'v_{1}'), ('m_{6}', 'c_{5}', 'm_{8}'), ('m_{13}', 'c_{13}', 'm_{8}'), ('v_{1}', 't_{6}', 'm_{4}'), ('v_{6}', 'm_{9}', 's_{5}'), ('m_{4}', 'v_{6}', 't_{6}'), ('v_{1}', 't_{8}', 'm_{4}'), ('v_{6}', 'm_{9}', 's_{10}'), ('c_{3}', 'v_{6}', 't_{6}'), ('t_{7}', 'v_{10}', 'm_{7}'), ('m_{6}', 's_{5}', 'v_{1}'), ('c_{5}', 'm_{7}', 'm_{13}'), ('m_{4}', 'm_{9}', 'c_{9}'), ('s_{5}', 'm_{7}', 'v_{1}'), ('m_{6}', 'v_{7}', 's_{6}'), ('v_{8}', 's_{5}', 'm_{7}'), ('m_{9}', 'm_{2}', 'c_{9}'), ('m_{4}', 't_{5}', 'v_{1}'), ('c_{7}', 'm_{3}', 'm_{8}'), ('s_{1}', 'm_{7}', 'v_{1}'), ('t_{7}', 'v_{10}', 'c_{3}'), ('t_{7}', 'v_{10}', 'm_{4}'), ('v_{1}', 'm_{2}', 't_{7}'), ('m_{9}', 'c_{6}', 'c_{13}'), ('s_{9}', 'm_{8}', 'v_{10}'), ('c_{7}', 'm_{13}', 'm_{7}'), ('m_{9}', 's_{2}', 'v_{1}'), ('v_{1}', 's_{6}', 'm_{7}'), ('c_{6}', 'm_{7}', 'c_{3}'), ('t_{5}', 'm_{4}', 'v_{2}'), ('m_{9}', 'c_{5}', 'm_{4}'), ('v_{6}', 't_{8}', 'm_{13}'), ('m_{2}', 'm_{6}', 'c_{6}'), ('m_{9}', 'c_{5}', 'c_{3}'), ('m_{2}', 't_{5}', 'v_{1}'), ('t_{5}', 'c_{3}', 'v_{1}'), ('t_{5}', 'm_{4}', 'v_{1}'), ('m_{9}', 'c_{9}', 'm_{4}'), ('c_{5}', 'm_{8}', 'm_{13}'), ('m_{7}', 'c_{13}', 'm_{8}'), ('c_{9}', 'm_{8}', 'm_{13}'), ('m_{2}', 't_{7}', 'v_{1}'), ('m_{6}', 'c_{3}', 'm_{6}'), ('v_{6}', 't_{5}', 'm_{4}'), ('m_{9}', 'v_{1}', 's_{2}'), ('c_{7}', 'c_{14}', 'm_{8}'), ('c_{10}', 'c_{14}', 'm_{8}'), ('m_{6}', 's_{6}', 'v_{1}'), ('m_{9}', 'c_{5}', 'm_{3}'), ('m_{9}', 'c_{6}', 'c_{3}'), ('m_{9}', 'c_{6}', 'm_{4}'), ('c_{3}', 'c_{9}', 'm_{8}'), ('s_{2}', 'm_{7}', 'v_{1}'), ('t_{8}', 'v_{3}', 'm_{13}'), ('s_{2}', 'v_{9}', 'm_{7}'), ('v_{6}', 'm_{6}', 's_{10}'), ('v_{6}', 'm_{6}', 's_{9}'), ('m_{6}', 'c_{7}', 'm_{6}'), ('m_{4}', 't_{7}', 'v_{10}'), ('v_{3}', 'm_{2}', 't_{7}'), ('c_{7}', 'm_{6}', 'm_{8}'), ('m_{2}', 't_{7}', 'v_{10}'), ('s_{2}', 'm_{7}', 'v_{10}'), ('v_{6}', 'm_{6}', 's_{2}'), ('m_{9}', 'c_{3}', 'm_{3}'), ('m_{9}', 'c_{9}', 'm_{13}'), ('m_{9}', 's_{9}', 'v_{1}'), ('m_{9}', 'c_{3}', 'c_{5}'), ('s_{2}', 'v_{11}', 'm_{8}'), ('s_{9}', 'v_{9}', 'm_{7}'), ('v_{1}', 't_{8}', 'm_{7}'), ('m_{9}', 'v_{7}', 's_{2}'), ('c_{7}', 'm_{13}', 'm_{8}'), ('v_{1}', 'm_{6}', 's_{5}'), ('m_{4}', 'm_{6}', 'c_{9}'), ('t_{8}', 'v_{10}', 'c_{3}'), ('t_{8}', 'v_{9}', 'm_{7}'), ('c_{3}', 'm_{8}', 'm_{8}'), ('m_{9}', 'm_{4}', 'c_{9}'), ('v_{6}', 't_{7}', 'm_{4}'), ('c_{9}', 'm_{7}', 'm_{13}'), ('m_{9}', 'c_{7}', 'm_{6}'), ('v_{8}', 's_{5}', 'm_{8}'), ('m_{9}', 'm_{11}', 'c_{14}'), ('m_{9}', 'v_{8}', 's_{6}'), ('m_{9}', 'c_{9}', 'm_{3}'), ('m_{9}', 'c_{10}', 'm_{13}'), ('v_{1}', 'm_{9}', 's_{2}'), ('m_{4}', 't_{5}', 'v_{10}'), ('m_{11}', 'c_{14}', 'm_{7}'), ('m_{4}', 'c_{3}', 'm_{7}'), ('v_{2}', 'c_{3}', 't_{7}'), ('m_{9}', 'm_{4}', 'c_{5}'), ('v_{6}', 't_{7}', 'm_{7}'), ('c_{3}', 't_{5}', 'v_{1}'), ('m_{2}', 't_{6}', 'v_{1}'), ('c_{9}', 'm_{8}', 'm_{7}'), ('m_{6}', 'c_{10}', 'm_{13}'), ('c_{3}', 'v_{6}', 't_{5}'), ('m_{9}', 'c_{3}', 'm_{13}'), ('t_{7}', 'v_{9}', 'm_{7}'), ('t_{7}', 'm_{7}', 'v_{10}'), ('s_{9}', 'm_{8}', 'v_{1}'), ('s_{1}', 'v_{9}', 'm_{7}'), ('c_{3}', 't_{7}', 'v_{10}'), ('m_{6}', 'c_{9}', 'm_{4}'), ('m_{6}', 'm_{8}', 'c_{14}'), ('v_{6}', 't_{6}', 'c_{3}'), ('m_{2}', 't_{8}', 'v_{1}'), ('m_{6}', 'v_{7}', 's_{2}'), ('c_{3}', 'm_{8}', 'm_{7}'), ('c_{3}', 'm_{9}', 'c_{10}'), ('m_{4}', 'c_{7}', 'm_{8}'), ('s_{6}', 'v_{11}', 'm_{7}'), ('t_{6}', 'm_{4}', 'v_{2}'), ('v_{6}', 't_{8}', 'c_{3}'), ('t_{6}', 'c_{3}', 'v_{3}'), ('m_{6}', 'c_{10}', 'm_{4}'), ('m_{9}', 's_{10}', 'v_{1}'), ('s_{2}', 'v_{9}', 'm_{8}'), ('s_{5}', 'm_{7}', 'v_{10}'), ('m_{9}', 's_{1}', 'v_{11}'), ('t_{5}', 'v_{2}', 'c_{3}'), ('v_{1}', 't_{6}', 'm_{13}'), ('t_{7}', 'm_{13}', 'v_{1}'), ('m_{7}', 'c_{13}', 'm_{7}'), ('c_{9}', 'm_{8}', 'c_{3}'), ('c_{5}', 'm_{8}', 'c_{3}'), ('m_{6}', 'c_{5}', 'm_{4}'), ('c_{3}', 't_{7}', 'v_{1}'), 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'm_{10}'), ('m_{4}', 's_{10}', 'v_{1}'), ('m_{4}', 's_{9}', 'v_{11}'), ('v_{1}', 's_{5}', 'm_{5}'), ('m_{11}', 'v_{2}', 's_{10}'), ('v_{1}', 's_{8}', 'm_{5}'), ('t_{1}', 'v_{5}', 'm_{1}'), ('m_{11}', 'c_{6}', 'c_{13}'), ('c_{3}', 'm_{5}', 'm_{12}'), ('c_{8}', 'm_{10}', 'm_{3}'), ('v_{1}', 's_{6}', 'm_{5}'), ('c_{3}', 'c_{13}', 'm_{10}'), ('t_{1}', 'v_{1}', 'm_{1}'), ('m_{11}', 'c_{3}', 'm_{8}'), ('c_{8}', 'm_{12}', 'm_{5}'), ('m_{11}', 'c_{10}', 'm_{7}'), ('c_{8}', 'm_{12}', 'm_{10}'), ('m_{11}', 's_{10}', 'v_{1}'), ('m_{4}', 'v_{3}', 's_{8}'), ('m_{11}', 'c_{3}', 'm_{13}'), ('t_{2}', 'm_{1}', 'v_{1}'), ('m_{11}', 'c_{3}', 'c_{13}'), ('s_{7}', 'm_{10}', 'v_{1}'), ('m_{4}', 'v_{1}', 's_{10}'), ('s_{6}', 'v_{11}', 'm_{10}'), ('m_{11}', 'c_{7}', 'm_{3}'), ('c_{10}', 'm_{7}', 'm_{10}'), ('m_{4}', 'm_{11}', 'c_{14}'), ('m_{4}', 's_{6}', 'v_{11}'), ('s_{5}', 'm_{5}', 'v_{1}'), ('m_{11}', 'm_{13}', 'c_{13}'), ('m_{12}', 'c_{6}', 'm_{5}'), ('c_{4}', 'm_{5}', 'm_{1}'), ('c_{7}', 'm_{8}', 'm_{10}'), ('t_{2}', 'm_{12}', 'v_{1}'), ('c_{3}', 'm_{8}', 'm_{5}'), ('t_{2}', 'm_{12}', 'v_{8}'), ('m_{11}', 'c_{4}', 'c_{6}'), ('c_{7}', 'm_{8}', 'm_{5}'), ('v_{8}', 's_{5}', 'm_{5}'), ('m_{11}', 'c_{7}', 'c_{14}'), ('c_{4}', 'm_{12}', 'm_{5}'), ('c_{8}', 'm_{10}', 'm_{5}'), ('m_{4}', 'c_{8}', 'c_{10}'), ('m_{4}', 'c_{4}', 'm_{1}'), ('m_{10}', 'c_{10}', 'm_{10}'), ('s_{7}', 'v_{9}', 'm_{10}'), ('t_{4}', 'v_{1}', 'm_{1}'), ('c_{8}', 'm_{10}', 'm_{1}'), ('t_{3}', 'v_{5}', 'm_{3}'), ('s_{9}', 'v_{4}', 'm_{10}'), ('t_{3}', 'm_{1}', 'v_{1}'), ('m_{11}', 'c_{7}', 'm_{5}'), ('s_{5}', 'm_{10}', 'v_{1}'), ('m_{4}', 's_{10}', 'v_{11}'), ('t_{1}', 'm_{3}', 'v_{11}'), ('c_{8}', 'c_{10}', 'm_{5}'), ('m_{4}', 'm_{12}', 'c_{10}'), ('s_{5}', 'v_{11}', 'm_{5}'), ('m_{4}', 'm_{7}', 'c_{14}'), ('s_{9}', 'm_{5}', 'v_{1}'), ('m_{12}', 'c_{10}', 'm_{10}'), ('m_{11}', 'v_{2}', 's_{9}'), ('m_{7}', 'c_{13}', 'm_{5}'), ('m_{11}', 'm_{11}', 'c_{7}'), ('t_{2}', 'v_{1}', 'm_{1}'), ('s_{8}', 'v_{9}', 'm_{10}'), ('s_{10}', 'v_{11}', 'm_{5}'), ('m_{8}', 'c_{13}', 'm_{10}'), ('m_{4}', 'v_{2}', 's_{10}'), ('v_{1}', 's_{5}', 'm_{10}'), ('m_{11}', 's_{9}', 'v_{11}'), ('m_{4}', 'c_{8}', 'm_{3}'), ('t_{2}', 'm_{1}', 'v_{11}'), ('m_{11}', 'c_{3}', 'm_{12}'), ('m_{4}', 'v_{2}', 's_{5}'), ('c_{8}', 'c_{10}', 'm_{10}'), ('v_{3}', 's_{8}', 'm_{5}'), ('m_{4}', 'v_{1}', 's_{9}'), ('m_{11}', 'c_{7}', 'm_{12}'), ('m_{11}', 'c_{6}', 'm_{7}'), ('m_{11}', 'c_{8}', 'm_{1}'), ('m_{13}', 'c_{14}', 'm_{10}'), ('c_{7}', 'm_{10}', 'm_{1}'), ('m_{11}', 'm_{7}', 'c_{13}'), ('m_{4}', 'v_{2}', 's_{6}'), ('m_{11}', 'v_{8}', 's_{5}'), ('t_{2}', 'v_{5}', 'm_{3}'), ('s_{6}', 'v_{11}', 'm_{5}'), ('s_{8}', 'm_{5}', 'v_{5}'), ('m_{11}', 'v_{3}', 's_{7}'), ('c_{4}', 'm_{12}', 'm_{10}'), ('m_{11}', 'c_{8}', 'c_{10}'), ('m_{11}', 'c_{14}', 'm_{10}'), ('m_{11}', 'c_{8}', 'm_{3}'), ('m_{11}', 'm_{10}', 'c_{6}'), ('s_{10}', 'm_{10}', 'v_{5}'), ('s_{6}', 'v_{4}', 'm_{5}'), ('m_{4}', 'm_{11}', 'c_{7}'), ('s_{8}', 'v_{9}', 'm_{5}'), ('s_{10}', 'v_{11}', 'm_{10}'), ('m_{12}', 'c_{6}', 'm_{10}'), ('m_{11}', 'm_{12}', 'c_{10}'), ('t_{4}', 'm_{3}', 'v_{11}'), ('m_{11}', 'v_{1}', 's_{9}'), ('m_{11}', 'm_{8}', 'c_{14}'), ('m_{10}', 'c_{6}', 'm_{10}'), ('m_{4}', 'c_{6}', 'c_{13}'), ('m_{11}', 'c_{4}', 'm_{1}'), ('m_{10}', 'c_{6}', 'm_{5}'), ('t_{3}', 'm_{3}', 'v_{1}'), ('c_{10}', 'm_{7}', 'm_{5}'), ('m_{4}', 'v_{2}', 's_{7}'), ('m_{11}', 'm_{11}', 'c_{14}'), ('m_{4}', 'c_{4}', 'c_{6}'), ('c_{4}', 'c_{6}', 'm_{10}'), ('m_{11}', 's_{10}', 'v_{11}'), ('c_{6}', 'm_{7}', 'm_{5}'), ('m_{4}', 'c_{10}', 'm_{7}'), ('t_{1}', 'm_{1}', 'v_{11}'), ('m_{4}', 'c_{7}', 'm_{12}'), ('c_{7}', 'm_{5}', 'm_{12}'), ('m_{8}', 'c_{14}', 'm_{5}'), ('s_{7}', 'v_{9}', 'm_{5}'), ('m_{11}', 's_{8}', 'v_{1}'), ('c_{8}', 'm_{5}', 'm_{1}'), ('s_{10}', 'm_{5}', 'v_{5}'), ('s_{7}', 'm_{5}', 'v_{5}'), ('m_{11}', 's_{9}', 'v_{1}'), ('m_{7}', 'c_{14}', 'm_{10}'), ('t_{4}', 'm_{1}', 'v_{11}'), ('s_{5}', 'v_{11}', 'm_{10}'), ('v_{3}', 's_{7}', 'm_{5}'), ('v_{1}', 's_{7}', 'm_{5}'), ('m_{4}', 'c_{8}', 'm_{1}'), ('m_{4}', 'm_{7}', 'c_{13}'), ('m_{4}', 's_{5}', 'v_{1}'), ('c_{7}', 'm_{10}', 'm_{3}'), ('v_{8}', 's_{6}', 'm_{5}'), ('t_{3}', 'm_{1}', 'v_{11}'), ('m_{11}', 'c_{3}', 'm_{5}'), ('m_{4}', 's_{7}', 'v_{9}'), ('c_{10}', 'c_{14}', 'm_{5}'), ('t_{4}', 'm_{12}', 'v_{8}'), ('m_{11}', 'c_{3}', 'm_{3}'), ('c_{10}', 'c_{14}', 'm_{10}'), ('t_{1}', 'm_{3}', 'v_{1}'), ('m_{7}', 'c_{14}', 'm_{5}'), ('m_{4}', 'c_{7}', 'm_{1}'), ('c_{7}', 'c_{14}', 'm_{10}'), ('s_{9}', 'm_{10}', 'v_{5}'), ('s_{5}', 'v_{4}', 'm_{5}'), ('c_{4}', 'm_{10}', 'm_{5}'), ('m_{11}', 'v_{2}', 's_{6}'), ('s_{7}', 'm_{10}', 'v_{5}'), ('c_{4}', 'm_{10}', 'm_{1}'), ('m_{4}', 'm_{11}', 'c_{13}'), ('m_{4}', 's_{7}', 'v_{1}'), ('c_{7}', 'm_{13}', 'm_{10}'), ('t_{3}', 'm_{12}', 'v_{1}'), ('m_{11}', 'm_{11}', 'c_{13}'), ('v_{1}', 's_{6}', 'm_{10}'), ('t_{1}', 'm_{1}', 'v_{1}'), ('m_{11}', 'm_{8}', 'c_{13}'), ('m_{11}', 'm_{7}', 'c_{14}'), ('c_{3}', 'm_{5}', 'm_{1}'), ('v_{8}', 's_{5}', 'm_{10}'), ('c_{3}', 'm_{10}', 'm_{12}'), ('m_{11}', 'v_{1}', 's_{10}'), ('s_{5}', 'v_{4}', 'm_{10}'), ('m_{11}', 's_{5}', 'v_{11}'), ('m_{4}', 'm_{11}', 'c_{3}'), ('t_{3}', 'm_{3}', 'v_{11}'), ('m_{11}', 'v_{2}', 's_{5}'), ('s_{8}', 'm_{10}', 'v_{5}'), ('m_{11}', 'v_{8}', 's_{6}'), ('m_{11}', 'c_{4}', 'm_{3}'), ('t_{3}', 'v_{8}', 'm_{3}'), ('m_{11}', 'c_{10}', 'c_{14}'), ('t_{4}', 'm_{3}', 'v_{1}'), ('m_{11}', 'm_{10}', 'c_{10}'), ('m_{4}', 'c_{3}', 'm_{13}'), ('m_{11}', 'c_{3}', 'm_{1}'), ('m_{4}', 'c_{7}', 'm_{3}'), ('m_{4}', 's_{8}', 'v_{1}'), ('t_{2}', 'v_{8}', 'm_{3}'), ('v_{3}', 's_{8}', 'm_{10}'), ('m_{4}', 'c_{3}', 'c_{13}'), ('m_{4}', 'v_{2}', 's_{8}'), ('t_{4}', 'v_{5}', 'm_{1}'), ('m_{11}', 'm_{13}', 'c_{14}'), ('c_{4}', 'm_{10}', 'm_{3}'), ('m_{11}', 'c_{3}', 'c_{4}'), ('c_{3}', 'c_{4}', 'm_{5}'), ('c_{7}', 'c_{8}', 'm_{10}'), ('c_{7}', 'c_{8}', 'm_{5}'), ('m_{4}', 'c_{4}', 'm_{5}'), ('m_{4}', 'c_{3}', 'c_{4}'), ('m_{4}', 'c_{3}', 'm_{5}'), ('m_{11}', 'c_{7}', 'c_{8}'), ('m_{4}', 'c_{7}', 'c_{8}'), ('m_{4}', 'c_{8}', 'm_{5}'), ('c_{3}', 'c_{4}', 'm_{10}'), ('m_{4}', 'c_{7}', 'm_{5}')],
            'h1_0': [('m_{4}', 'm_{4}', 'v_{1}'), ('m_{11}', 'm_{4}', 'v_{2}'), ('m_{4}', 'm_{4}', 'v_{2}'), ('m_{4}', 'v_{2}', 'm_{4}'), ('m_{11}', 'v_{2}', 'm_{4}'), ('m_{4}', 'v_{1}', 'm_{4}'), ('m_{11}', 'v_{1}', 'm_{4}'), ('m_{11}', 'm_{4}', 'v_{1}')],
            'h1_1': [('v_{1}', 'c_{7}', 'c_{3}'), ('c_{7}', 'm_{4}', 'v_{2}'), ('c_{7}', 'c_{3}', 'v_{1}'), ('c_{7}', 'm_{4}', 'v_{1}'), ('v_{2}', 'c_{7}', 'c_{3}'), ('v_{2}', 'c_{3}', 'm_{4}'), ('c_{3}', 'v_{1}', 'm_{4}'), ('m_{4}', 'c_{3}', 'v_{3}'), ('m_{4}', 'c_{3}', 'v_{1}'), ('v_{1}', 'c_{3}', 'c_{3}'), ('c_{3}', 'v_{2}', 'c_{3}'), ('c_{7}', 'v_{3}', 'm_{4}'), ('c_{3}', 'v_{3}', 'm_{4}'), ('m_{4}', 'c_{7}', 'v_{3}'), ('c_{3}', 'm_{4}', 'v_{2}'), ('v_{1}', 'c_{7}', 'm_{4}'), ('v_{2}', 'c_{7}', 'm_{4}'), ('v_{2}', 'c_{3}', 'c_{3}'), ('c_{3}', 'c_{3}', 'v_{1}'), ('c_{7}', 'v_{1}', 'm_{4}'), ('v_{1}', 'c_{3}', 'm_{4}'), ('c_{3}', 'm_{4}', 'v_{1}'), ('c_{3}', 'v_{3}', 'c_{3}'), ('c_{7}', 'v_{3}', 'c_{3}'), ('c_{7}', 'v_{2}', 'c_{3}'), ('c_{3}', 'c_{3}', 'v_{3}'), ('m_{4}', 'c_{7}', 'v_{1}'), ('c_{7}', 'c_{3}', 'v_{3}')],
            'h1_2': [('m_{9}', 'v_{2}', 'c_{3}'), ('c_{3}', 'v_{6}', 'm_{6}'), ('m_{6}', 'v_{7}', 'm_{2}'), ('m_{6}', 'm_{2}', 'v_{6}'), ('v_{1}', 'm_{6}', 'm_{4}'), ('v_{2}', 'c_{3}', 'm_{6}'), ('v_{6}', 'm_{6}', 'c_{3}'), ('v_{3}', 'm_{2}', 'm_{6}'), ('v_{1}', 'c_{3}', 'm_{9}'), ('m_{2}', 'm_{9}', 'v_{1}'), ('v_{1}', 'c_{3}', 'm_{6}'), ('v_{6}', 'm_{9}', 'm_{6}'), ('v_{6}', 'm_{6}', 'm_{6}'), ('m_{6}', 'v_{7}', 'c_{3}'), ('m_{9}', 'c_{3}', 'v_{1}'), ('c_{3}', 'm_{6}', 'v_{1}'), ('m_{9}', 'v_{7}', 'c_{3}'), ('m_{9}', 'm_{4}', 'v_{2}'), ('v_{1}', 'm_{9}', 'm_{4}'), ('m_{2}', 'm_{6}', 'v_{1}'), ('v_{3}', 'm_{2}', 'm_{9}'), ('m_{6}', 'v_{6}', 'm_{6}'), ('v_{1}', 'm_{6}', 'c_{3}'), ('m_{9}', 'v_{3}', 'm_{2}'), ('c_{3}', 'v_{3}', 'm_{9}'), ('m_{9}', 'm_{6}', 'v_{1}'), ('m_{4}', 'v_{2}', 'm_{9}'), ('m_{4}', 'm_{6}', 'v_{1}'), ('m_{4}', 'v_{6}', 'm_{6}'), ('v_{1}', 'm_{9}', 'm_{2}'), ('m_{2}', 'm_{6}', 'v_{7}'), ('m_{6}', 'c_{3}', 'v_{3}'), ('m_{4}', 'v_{6}', 'm_{9}'), ('m_{6}', 'm_{6}', 'v_{7}'), ('v_{1}', 'm_{6}', 'm_{2}'), ('m_{9}', 'm_{6}', 'v_{7}'), ('m_{4}', 'm_{9}', 'v_{7}'), ('m_{6}', 'c_{3}', 'v_{1}'), ('m_{2}', 'm_{9}', 'v_{7}'), ('c_{3}', 'v_{6}', 'm_{9}'), ('v_{1}', 'm_{2}', 'm_{9}'), ('m_{9}', 'c_{3}', 'v_{3}'), ('v_{6}', 'm_{6}', 'm_{4}'), ('v_{6}', 'm_{9}', 'm_{2}'), ('c_{3}', 'v_{3}', 'm_{6}'), ('v_{6}', 'm_{9}', 'c_{3}'), ('m_{6}', 'm_{4}', 'v_{2}'), ('m_{9}', 'v_{1}', 'm_{4}'), ('m_{4}', 'm_{6}', 'v_{7}'), ('v_{1}', 'm_{9}', 'c_{3}'), ('c_{3}', 'm_{9}', 'v_{1}'), ('v_{1}', 'm_{9}', 'm_{6}'), ('m_{6}', 'm_{6}', 'v_{1}'), ('v_{2}', 'c_{3}', 'm_{9}'), ('m_{4}', 'v_{2}', 'm_{6}'), ('v_{1}', 'm_{6}', 'm_{6}'), ('m_{6}', 'v_{7}', 'm_{6}'), ('m_{6}', 'v_{3}', 'm_{2}'), ('m_{9}', 'v_{7}', 'm_{4}'), ('m_{9}', 'm_{4}', 'v_{1}'), ('v_{1}', 'm_{2}', 'm_{6}'), ('v_{6}', 'm_{6}', 'm_{2}'), ('v_{6}', 'm_{9}', 'm_{4}'), ('m_{6}', 'v_{1}', 'm_{4}'), ('m_{4}', 'm_{9}', 'v_{1}'), ('m_{9}', 'v_{7}', 'm_{2}'), ('m_{6}', 'v_{7}', 'm_{4}'), ('m_{6}', 'm_{4}', 'v_{1}'), ('m_{9}', 'v_{7}', 'm_{6}'), ('m_{6}', 'v_{2}', 'c_{3}'), ('m_{9}', 'v_{6}', 'm_{6}'), ('m_{6}', 'm_{2}', 'v_{1}'), ('c_{3}', 'm_{9}', 'v_{7}'), ('m_{9}', 'm_{2}', 'v_{1}'), ('m_{9}', 'm_{2}', 'v_{6}'), ('c_{3}', 'm_{6}', 'v_{7}')]
            }

partial_derivative_g3 = {'h2_1': [(['c_{10}', 'c_{6}', 'm_{7}', 'm_{8}'], ['c_{9}'], ['m_{2}']), (['m_{8}', 'm_{7}'], ['c_{9}'], ['m_{5}']), (['m_{8}', 'm_{7}'], ['c_{9}'], ['m_{12}']), (['m_{8}', 'm_{7}'], ['c_{9}'], ['m_{9}']), (['m_{7}', 'm_{8}'], ['c_{9}'], ['c_{8}']), (['m_{5}'], ['m_{3}'], ['m_{10}']), (['v_{3}'], ['c_{13}'], ['a_{2}']), (['v_{3}'], ['c_{13}'], ['a_{4}']), (['a_{1}'], ['v_{4}'], ['m_{12}']), (['v_{1}'], ['c_{10}', 'c_{6}'], ['s_{4}']), (['v_{1}'], ['c_{6}', 'c_{10}'], ['s_{12}']), (['v_{3}'], ['v_{10}', 'v_{11}'], ['D']), (['v_{11}', 'v_{8}'], ['m_{8}'], ['a_{2}']), (['s_{11}'], ['v_{5}', 'v_{6}'], ['m_{2}']), (['t_{6}', 't_{5}', 't_{8}', 't_{7}'], ['v_{10}', 'v_{9}'], ['m_{7}']), (['m_{14}'], ['s_{5}'], ['v_{8}']), (['c_{9}'], ['c_{5}'], ['c_{5}']), (['v_{5}'], ['s_{3}'], ['m_{12}', 'm_{9}', 'c_{5}', 'c_{16}']), (['m_{14}'], ['v_{1}', 'v_{5}'], ['s_{4}']), (['m_{14}'], ['v_{1}', 'v_{5}'], ['s_{12}']), (['v_{10}', 'v_{1}'], ['c_{1}'], ['s_{11}']), (['v_{10}', 'v_{1}'], ['c_{1}'], ['s_{3}']), (['v_{10}', 'v_{1}'], ['c_{1}'], ['s_{12}']), (['v_{10}', 'v_{1}'], ['c_{1}'], ['s_{4}']), (['m_{12}'], ['a_{3}'], ['v_{1}']), (['c_{6}'], ['m_{1}', 'm_{14}'], ['m_{10}']), (['c_{9}'], ['m_{10}'], ['c_{15}']), (['c_{9}'], ['v_{5}'], ['s_{4}']), (['m_{13}'], ['m_{2}'], ['c_{9}', 'c_{5}']), (['v_{10}', 'v_{11}', 'v_{9}'], ['a_{1}'], ['m_{5}']), (['v_{8}', 'v_{9}'], ['a_{1}'], ['c_{4}']), (['v_{6}', 'v_{9}'], ['a_{1}'], ['m_{12}']), (['s_{2}'], ['v_{11}', 'v_{9}'], ['m_{7}', 'm_{8}']), (['s_{12}'], ['m_{7}', 'm_{8}'], ['v_{6}']), (['v_{1}', 'v_{8}'], ['s_{5}'], ['m_{8}', 'm_{7}']), (['v_{1}'], ['s_{5}'], ['c_{10}']), (['v_{1}'], ['s_{5}'], ['m_{13}']), (['v_{1}'], ['s_{5}'], ['c_{8}']), (['v_{1}'], ['s_{5}'], ['c_{15}']), (['v_{1}'], ['s_{5}'], ['m_{10}']), (['c_{18}'], ['a_{2}'], ['v_{6}']), (['m_{1}', 'm_{14}'], ['m_{9}'], ['m_{3}']), (['v_{11}', 'v_{6}'], ['m_{9}'], ['a_{1}']), (['v_{11}', 'v_{6}'], ['m_{9}'], ['a_{3}']), (['m_{14}'], ['m_{7}'], ['c_{8}']), (['m_{14}'], ['m_{7}'], ['m_{10}']), (['m_{14}'], ['m_{7}'], ['m_{3}']), (['c_{15}'], ['c_{13}'], ['m_{13}']), (['c_{15}'], ['s_{5}'], ['v_{8}']), (['c_{14}'], ['c_{4}'], ['m_{2}']), (['c_{14}'], ['c_{4}'], ['c_{4}']), (['c_{14}'], ['c_{4}'], ['m_{5}']), (['s_{3}'], ['v_{5}'], ['m_{6}', 'm_{9}']), (['s_{3}'], ['v_{5}'], ['c_{5}']), (['s_{3}'], ['v_{5}'], ['m_{12}']), (['c_{15}', 'c_{16}'], ['m_{10}'], ['m_{6}']), (['v_{11}', 'v_{8}'], ['s_{11}'], ['m_{12}']), (['v_{6}', 'v_{8}'], ['s_{11}'], ['m_{2}']), (['D'], ['v_{8}'], ['v_{5}', 'v_{9}']), (['c_{2}'], ['c_{14}'], ['c_{8}']), (['v_{6}'], ['s_{5}'], ['m_{12}', 'm_{13}', 'c_{10}', 'c_{4}', 'm_{10}']), (['v_{6}'], ['s_{5}'], ['m_{2}']), (['c_{10}', 'c_{6}', 'm_{7}', 'm_{8}'], ['v_{6}'], ['s_{12}']), (['m_{12}'], ['v_{1}', 'v_{8}'], ['s_{12}']), (['m_{12}'], ['v_{1}'], ['s_{11}']), (['a_{4}'], ['v_{11}'], ['c_{4}']), (['a_{4}'], ['v_{11}', 'v_{1}'], ['c_{5}']), (['a_{4}'], ['v_{10}', 'v_{11}', 'v_{1}'], ['m_{13}']), (['v_{8}'], ['D'], ['v_{1}', 'v_{3}', 'v_{5}']), (['m_{7}', 'm_{8}'], ['a_{2}'], ['v_{5}']), (['m_{1}'], ['c_{18}', 'm_{14}'], ['c_{15}']), (['c_{10}'], ['m_{12}'], ['c_{16}']), (['c_{6}'], ['m_{9}'], ['m_{2}']), (['c_{6}'], ['m_{9}'], ['c_{8}']), (['c_{16}', 'c_{15}'], ['m_{3}'], ['m_{10}']), (['m_{14}'], ['m_{3}'], ['c_{6}', 'c_{10}']), (['m_{14}'], ['m_{3}'], ['c_{8}']), (['m_{14}'], ['m_{3}'], ['m_{10}']), (['m_{14}'], ['m_{3}'], ['c_{13}']), (['m_{14}'], ['m_{3}'], ['c_{15}']), (['m_{7}'], ['s_{11}'], ['v_{5}', 'v_{6}']), (['a_{3}'], ['m_{14}'], ['v_{11}']), (['m_{7}'], ['a_{4}'], ['v_{10}', 'v_{1}', 'v_{6}', 'v_{7}', 'v_{8}']), (['c_{16}'], ['m_{14}'], ['m_{12}']), (['c_{5}'], ['c_{15}'], ['m_{6}']), (['c_{5}'], ['c_{15}'], ['m_{1}']), (['c_{5}'], ['c_{15}'], ['m_{3}']), (['m_{12}'], ['a_{2}'], ['v_{5}', 'v_{6}']), (['m_{6}', 'm_{9}'], ['m_{1}'], ['c_{5}']), (['m_{5}'], ['v_{10}'], ['s_{4}']), (['m_{5}'], ['v_{10}', 'v_{3}'], ['s_{12}']), (['s_{4}'], ['v_{1}', 'v_{6}'], ['m_{9}']), (['s_{4}'], ['v_{6}', 'v_{7}', 'v_{8}'], ['c_{9}']), (['a_{4}'], ['v_{1}', 'v_{5}', 'v_{9}'], ['m_{5}']), (['a_{4}'], ['v_{1}'], ['c_{13}']), (['a_{4}'], ['v_{1}'], ['c_{6}']), (['a_{4}'], ['v_{10}', 'v_{1}'], ['m_{7}']), (['v_{10}', 'v_{3}'], ['c_{5}'], ['s_{4}']), (['m_{2}'], ['a_{4}'], ['v_{5}']), (['s_{12}'], ['c_{13}'], ['v_{3}', 'v_{5}']), (['v_{7}', 'v_{8}'], ['a_{1}'], ['m_{2}']), (['m_{6}', 'm_{9}'], ['s_{5}'], ['v_{11}', 'v_{1}', 'v_{3}']), (['m_{7}'], ['c_{10}'], ['c_{5}']), (['m_{7}'], ['c_{10}'], ['m_{12}']), (['m_{7}'], ['c_{10}'], ['m_{9}']), (['s_{5}'], ['m_{3}'], ['v_{8}']), (['a_{1}'], ['m_{7}'], ['v_{10}']), (['c_{16}'], ['m_{1}', 'c_{17}'], ['c_{8}']), (['v_{6}'], ['s_{3}'], ['m_{12}']), (['v_{6}'], ['s_{3}'], ['m_{9}']), (['v_{6}', 'v_{8}'], ['s_{3}'], ['c_{6}']), (['v_{6}'], ['s_{3}'], ['c_{5}']), (['v_{6}', 'v_{8}'], ['s_{3}'], ['m_{2}']), (['a_{4}'], ['v_{3}'], ['c_{4}', 'm_{5}', 'm_{2}', 'c_{15}']), (['v_{10}', 'v_{3}'], ['s_{3}'], ['c_{9}', 'c_{5}']), (['s_{12}'], ['m_{1}'], ['v_{3}']), (['c_{10}', 'c_{6}'], ['c_{16}'], ['c_{15}', 'c_{16}']), (['m_{13}'], ['m_{5}'], ['c_{9}', 'c_{5}']), (['t_{5}', 't_{8}', 't_{6}', 't_{7}'], ['m_{13}'], ['v_{1}', 'v_{9}']), (['c_{10}'], ['m_{7}'], ['m_{3}']), (['a_{1}'], ['v_{6}'], ['c_{5}']), (['a_{1}'], ['v_{6}'], ['m_{3}']), (['c_{2}'], ['s_{5}'], ['v_{6}', 'v_{8}']), (['m_{7}'], ['m_{3}'], ['c_{8}']), (['m_{7}'], ['m_{3}'], ['c_{13}']), (['m_{7}'], ['m_{3}'], ['m_{5}']), (['m_{7}'], ['m_{3}'], ['m_{14}']), (['m_{7}'], ['m_{3}'], ['m_{7}']), (['m_{3}'], ['c_{6}'], ['m_{14}']), (['m_{3}'], ['c_{6}'], ['m_{10}']), (['m_{3}'], ['c_{6}'], ['m_{12}']), (['m_{1}'], ['c_{6}'], ['c_{15}']), (['v_{10}', 'v_{11}'], ['m_{2}'], ['s_{3}']), (['m_{13}'], ['c_{2}'], ['c_{10}', 'c_{14}', 'm_{3}', 'm_{7}']), (['c_{3}', 'c_{5}', 'c_{7}', 'c_{9}'], ['m_{3}'], ['m_{7}', 'm_{8}']), (['m_{8}', 'm_{7}'], ['v_{11}'], ['a_{2}']), (['m_{8}', 'm_{7}'], ['v_{11}'], ['a_{4}']), (['c_{8}'], ['m_{3}'], ['c_{16}']), (['c_{3}'], ['v_{3}', 'v_{6}'], ['t_{5}', 't_{7}', 't_{8}', 't_{6}']), (['m_{2}'], ['m_{1}'], ['m_{2}']), (['a_{1}'], ['m_{1}'], ['v_{4}', 'v_{5}', 'v_{9}']), (['m_{11}'], ['c_{13}', 'c_{14}'], ['m_{8}', 'm_{7}']), (['c_{9}'], ['a_{1}'], ['v_{6}']), (['v_{6}'], ['a_{4}', 'a_{1}', 'a_{3}', 'a_{2}'], ['c_{5}']), (['c_{4}'], ['a_{3}'], ['v_{5}']), (['c_{15}'], ['c_{18}'], ['c_{5}']), (['a_{1}'], ['m_{14}'], ['v_{11}']), (['c_{5}'], ['v_{6}', 'v_{8}'], ['a_{3}']), (['c_{5}'], ['v_{6}', 'v_{8}'], ['a_{1}']), (['v_{1}'], ['c_{5}'], ['s_{6}']), (['c_{10}'], ['m_{9}', 'm_{6}'], ['m_{5}']), (['c_{10}'], ['m_{9}', 'm_{6}'], ['c_{16}']), (['v_{6}'], ['D'], ['v_{1}', 'v_{3}', 'v_{8}']), (['c_{5}'], ['c_{5}', 'm_{12}', 'c_{15}', 'm_{9}'], ['c_{6}', 'c_{10}']), (['c_{13}'], ['c_{6}'], ['m_{9}']), (['c_{13}'], ['c_{6}'], ['c_{5}']), (['v_{8}'], ['m_{3}'], ['a_{1}']), (['v_{8}'], ['m_{3}'], ['a_{3}']), (['v_{6}', 'v_{8}'], ['m_{3}'], ['s_{3}']), (['c_{3}', 'c_{7}'], ['m_{8}'], ['m_{8}', 'm_{7}']), (['c_{9}', 'c_{5}'], ['v_{8}'], ['s_{3}']), (['v_{1}', 'v_{5}', 'v_{6}'], ['a_{1}'], ['m_{9}']), (['v_{6}'], ['a_{1}'], ['c_{11}']), (['m_{7}', 'm_{8}'], ['a_{4}'], ['v_{3}']), (['v_{5}', 'v_{6}'], ['m_{12}'], ['a_{2}']), (['v_{5}', 'v_{6}'], ['m_{12}'], ['a_{4}']), (['a_{4}'], ['v_{4}'], ['m_{2}']), (['m_{13}'], ['c_{13}'], ['m_{14}', 'm_{1}']), (['c_{9}'], ['c_{1}'], ['c_{5}', 'c_{9}']), (['m_{6}'], ['c_{6}', 'c_{10}'], ['m_{7}']), (['m_{6}'], ['c_{6}', 'c_{10}'], ['m_{5}']), (['v_{8}'], ['m_{13}'], ['a_{2}']), (['v_{10}', 'v_{3}'], ['c_{2}'], ['s_{6}']), (['m_{8}', 'm_{7}'], ['c_{5}', 'c_{9}'], ['c_{9}']), (['m_{7}'], ['s_{5}'], ['v_{1}', 'v_{9}']), (['v_{10}'], ['c_{13}', 'c_{14}'], ['s_{3}']), (['m_{12}'], ['a_{4}'], ['v_{5}', 'v_{6}']), (['c_{9}', 'c_{5}'], ['c_{10}'], ['c_{11}']), (['m_{14}', 'm_{1}'], ['c_{6}'], ['c_{6}']), (['m_{14}', 'c_{18}'], ['a_{3}'], ['v_{7}']), (['c_{5}', 'c_{9}'], ['c_{4}'], ['m_{12}']), (['m_{13}'], ['c_{14}'], ['c_{8}', 'm_{2}', 'c_{16}', 'm_{5}']), (['v_{11}'], ['v_{11}', 'v_{3}'], ['D']), (['c_{17}', 'm_{1}'], ['c_{6}'], ['m_{8}']), (['m_{9}'], ['v_{3}'], ['a_{4}']), (['m_{12}'], ['c_{5}', 'c_{9}'], ['m_{5}']), (['m_{12}'], ['c_{9}', 'c_{5}'], ['c_{8}']), (['v_{1}', 'v_{2}'], ['c_{3}'], ['t_{7}', 't_{5}', 't_{6}', 't_{8}']), (['c_{10}'], ['m_{5}'], ['m_{2}']), (['m_{2}', 'c_{16}', 'c_{8}', 'm_{5}'], ['c_{10}'], ['c_{4}', 'c_{8}']), (['a_{3}'], ['c_{5}'], ['v_{8}']), (['m_{14}'], ['s_{6}'], ['v_{10}', 'v_{3}', 'v_{5}']), (['a_{3}'], ['m_{2}'], ['v_{7}']), (['c_{6}'], ['m_{3}', 'm_{7}', 'c_{6}', 'c_{13}'], ['m_{14}']), (['c_{11}'], ['c_{6}', 'c_{10}'], ['m_{2}', 'c_{9}', 'c_{10}', 'm_{13}', 'm_{9}']), (['c_{14}'], ['m_{5}'], ['m_{2}']), (['c_{14}'], ['m_{5}'], ['c_{4}']), (['c_{14}'], ['m_{5}'], ['m_{5}']), (['v_{8}'], ['s_{3}'], ['m_{7}']), (['v_{8}'], ['s_{3}'], ['c_{16}']), (['v_{8}'], ['s_{3}'], ['c_{14}']), (['v_{7}', 'v_{8}'], ['s_{3}'], ['m_{1}']), (['s_{3}'], ['v_{4}'], ['m_{6}']), (['m_{6}', 'm_{9}'], ['c_{3}', 'c_{7}'], ['m_{8}']), (['m_{6}', 'm_{9}'], ['c_{10}', 'c_{3}', 'c_{5}', 'c_{6}', 'c_{7}', 'c_{9}'], ['m_{13}']), (['m_{9}', 'm_{6}'], ['c_{3}', 'c_{7}'], ['m_{6}']), (['m_{9}', 'm_{6}'], ['c_{3}', 'c_{7}'], ['m_{2}']), (['m_{6}', 'm_{9}'], ['c_{3}', 'c_{5}', 'c_{7}', 'c_{9}'], ['m_{3}']), (['c_{6}', 'c_{10}'], ['m_{7}'], ['m_{8}']), (['v_{1}', 'v_{8}'], ['c_{10}'], ['s_{6}']), (['a_{1}', 'a_{4}', 'a_{3}', 'a_{2}'], ['c_{2}'], ['v_{10}']), (['m_{9}'], ['v_{9}'], ['a_{2}']), (['v_{10}', 'v_{6}', 'v_{9}'], ['a_{2}'], ['c_{4}']), (['v_{6}', 'v_{9}'], ['a_{2}'], ['m_{5}']), (['v_{10}', 'v_{3}'], ['m_{7}'], ['a_{3}']), (['v_{10}', 'v_{3}'], ['m_{7}'], ['a_{1}']), (['c_{15}'], ['m_{9}'], ['m_{2}']), (['m_{6}', 'm_{9}'], ['m_{2}'], ['c_{9}', 'c_{5}']), (['m_{9}', 'm_{6}'], ['m_{2}'], ['m_{2}']), (['m_{6}', 'm_{9}'], ['m_{4}'], ['c_{9}', 'c_{5}']), (['v_{3}'], ['m_{7}', 'm_{8}'], ['s_{12}']), (['c_{15}'], ['a_{2}'], ['v_{1}', 'v_{7}']), (['m_{7}', 'm_{8}'], ['m_{7}'], ['c_{6}', 'c_{10}']), (['m_{8}', 'm_{7}'], ['m_{7}'], ['c_{14}']), (['c_{1}'], ['m_{5}'], ['c_{4}', 'm_{12}', 'm_{5}', 'm_{9}', 'c_{5}', 'm_{2}']), (['m_{14}'], ['c_{10}'], ['c_{8}']), (['m_{12}'], ['s_{11}'], ['v_{6}', 'v_{7}']), (['v_{1}'], ['m_{3}'], ['s_{5}']), (['m_{3}'], ['v_{10}', 'v_{1}'], ['s_{8}']), (['m_{3}'], ['v_{10}'], ['a_{2}']), (['m_{3}'], ['v_{10}', 'v_{6}'], ['s_{6}']), (['m_{2}'], ['v_{10}'], ['s_{4}']), (['m_{13}'], ['a_{2}'], ['v_{10}', 'v_{9}']), (['c_{13}'], ['c_{13}'], ['m_{9}']), (['c_{13}'], ['c_{13}'], ['c_{5}']), (['m_{8}'], ['m_{9}'], ['m_{2}']), (['m_{8}'], ['m_{9}'], ['c_{8}']), (['m_{8}'], ['m_{9}'], ['m_{5}']), (['s_{5}'], ['m_{14}'], ['v_{8}']), (['c_{6}'], ['a_{2}'], ['v_{5}']), (['v_{5}', 'v_{6}'], ['c_{13}'], ['s_{4}']), (['v_{1}', 'v_{5}'], ['c_{13}'], ['s_{8}']), (['v_{1}', 'v_{8}'], ['a_{3}'], ['m_{3}']), (['c_{6}'], ['v_{3}', 'v_{9}'], ['a_{1}']), (['c_{6}'], ['v_{3}', 'v_{9}'], ['a_{3}']), (['m_{1}'], ['a_{2}'], ['v_{5}']), (['a_{4}'], ['v_{9}'], ['c_{17}', 'm_{1}']), (['a_{4}'], ['v_{10}', 'v_{9}'], ['m_{3}']), (['c_{1}'], ['v_{3}', 'v_{5}'], ['s_{11}']), (['c_{1}'], ['v_{3}', 'v_{5}'], ['s_{3}']), (['c_{16}'], ['m_{10}'], ['c_{5}']), (['c_{16}'], ['m_{10}'], ['m_{12}']), (['c_{8}'], ['c_{13}'], ['c_{8}']), (['c_{8}'], ['c_{13}'], ['m_{10}']), (['c_{3}'], ['t_{7}', 't_{6}', 't_{8}', 't_{5}'], ['v_{10}', 'v_{1}']), (['a_{2}'], ['v_{8}'], ['c_{10}']), (['a_{2}'], ['v_{8}'], ['c_{15}']), (['m_{7}', 'm_{8}'], ['v_{5}'], ['s_{6}']), (['m_{13}'], ['v_{8}'], ['s_{3}']), (['m_{13}'], ['v_{10}', 'v_{8}'], ['s_{12}']), (['s_{4}'], ['c_{14}'], ['v_{1}', 'v_{3}']), (['s_{3}'], ['m_{1}'], ['v_{1}', 'v_{5}']), (['s_{12}'], ['v_{10}'], ['c_{16}', 'c_{9}', 'm_{10}', 'm_{12}', 'm_{5}', 'm_{9}']), (['v_{10}', 'v_{1}'], ['m_{2}'], ['s_{11}']), (['v_{10}', 'v_{8}'], ['s_{12}'], ['m_{12}']), (['v_{10}', 'v_{6}'], ['s_{12}'], ['m_{2}']), (['s_{3}'], ['m_{7}', 'm_{8}'], ['v_{5}']), (['c_{15}', 'c_{16}'], ['m_{5}'], ['c_{15}']), (['c_{15}', 'c_{16}', 'c_{5}', 'c_{9}'], 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['s_{5}']), (['v_{10}'], ['c_{13}'], ['a_{1}']), (['m_{6}'], ['c_{18}'], ['c_{5}']), (['c_{8}'], ['a_{2}'], ['v_{5}']), (['c_{5}', 'c_{9}'], ['a_{2}'], ['v_{6}', 'v_{8}']), (['a_{4}'], ['m_{1}'], ['v_{4}', 'v_{7}', 'v_{9}']), (['m_{3}'], ['v_{3}'], ['a_{2}', 'a_{1}', 'a_{4}', 'a_{3}']), (['m_{14}'], ['c_{5}'], ['m_{7}']), (['m_{14}'], ['c_{5}'], ['c_{14}']), (['m_{14}'], ['c_{5}'], ['m_{3}']), (['s_{12}'], ['m_{8}'], ['v_{5}']), (['v_{8}'], ['a_{4}'], ['c_{11}']), (['v_{8}'], ['a_{4}'], ['c_{8}']), (['v_{8}'], ['a_{4}'], ['m_{10}']), (['m_{9}'], ['m_{14}'], ['m_{9}']), (['m_{9}'], ['m_{14}'], ['m_{2}']), (['v_{9}'], ['a_{4}'], ['m_{14}']), (['D'], ['v_{5}'], ['v_{3}']), (['m_{6}'], ['m_{7}', 'c_{13}', 'm_{3}', 'c_{6}'], ['c_{4}']), (['v_{6}'], ['v_{7}'], ['D']), (['m_{6}'], ['c_{1}'], ['c_{9}', 'c_{5}']), (['c_{6}'], ['m_{7}'], ['m_{9}']), (['c_{6}'], ['m_{7}'], ['c_{6}']), (['c_{6}'], ['m_{7}'], ['m_{7}']), (['c_{6}'], ['m_{7}'], ['m_{5}']), (['a_{3}'], ['v_{3}'], ['m_{12}']), (['m_{3}'], ['m_{1}'], ['c_{13}']), (['m_{3}'], ['m_{1}'], ['c_{6}']), (['m_{3}'], ['m_{1}'], ['m_{7}']), (['c_{10}'], ['s_{12}'], ['v_{3}', 'v_{5}', 'v_{6}', 'v_{8}']), (['s_{4}'], ['v_{9}'], ['m_{14}']), (['s_{5}'], ['v_{1}'], ['c_{4}']), (['s_{5}'], ['v_{1}'], ['m_{2}']), (['s_{5}'], ['v_{1}'], ['m_{9}']), (['s_{5}'], ['v_{1}'], ['m_{5}']), (['s_{5}'], ['v_{1}'], ['c_{5}']), (['c_{12}', 'c_{2}', 'm_{6}', 'm_{9}'], ['c_{14}'], ['m_{5}']), (['c_{6}'], ['m_{13}'], ['m_{1}', 'm_{14}']), (['s_{5}'], ['v_{8}'], ['c_{6}']), (['s_{5}'], ['v_{8}'], ['m_{3}']), (['m_{13}'], ['m_{13}'], ['m_{14}', 'm_{1}']), (['v_{6}'], ['m_{8}'], ['s_{4}']), (['v_{6}'], ['m_{8}'], ['s_{12}']), (['m_{8}', 'm_{7}'], ['m_{12}'], ['m_{7}', 'c_{14}', 'm_{3}', 'c_{10}']), (['m_{2}'], ['t_{7}', 't_{6}', 't_{8}', 't_{5}'], ['v_{10}', 'v_{1}']), (['s_{6}'], ['v_{5}'], ['c_{16}']), (['m_{8}'], ['m_{7}'], ['m_{2}']), (['m_{8}'], ['m_{7}'], ['c_{8}']), (['m_{8}'], ['m_{7}'], ['m_{5}']), (['m_{8}'], ['m_{7}'], ['c_{13}']), (['c_{5}', 'c_{9}'], ['s_{3}'], ['v_{6}']), (['s_{3}'], ['c_{10}'], ['v_{1}']), (['v_{8}'], ['c_{15}'], ['s_{6}']), (['m_{6}', 'm_{9}'], ['c_{3}'], ['c_{13}']), (['m_{9}', 'm_{6}'], ['c_{3}'], ['c_{5}']), (['c_{15}'], ['c_{6}', 'm_{3}', 'c_{13}', 'm_{7}'], ['c_{10}']), (['m_{12}'], ['c_{13}'], ['c_{3}']), (['c_{6}'], ['v_{11}'], ['s_{5}']), (['c_{17}'], ['m_{14}'], ['m_{5}']), (['m_{9}', 'm_{6}'], ['m_{11}'], ['c_{14}', 'c_{13}']), (['m_{13}'], ['c_{4}'], ['c_{9}', 'c_{5}']), (['m_{3}'], ['c_{17}'], ['c_{4}']), (['m_{3}'], ['c_{17}'], ['m_{10}']), (['m_{1}'], ['v_{1}'], ['s_{5}']), (['s_{5}'], ['m_{1}'], ['v_{5}']), (['m_{1}'], ['c_{10}'], ['c_{14}']), (['m_{1}'], ['c_{10}'], ['m_{3}']), (['m_{6}', 'm_{9}'], ['v_{7}', 'v_{8}'], ['s_{6}']), (['m_{6}', 'm_{9}'], ['v_{7}', 'v_{8}'], ['s_{5}']), (['c_{5}'], ['c_{13}'], ['c_{3}']), (['a_{3}'], ['v_{11}'], ['m_{5}', 'm_{10}']), (['c_{16}'], ['s_{6}'], ['v_{6}']), (['s_{5}'], ['c_{6}'], ['v_{10}', 'v_{8}']), (['m_{3}'], ['a_{1}'], ['v_{11}', 'v_{3}', 'v_{8}']), (['c_{10}', 'c_{6}'], ['c_{14}'], ['m_{7}']), (['c_{6}', 'c_{10}'], ['c_{14}'], ['m_{3}']), (['v_{11}'], ['c_{13}'], ['s_{3}']), (['m_{9}'], ['m_{3}'], ['m_{9}', 'c_{9}', 'c_{15}', 'm_{12}']), (['m_{9}'], ['m_{3}'], ['c_{3}']), (['m_{12}', 'c_{5}', 'm_{6}', 'c_{15}'], ['c_{11}'], ['c_{5}']), (['m_{7}'], ['v_{6}'], ['s_{6}']), (['m_{7}'], ['v_{6}'], ['s_{11}']), (['m_{7}'], ['v_{6}'], ['s_{3}']), (['c_{12}'], ['c_{10}'], ['c_{5}']), (['v_{10}'], ['a_{4}'], ['m_{10}', 'm_{5}']), (['v_{10}'], ['a_{4}'], ['c_{17}']), (['v_{9}'], ['s_{6}'], ['c_{5}', 'c_{9}']), (['v_{9}'], ['s_{6}'], ['m_{7}']), (['c_{12}'], ['m_{7}'], ['m_{9}']), (['c_{12}'], ['m_{7}'], ['c_{5}']), (['a_{4}'], ['m_{14}'], ['v_{6}']), (['m_{9}'], ['a_{1}'], ['v_{3}']), (['m_{9}'], ['m_{2}'], ['m_{6}']), (['c_{6}', 'c_{10}'], ['c_{9}'], ['c_{4}', 'c_{8}']), (['a_{4}'], ['c_{10}'], ['v_{4}']), (['m_{7}'], ['s_{6}'], ['v_{8}']), (['a_{4}'], ['c_{4}'], ['v_{6}']), (['c_{16}'], ['c_{6}'], ['m_{14}']), (['c_{16}'], ['c_{6}'], ['c_{8}']), (['c_{16}'], ['c_{6}'], ['m_{10}']), (['c_{16}', 'm_{9}', 'c_{9}', 'm_{12}'], ['m_{13}'], ['m_{5}', 'm_{10}']), (['c_{18}'], ['v_{9}'], ['a_{3}']), (['c_{16}'], ['m_{5}'], ['m_{6}']), (['s_{12}'], ['m_{7}'], ['v_{3}']), (['c_{9}'], ['m_{7}'], ['m_{10}'])]
                         }

partial_derivative_g3 = chain_map_mod(expand_map_all(partial_derivative_g3))

diff = add_maps_mod_2(nabla_g3, partial_derivative_g3)

diff = {h: factorize_cycles(chain, BR_C) for h, chain in diff.iteritems()}

print "diff = ", format_morphism(diff)


remainder = {
    'h2_1': [
        (['m_{4}'], ['c_{13}', 'c_{14}'], ['m_{7}', 'm_{8}']),
        (['m_{11}'], ['c_{13}', 'c_{14}'], ['m_{7}', 'm_{8}']),
        (['m_{9}', 'm_{6}'], ['m_{4}'], ['c_{13}', 'c_{14}']),
        (['m_{9}', 'm_{6}'], ['m_{11}'], ['c_{14}', 'c_{13}']),
        (['c_{9}'], ['c_{10}'], ['m_{8}', 'm_{7}']),
        (['c_{6}', 'c_{10}'], ['c_{10}'], ['m_{8}', 'm_{7}']),
        (['c_{6}', 'c_{10}'], ['m_{3}'], ['m_{8}', 'm_{7}']),
        (['c_{10}', 'c_{6}'], ['m_{7}'], ['m_{7}']),
        (['c_{6}', 'c_{10}'], ['m_{7}'], ['m_{8}']),
        (['c_{5}'], ['c_{13}', 'c_{14}'], ['m_{8}', 'm_{7}']),
        (['m_{9}'], ['c_{6}', 'c_{10}'], ['m_{8}']),
        (['m_{6}'], ['c_{10}', 'c_{6}'], ['m_{8}']),
        (['m_{9}', 'm_{6}'], ['c_{9}'], ['c_{13}', 'c_{14}']),
        (['m_{6}', 'm_{9}'], ['c_{3}'], ['c_{13}', 'c_{14}']),
        (['m_{9}', 'm_{6}'], ['m_{2}'], ['c_{13}', 'c_{14}']),
        (['m_{9}', 'm_{6}'], ['m_{6}'], ['c_{13}', 'c_{14}']),
        (['m_{9}', 'm_{6}'], ['m_{13}'], ['c_{14}', 'c_{13}']),
        (['m_{9}', 'm_{6}'], ['c_{3}'], ['c_{13}']),
        (['m_{9}', 'm_{6}'], ['c_{6}'], ['c_{13}']),
        (['m_{9}', 'm_{6}'], ['c_{6}', 'c_{10}'], ['c_{6}']),
        (['m_{9}', 'm_{6}'], ['c_{6}', 'c_{10}'], ['m_{3}']),
        (['m_{9}', 'm_{6}'], ['c_{10}'], ['c_{14}']),
        (['m_{6}', 'm_{9}'], ['c_{7}'], ['c_{14}']),
        (['m_{6}', 'm_{9}'], ['c_{3}'], ['c_{9}']),
        (['m_{6}', 'm_{9}'], ['c_{7}'], ['c_{9}']),
        (['m_{9}', 'm_{6}'], ['c_{7}', 'c_{3}'], ['m_{13}']),
        (['m_{6}', 'm_{9}'], ['c_{3}', 'c_{7}'], ['m_{2}']),
        (['m_{9}', 'm_{6}'], ['c_{3}', 'c_{7}'], ['m_{8}']),
        (['m_{6}', 'm_{9}'], ['c_{3}', 'c_{7}'], ['m_{6}']),
        (['m_{6}', 'm_{9}'], ['c_{7}', 'c_{3}'], ['m_{3}']),
        (['m_{2}'], ['c_{13}', 'c_{14}'], ['m_{7}', 'm_{8}']),
        (['m_{6}'], ['c_{13}', 'c_{14}'], ['m_{7}', 'm_{8}']),
        (['m_{13}'], ['c_{13}', 'c_{14}'], ['m_{7}', 'm_{8}']),
        (['c_{3}'], ['c_{14}'], ['m_{7}', 'm_{8}']),
        (['c_{7}', 'c_{3}'], ['m_{2}'], ['m_{8}', 'm_{7}']),
        (['c_{7}', 'c_{3}'], ['m_{13}'], ['m_{8}', 'm_{7}']),
        (['c_{7}', 'c_{3}'], ['m_{3}'], ['m_{8}', 'm_{7}']),
        (['c_{3}', 'c_{7}'], ['c_{9}'], ['m_{8}', 'm_{7}']),
        (['c_{3}', 'c_{7}'], ['m_{8}'], ['m_{8}', 'm_{7}']),
        (['c_{3}', 'c_{7}'], ['m_{6}'], ['m_{8}', 'm_{7}']),
        (['c_{7}'], ['c_{14}'], ['m_{8}', 'm_{7}']),
        (['c_{9}'], ['c_{10}'], ['m_{7}', 'm_{8}']),
        (['c_{6}'], ['c_{13}'], ['m_{7}', 'm_{8}']),
        (['c_{10}'], ['c_{14}'], ['m_{7}', 'm_{8}'])],

    'h2_0': [
        (['m_{11}', 'm_{4}'], ['c_{7}'], ['c_{8}']),
        (['m_{11}', 'm_{4}'], ['c_{3}'], ['c_{8}']),
        (['m_{11}', 'm_{4}'], ['c_{7}', 'c_{3}'], ['m_{5}']),
        (['m_{11}', 'm_{4}'], ['c_{7}', 'c_{3}'], ['m_{12}']),
        (['m_{11}', 'm_{4}'], ['c_{7}', 'c_{3}'], ['m_{3}']),
        (['m_{4}', 'm_{11}'], ['c_{7}', 'c_{3}'], ['m_{13}']),
        (['m_{4}', 'm_{11}'], ['c_{3}', 'c_{7}'], ['m_{8}']),
        (['m_{4}', 'm_{11}'], ['c_{7}'], ['c_{14}']),
        (['m_{4}', 'm_{11}'], ['c_{3}'], ['c_{14}']),
        (['m_{6}', 'm_{9}'], ['c_{3}', 'c_{7}'], ['m_{4}', 'm_{11}']),
        (['m_{4}', 'm_{11}'], ['m_{9}', 'm_{6}'], ['c_{7}', 'c_{3}']),
        (['m_{8}', 'm_{7}'], ['c_{14}', 'c_{13}'], ['m_{5}', 'm_{10}']),
        (['m_{4}', 'm_{11}'], ['m_{8}', 'm_{7}'], ['c_{13}', 'c_{14}']),
        (['m_{4}', 'm_{11}'], ['m_{11}'], ['c_{13}', 'c_{14}']),
        (['m_{4}', 'm_{11}'], ['m_{4}'], ['c_{13}', 'c_{14}']),
        (['m_{4}', 'm_{11}'], ['m_{4}'], ['c_{3}', 'c_{7}']),
        (['m_{11}', 'm_{4}'], ['m_{11}'], ['c_{7}', 'c_{3}']),
        (['c_{10}', 'c_{6}'], ['m_{7}'], ['m_{5}', 'm_{10}']),
        (['c_{6}', 'c_{10}'], ['m_{8}'], ['m_{10}', 'm_{5}']),
        (['m_{4}', 'm_{11}'], ['c_{8}', 'c_{4}'], ['m_{3}']),
        (['m_{4}', 'm_{11}'], ['c_{8}', 'c_{4}'], ['m_{7}']),
        (['m_{4}', 'm_{11}'], ['c_{8}'], ['c_{10}']),
        (['m_{11}', 'm_{4}'], ['c_{4}'], ['c_{10}']),
        (['m_{11}', 'm_{4}'], ['c_{8}', 'c_{4}'], ['c_{13}']),
        (['c_{6}', 'c_{10}'], ['m_{12}'], ['m_{10}', 'm_{5}']),
        (['c_{6}', 'c_{10}'], ['c_{6}'], ['m_{10}', 'm_{5}']),
        (['c_{6}', 'c_{10}'], ['m_{10}'], ['m_{10}', 'm_{5}']),
        (['c_{6}', 'c_{10}'], ['m_{13}'], ['m_{10}', 'm_{5}']),
        (['c_{6}', 'c_{10}'], ['c_{8}'], ['m_{10}', 'm_{5}']),
        (['m_{10}'], ['c_{6}', 'c_{10}'], ['m_{10}', 'm_{5}']),
        (['m_{12}'], ['c_{6}', 'c_{10}'], ['m_{10}', 'm_{5}']),
        (['c_{6}'], ['c_{6}', 'c_{10}'], ['m_{5}', 'm_{10}']),
        (['m_{13}'], ['c_{6}', 'c_{10}'], ['m_{5}', 'm_{10}']),
        (['c_{8}'], ['c_{6}'], ['m_{10}', 'm_{5}']),
        (['c_{8}'], ['c_{10}'], ['m_{5}', 'm_{10}']),
        (['m_{11}'], ['c_{14}', 'c_{13}'], ['m_{10}', 'm_{5}']),
        (['m_{4}'], ['c_{13}', 'c_{14}'], ['m_{5}', 'm_{10}']),
        (['m_{11}', 'm_{4}'], ['c_{10}'], ['c_{13}']),
        (['m_{4}', 'm_{11}'], ['c_{10}'], ['c_{14}']),
        (['m_{4}', 'm_{11}'], ['c_{4}'], ['c_{13}', 'c_{14}']),
        (['m_{4}', 'm_{11}'], ['m_{13}'], ['c_{13}', 'c_{14}']),
        (['m_{4}', 'm_{11}'], ['m_{12}'], ['c_{13}', 'c_{14}']),
        (['m_{4}', 'm_{11}'], ['m_{10}'], ['c_{13}', 'c_{14}'])
    ]
}

remainder = chain_map_mod(expand_map_all(remainder))

d_remainder = derivative(remainder, BR_C)
d_remainder = chain_map_mod(expand_map_all(d_remainder))
print "d(remainder) =", format_morphism(d_remainder)

remainder_factored = {h: factorize_cycles(chain, BR_C) for h, chain in remainder.iteritems()}
print "remainder =", format_morphism(remainder_factored)

BR_g = {'h0_0': ['v_{1}'], 'h2_1': ['t_{5}', 't_{6}', 't_{7}', 't_{8}'], 'h2_0': ['t_{1}', 't_{2}', 't_{3}', 't_{4}'], 'h1_0': ['m_{11}', 'm_{4}'], 'h1_1': ['c_{3}', 'c_{7}'], 'h1_2': ['m_{6}', 'm_{9}']}


def g_tensor(tp):
    return tuple(map(lambda c: BR_g[c], list(tp)))


f_BR, integrate_BR = generate_f_integral(BR_C, BR_g)

BR_min_remainder_fd = {h: [tuple(map(f_BR, list(cycle))) for cycle in cycles] for h, cycles in remainder_factored.iteritems()}
print "\nf(remainder) =", format_morphism(BR_min_remainder_fd)


"""
MORE FACTORING
"""

last_cycles = [
    (['c_{6}', 'c_{10}'], ['m_{3}', 'm_{7}', 'c_{10}', 'c_{14}'], ['m_{7}', 'm_{8}']),
    (['m_{6}', 'm_{9}'], ['m_{2}', 'm_{6}', 'm_{13}', 'c_{6}', 'c_{9}'], ['c_{13}', 'c_{14}']),
    (['m_{6}', 'm_{9}'], ['c_{6}', 'c_{10}'], ['m_{3}', 'm_{8}', 'c_{6}', 'c_{14}']),
    (['m_{2}', 'm_{6}', 'm_{13}', 'c_{5}', 'c_{6}'], ['c_{13}', 'c_{14}'], ['m_{7}', 'm_{8}'])
]

last_cycles_fd = [(t, tuple(map(f_BR, list(t)))) for t in last_cycles]
print "\nf(last_cycles) =", last_cycles_fd


"""
Testing Phi_1
"""

phi_1 = {'h0_0': [], 'h2_1': [('m_{6}', 'c_{9}', 'm_{3}'), ('m_{2}', 'm_{9}', 'c_{5}'), ('t_{7}', 'm_{4}', 'v_{2}'), ('m_{6}', 'c_{5}', 'c_{3}'), ('s_{6}', 'v_{9}', 'm_{8}'), ('v_{8}', 's_{6}', 'm_{7}'), ('t_{6}', 'm_{7}', 'v_{1}'), ('v_{6}', 't_{5}', 'm_{7}'), ('t_{7}', 'c_{3}', 'v_{1}'), ('m_{6}', 'c_{3}', 'm_{3}'), ('m_{9}', 'm_{6}', 'c_{5}'), ('c_{3}', 'c_{6}', 'm_{7}'), ('t_{6}', 'v_{10}', 'm_{13}'), ('m_{6}', 'c_{3}', 'c_{5}'), ('c_{6}', 'm_{8}', 'm_{4}'), ('m_{2}', 'm_{9}', 'c_{9}'), ('m_{6}', 's_{1}', 'v_{11}'), ('m_{6}', 's_{5}', 'v_{11}'), ('m_{9}', 'c_{7}', 'm_{8}'), ('c_{6}', 'm_{7}', 'm_{13}'), ('m_{9}', 'm_{6}', 'c_{9}'), ('m_{11}', 'c_{13}', 'm_{7}'), ('m_{4}', 'v_{2}', 't_{5}'), ('c_{6}', 'm_{7}', 'm_{8}'), ('m_{6}', 's_{10}', 'v_{1}'), ('m_{6}', 'v_{7}', 's_{5}'), ('m_{13}', 'c_{14}', 'm_{8}'), ('m_{4}', 't_{8}', 'v_{1}'), ('m_{6}', 'c_{3}', 'm_{2}'), ('m_{6}', 'v_{7}', 's_{10}'), ('c_{10}', 'm_{7}', 'm_{13}'), ('m_{9}', 'c_{3}', 'c_{13}'), ('v_{6}', 'm_{6}', 's_{6}'), ('m_{8}', 'c_{13}', 'm_{7}'), ('m_{9}', 's_{6}', 'v_{11}'), ('m_{6}', 'c_{6}', 'm_{13}'), ('m_{4}', 'm_{6}', 'c_{6}'), ('v_{6}', 'm_{9}', 's_{9}'), ('v_{1}', 't_{7}', 'm_{4}'), ('t_{8}', 'm_{13}', 'v_{9}'), ('t_{7}', 'v_{1}', 'm_{4}'), ('c_{6}', 'm_{7}', 'm_{4}'), ('m_{13}', 'c_{14}', 'm_{7}'), ('m_{6}', 'v_{8}', 's_{5}'), ('t_{5}', 'm_{13}', 'v_{9}'), ('c_{9}', 'm_{7}', 'm_{7}'), ('v_{1}', 't_{5}', 'm_{4}'), ('c_{5}', 'm_{7}', 'c_{3}'), ('c_{5}', 'm_{3}', 'm_{7}'), ('s_{5}', 'v_{11}', 'm_{8}'), ('m_{11}', 'c_{3}', 'm_{8}'), ('c_{7}', 'c_{14}', 'm_{7}'), ('m_{9}', 'v_{7}', 's_{6}'), ('v_{1}', 'm_{9}', 's_{5}'), ('c_{3}', 'm_{6}', 'c_{10}'), ('m_{4}', 'c_{6}', 'm_{8}'), ('c_{3}', 'v_{3}', 't_{6}'), ('s_{6}', 'm_{8}', 'v_{1}'), ('t_{7}', 'm_{13}', 'v_{9}'), ('m_{2}', 'c_{6}', 'm_{8}'), ('c_{6}', 'c_{13}', 'm_{7}'), ('c_{6}', 'm_{8}', 'c_{3}'), ('m_{6}', 's_{2}', 'v_{11}'), ('m_{11}', 'c_{3}', 'm_{7}'), ('t_{5}', 'v_{10}', 'c_{3}'), ('m_{9}', 'm_{11}', 'c_{13}'), ('m_{9}', 'c_{9}', 'c_{3}'), ('v_{1}', 'c_{3}', 't_{6}'), ('m_{9}', 'm_{7}', 'c_{13}'), ('s_{10}', 'm_{7}', 'v_{10}'), ('c_{3}', 'm_{9}', 'c_{9}'), ('c_{9}', 'm_{3}', 'm_{7}'), ('m_{9}', 'c_{5}', 'm_{13}'), ('s_{10}', 'm_{8}', 'v_{10}'), ('c_{6}', 'c_{13}', 'm_{8}'), ('v_{1}', 'm_{6}', 's_{1}'), ('c_{3}', 't_{6}', 'v_{1}'), ('m_{4}', 't_{8}', 'v_{10}'), ('m_{4}', 'v_{6}', 't_{5}'), ('s_{9}', 'v_{11}', 'm_{7}'), ('m_{4}', 'c_{7}', 'm_{7}'), ('m_{7}', 'c_{14}', 'm_{7}'), ('m_{9}', 'v_{1}', 's_{1}'), ('c_{5}', 'm_{8}', 'm_{4}'), ('t_{8}', 'c_{3}', 'v_{3}'), ('m_{9}', 's_{9}', 'v_{11}'), ('c_{7}', 'm_{2}', 'm_{8}'), ('v_{2}', 'c_{3}', 't_{5}'), ('v_{6}', 't_{7}', 'm_{13}'), ('c_{7}', 'm_{3}', 'm_{7}'), ('m_{9}', 'v_{8}', 's_{5}'), ('m_{4}', 'm_{6}', 'c_{10}'), ('m_{6}', 'c_{7}', 'c_{9}'), ('s_{1}', 'm_{8}', 'v_{10}'), ('c_{3}', 'm_{6}', 'm_{8}'), ('m_{6}', 'v_{1}', 's_{10}'), ('m_{9}', 'v_{1}', 's_{9}'), ('s_{5}', 'v_{9}', 'm_{7}'), ('m_{2}', 'c_{6}', 'm_{7}'), ('s_{6}', 'm_{7}', 'v_{10}'), ('m_{9}', 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'm_{5}'), ('v_{1}', 's_{7}', 'm_{5}'), ('m_{4}', 'c_{8}', 'm_{1}'), ('m_{4}', 'm_{7}', 'c_{13}'), ('m_{4}', 's_{5}', 'v_{1}'), ('m_{8}', 'c_{13}', 'm_{5}'), ('t_{3}', 'm_{1}', 'v_{11}'), ('m_{11}', 'c_{3}', 'm_{5}'), ('v_{3}', 's_{8}', 'm_{5}'), ('m_{4}', 's_{7}', 'v_{9}'), ('c_{10}', 'c_{14}', 'm_{5}'), ('t_{4}', 'm_{12}', 'v_{8}'), ('v_{8}', 's_{6}', 'm_{5}'), ('m_{11}', 'c_{13}', 'm_{5}'), ('t_{1}', 'm_{3}', 'v_{1}'), ('m_{7}', 'c_{14}', 'm_{5}'), ('m_{4}', 'c_{7}', 'm_{1}'), ('c_{7}', 'c_{14}', 'm_{10}'), ('s_{9}', 'm_{10}', 'v_{5}'), ('v_{3}', 's_{8}', 'm_{10}'), ('s_{5}', 'v_{4}', 'm_{5}'), ('c_{4}', 'm_{10}', 'm_{5}'), ('m_{11}', 'v_{2}', 's_{6}'), ('s_{7}', 'm_{10}', 'v_{5}'), ('m_{10}', 'c_{10}', 'm_{5}'), ('m_{4}', 'm_{11}', 'c_{13}'), ('m_{4}', 's_{7}', 'v_{1}'), ('c_{7}', 'm_{13}', 'm_{10}'), ('t_{3}', 'm_{12}', 'v_{1}'), ('m_{11}', 'm_{11}', 'c_{13}'), ('v_{1}', 's_{6}', 'm_{10}'), ('t_{1}', 'm_{1}', 'v_{1}'), ('m_{11}', 'm_{8}', 'c_{13}'), ('m_{11}', 'm_{7}', 'c_{14}'), ('m_{13}', 'c_{14}', 'm_{10}'), ('v_{8}', 's_{5}', 'm_{10}'), ('m_{11}', 'v_{1}', 's_{10}'), ('s_{5}', 'v_{4}', 'm_{10}'), ('m_{11}', 's_{5}', 'v_{11}'), ('m_{4}', 'm_{11}', 'c_{3}'), ('t_{3}', 'm_{3}', 'v_{11}'), ('m_{11}', 'v_{2}', 's_{5}'), ('s_{8}', 'm_{10}', 'v_{5}'), ('m_{11}', 'v_{8}', 's_{6}'), ('c_{7}', 'm_{10}', 'm_{3}'), ('m_{11}', 'c_{4}', 'm_{3}'), ('t_{3}', 'v_{8}', 'm_{3}'), ('m_{11}', 'c_{10}', 'c_{14}'), ('t_{4}', 'm_{3}', 'v_{1}'), ('m_{11}', 'm_{10}', 'c_{10}'), ('m_{4}', 'c_{3}', 'm_{13}'), ('m_{11}', 'c_{3}', 'm_{1}'), ('m_{4}', 'c_{7}', 'm_{3}'), ('m_{4}', 's_{8}', 'v_{1}'), ('t_{2}', 'v_{8}', 'm_{3}'), ('v_{3}', 's_{7}', 'm_{10}'), ('m_{4}', 'c_{3}', 'c_{13}'), ('m_{4}', 'v_{2}', 's_{8}'), ('t_{4}', 'v_{5}', 'm_{1}'), ('m_{11}', 'm_{13}', 'c_{14}'), ('c_{4}', 'm_{10}', 'm_{3}'), ('m_{11}', 'c_{3}', 'c_{4}'), ('c_{3}', 'c_{4}', 'm_{5}'), ('c_{7}', 'c_{8}', 'm_{10}'), ('c_{7}', 'c_{8}', 'm_{5}'), ('m_{4}', 'c_{4}', 'm_{5}'), ('m_{4}', 'c_{3}', 'c_{4}'), ('m_{4}', 'c_{3}', 'm_{5}'), ('m_{11}', 'c_{7}', 'c_{8}'), ('m_{4}', 'c_{7}', 'c_{8}'), ('m_{4}', 'c_{8}', 'm_{5}'), ('c_{3}', 'c_{4}', 'm_{10}'), ('m_{4}', 'c_{7}', 'm_{5}')], 'h1_0': [('m_{4}', 'm_{4}', 'v_{1}'), ('m_{11}', 'm_{4}', 'v_{2}'), ('m_{4}', 'm_{4}', 'v_{2}'), ('m_{4}', 'v_{2}', 'm_{4}'), ('m_{11}', 'v_{2}', 'm_{4}'), ('m_{4}', 'v_{1}', 'm_{4}'), ('m_{11}', 'v_{1}', 'm_{4}'), ('m_{11}', 'm_{4}', 'v_{1}')], 'h1_1': [('v_{1}', 'c_{7}', 'c_{3}'), ('c_{7}', 'm_{4}', 'v_{2}'), ('c_{7}', 'c_{3}', 'v_{1}'), ('c_{7}', 'm_{4}', 'v_{1}'), ('v_{2}', 'c_{7}', 'c_{3}'), ('v_{2}', 'c_{3}', 'm_{4}'), ('c_{3}', 'v_{1}', 'm_{4}'), ('m_{4}', 'c_{3}', 'v_{3}'), ('m_{4}', 'c_{3}', 'v_{1}'), ('v_{1}', 'c_{3}', 'c_{3}'), ('c_{3}', 'v_{2}', 'c_{3}'), ('c_{7}', 'v_{3}', 'm_{4}'), ('c_{3}', 'v_{3}', 'm_{4}'), ('m_{4}', 'c_{7}', 'v_{3}'), ('c_{3}', 'm_{4}', 'v_{2}'), ('v_{1}', 'c_{7}', 'm_{4}'), ('v_{2}', 'c_{7}', 'm_{4}'), ('v_{2}', 'c_{3}', 'c_{3}'), ('c_{3}', 'c_{3}', 'v_{1}'), ('c_{7}', 'v_{1}', 'm_{4}'), ('v_{1}', 'c_{3}', 'm_{4}'), ('c_{3}', 'm_{4}', 'v_{1}'), ('c_{3}', 'v_{3}', 'c_{3}'), ('c_{7}', 'v_{3}', 'c_{3}'), ('c_{7}', 'v_{2}', 'c_{3}'), ('c_{3}', 'c_{3}', 'v_{3}'), ('m_{4}', 'c_{7}', 'v_{1}'), ('c_{7}', 'c_{3}', 'v_{3}')], 'h1_2': [('m_{9}', 'v_{2}', 'c_{3}'), ('c_{3}', 'v_{6}', 'm_{6}'), ('m_{6}', 'v_{7}', 'm_{2}'), ('m_{6}', 'm_{2}', 'v_{6}'), ('v_{1}', 'm_{6}', 'm_{4}'), ('v_{2}', 'c_{3}', 'm_{6}'), ('v_{6}', 'm_{6}', 'c_{3}'), ('v_{3}', 'm_{2}', 'm_{6}'), ('v_{1}', 'c_{3}', 'm_{9}'), ('v_{1}', 'm_{9}', 'm_{2}'), ('v_{1}', 'c_{3}', 'm_{6}'), ('v_{6}', 'm_{9}', 'm_{6}'), ('v_{6}', 'm_{6}', 'm_{6}'), ('m_{6}', 'v_{7}', 'c_{3}'), ('m_{9}', 'c_{3}', 'v_{1}'), ('c_{3}', 'm_{6}', 'v_{1}'), ('m_{9}', 'v_{7}', 'c_{3}'), ('m_{9}', 'm_{4}', 'v_{2}'), ('v_{1}', 'm_{9}', 'm_{4}'), ('m_{2}', 'm_{6}', 'v_{1}'), ('v_{3}', 'm_{2}', 'm_{9}'), ('m_{6}', 'v_{6}', 'm_{6}'), ('v_{1}', 'm_{6}', 'c_{3}'), ('m_{9}', 'v_{3}', 'm_{2}'), ('c_{3}', 'v_{3}', 'm_{9}'), ('m_{9}', 'm_{6}', 'v_{1}'), ('m_{4}', 'v_{2}', 'm_{9}'), ('m_{4}', 'm_{6}', 'v_{1}'), ('m_{4}', 'v_{6}', 'm_{6}'), ('m_{2}', 'm_{9}', 'v_{1}'), ('m_{2}', 'm_{6}', 'v_{7}'), ('m_{6}', 'c_{3}', 'v_{3}'), ('m_{4}', 'v_{6}', 'm_{9}'), ('m_{6}', 'm_{6}', 'v_{7}'), ('v_{1}', 'm_{6}', 'm_{2}'), ('m_{9}', 'm_{6}', 'v_{7}'), ('m_{4}', 'm_{9}', 'v_{7}'), ('m_{6}', 'c_{3}', 'v_{1}'), ('m_{2}', 'm_{9}', 'v_{7}'), ('c_{3}', 'v_{6}', 'm_{9}'), ('v_{1}', 'm_{2}', 'm_{9}'), ('m_{9}', 'c_{3}', 'v_{3}'), ('v_{6}', 'm_{6}', 'm_{4}'), ('v_{6}', 'm_{9}', 'm_{2}'), ('c_{3}', 'v_{3}', 'm_{6}'), ('v_{6}', 'm_{9}', 'c_{3}'), ('m_{6}', 'm_{4}', 'v_{2}'), ('m_{9}', 'v_{1}', 'm_{4}'), ('m_{4}', 'm_{6}', 'v_{7}'), ('v_{1}', 'm_{9}', 'c_{3}'), ('c_{3}', 'm_{9}', 'v_{1}'), ('v_{1}', 'm_{9}', 'm_{6}'), ('m_{6}', 'm_{6}', 'v_{1}'), ('v_{2}', 'c_{3}', 'm_{9}'), ('m_{4}', 'v_{2}', 'm_{6}'), ('v_{1}', 'm_{6}', 'm_{6}'), ('m_{6}', 'v_{7}', 'm_{6}'), ('m_{6}', 'v_{3}', 'm_{2}'), ('m_{9}', 'v_{7}', 'm_{4}'), ('m_{9}', 'm_{4}', 'v_{1}'), ('v_{1}', 'm_{2}', 'm_{6}'), ('v_{6}', 'm_{6}', 'm_{2}'), ('v_{6}', 'm_{9}', 'm_{4}'), ('m_{6}', 'v_{1}', 'm_{4}'), ('m_{4}', 'm_{9}', 'v_{1}'), ('m_{9}', 'v_{7}', 'm_{2}'), ('m_{6}', 'v_{7}', 'm_{4}'), ('m_{6}', 'm_{4}', 'v_{1}'), ('m_{9}', 'v_{7}', 'm_{6}'), ('m_{6}', 'v_{2}', 'c_{3}'), ('m_{9}', 'v_{6}', 'm_{6}'), ('m_{6}', 'm_{2}', 'v_{1}'), ('c_{3}', 'm_{9}', 'v_{7}'), ('m_{9}', 'm_{2}', 'v_{1}'), ('m_{9}', 'm_{2}', 'v_{6}'), ('c_{3}', 'm_{6}', 'v_{7}')]}

h1_2_prebound = chain_integrate(phi_1['h1_2'], BR_C)
h1_2_prebound = factorize_cycles(h1_2_prebound, BR_C)
print "preboundary(phi['h1_2']) =", h1_2_prebound

delta3 = {'h2_1': [('h1_0', 'h1_1', 'h1_2'), ('h1_1', 'h1_0', 'h1_2'),
                   ('h1_2', 'h1_1', 'h1_0'), ('h1_2', 'h1_0', 'h1_1')],
          'h2_0': [('h1_0', 'h1_2', 'h1_1'), ('h1_2', 'h1_1', 'h1_0'),
                   ('h1_0', 'h1_1', 'h1_2'), ('h1_1', 'h1_2', 'h1_0')]}

g3 = {
    'h1_0': [(['m_{11}', 'm_{4}'], ['m_{4}'], ['m_{4}'])],
    'h1_1': [(['m_{4}'], ['c_{3}', 'c_{7}'], ['m_{4}', 'c_{3}']),
             (['c_{3}', 'c_{7}'], ['c_{3}'], ['m_{4}', 'c_{3}']),
             (['c_{3}', 'c_{7}'], ['m_{4}'], ['m_{4}'])],
    'h1_2': [
        (['m_{4}', 'c_{3}', 'm_{2}'], ['m_{6}', 'm_{9}'], ['m_{4}', 'c_{3}', 'm_{2}', 'm_{6}']),
        (['m_{4}'], ['c_{3}', 'm_{2}'], ['m_{6}', 'm_{9}']),
        (['c_{3}'], ['m_{2}'], ['m_{6}', 'm_{9}']),
        (['m_{6}', 'm_{9}'], ['m_{6}'], ['m_{6}']),
        (['m_{6}', 'm_{9}'], ['m_{2}', 'm_{6}'], ['m_{4}', 'c_{3}', 'm_{2}']),
        (['m_{6}', 'm_{9}'], ['c_{3}'], ['m_{4}', 'c_{3}']),
        (['m_{6}', 'm_{9}'], ['m_{4}'], ['m_{4}'])
    ],
    'h2_1': [
        (['m_{2}', 'c_{3}', 'm_{4}'], ['t_{7}', 't_{8}', 't_{6}', 't_{5}'], ['m_{4}', 'c_{3}', 'm_{13}', 'm_{7}']),
        (['c_{3}', 'm_{4}'], ['m_{2}', 'c_{3}'], ['t_{5}', 't_{6}', 't_{8}', 't_{7}']),
        (['c_{3}'], ['c_{3}'], ['t_{5}', 't_{6}', 't_{8}', 't_{7}']),
        (['t_{6}', 't_{5}', 't_{8}', 't_{7}'], ['m_{4}', 'c_{3}', 'm_{13}', 'm_{7}'], ['m_{4}', 'c_{3}', 'm_{13}', 'm_{7}']),
        (['t_{5}', 't_{7}', 't_{8}', 't_{6}'], ['m_{4}', 'c_{3}', 'm_{13}'], ['m_{7}']),
        (['t_{5}', 't_{8}', 't_{7}', 't_{6}'], ['m_{4}', 'c_{3}'], ['m_{13}']),
        (['t_{5}', 't_{8}', 't_{7}', 't_{6}'], ['m_{4}'], ['c_{3}']),
        (['m_{4}', 'm_{11}'], ['c_{3}', 'c_{7}'], ['t_{5}', 't_{6}']),
        (['m_{6}', 'm_{9}'], ['t_{5}', 't_{6}'], ['c_{13}', 'c_{14}']),
        (['m_{6}', 'm_{9}'], ['m_{6}', 'm_{9}'], ['s_{9}', 's_{10}']),
        (['t_{5}', 'm_{6}'], ['c_{5}', 'c_{9}'], ['m_{7}', 'm_{8}']),
        (['m_{7}', 'm_{8}'], ['s_{1}', 's_{2}', 's_{9}', 's_{10}'], ['m_{7}', 'm_{8}']),
        (['m_{4}', 'c_{3}', 'm_{2}'], ['m_{6}', 'm_{9}'], ['s_{1}', 's_{2}', 's_{5}', 's_{6}', 's_{9}', 's_{10}']),
        (['m_{6}', 'm_{9}'], ['s_{1}', 's_{2}', 's_{5}', 's_{6}', 's_{9}', 's_{10}'], ['m_{4}', 'c_{3}', 'm_{13}', 'c_{6}', 'm_{3}']),
        (['m_{9}', 'm_{6}'], ['m_{2}', 'c_{3}', 'm_{2}', 'm_{6}'], ['s_{1}', 's_{2}', 's_{9}', 's_{10}']),
        (['s_{1}', 's_{2}', 's_{5}', 's_{6}', 's_{9}', 's_{10}'], ['m_{7}', 'm_{8}'], ['m_{4}', 'c_{3}', 'm_{13}', 'm_{7}']),
        (['m_{4}', 'c_{3}', 'm_{2}', 'm_{6}', 'c_{5}'], ['s_{5}', 's_{6}'], ['m_{7}', 'm_{8}']),
        (['m_{6}', 'm_{9}'], ['c_{9}'], ['s_{5}', 's_{6}']),
        (['s_{1}', 's_{2}', 's_{5}', 's_{6}', 's_{9}', 's_{10}'], ['m_{3}', 'c_{10}'], ['m_{7}', 'm_{8}']),
        (['c_{6}', 'c_{10}'], ['s_{6}'], ['m_{8}', 'm_{7}']),
        (['m_{6}', 'm_{9}'], ['m_{4}'], ['s_{1}', 's_{2}', 's_{9}', 's_{10}']),
        (['m_{6}', 'm_{9}'], ['m_{2}'], ['s_{1}', 's_{2}', 's_{9}', 's_{10}']),
        (['m_{6}', 'm_{9}'], ['c_{3}', 'c_{7}'], ['s_{2}', 's_{10}', 'a_{1}', 'a_{3}']),
        (['c_{3}', 'c_{7}'], ['s_{2}', 's_{10}', 'a_{1}', 'a_{3}'], ['m_{7}', 'm_{8}']),
        (['c_{3}', 'c_{7}'], ['m_{4}', 'm_{11}'], ['t_{5}', 't_{6}']),
        (['m_{6}'], ['c_{5}', 'c_{9}'], ['m_{7}', 'm_{8}']),
        (['m_{6}', 'm_{9}'], ['c_{6}', 'c_{10}'], ['s_{5}']),
        (['m_{6}', 'm_{9}'], ['s_{2}', 's_{6}', 's_{10}', 'a_{1}', 'a_{3}'], ['c_{13}', 'c_{14}']),
        (['s_{1}', 's_{5}', 's_{9}', 'a_{1}', 'a_{3}'], ['c_{13}', 'c_{14}'], ['m_{7}', 'm_{8}']),
        (['t_{6}'], ['c_{5}', 'c_{9}'], ['m_{7}', 'm_{8}']),
        (['t_{5}', 't_{6}'], ['c_{6}', 'c_{10}'], ['m_{7}', 'm_{8}']),
        (['m_{7}', 'm_{8}'], ['s_{5}', 's_{6}'], ['m_{7}', 'm_{8}']),
        (['m_{6}', 'm_{9}'], ['t_{5}', 't_{6}'], ['c_{3}', 'c_{7}']),
        (['m_{6}', 'm_{9}'], ['m_{7}', 'm_{8}'], ['s_{9}', 's_{10}'])
    ],
    'h2_0': [
        (['t_{4}', 't_{2}', 't_{3}', 't_{1}'], ['m_{1}', 'm_{3}', 'm_{12}'], ['m_{1}']),
        (['t_{4}', 't_{2}', 't_{3}', 't_{1}'], ['m_{12}'], ['m_{3}']),
        (['s_{5}', 's_{6}', 's_{7}', 's_{8}', 's_{9}', 's_{10}'], ['m_{5}', 'm_{10}'], ['m_{1}', 'm_{3}', 'm_{12}']),
        (['m_{4}', 'm_{11}'], ['s_{5}', 's_{6}', 's_{9}', 's_{10}'], ['m_{1}']),
        (['s_{7}', 's_{8}'], ['m_{10}', 'm_{12}', 'c_{6}'], ['m_{5}', 'm_{10}']),
        (['m_{4}', 'c_{3}'], ['s_{7}', 's_{8}'], ['m_{5}', 'm_{10}']),
        (['m_{4}', 'm_{11}'], ['m_{4}'], ['s_{9}', 's_{10}']),
        (['m_{4}', 'm_{11}'], ['c_{3}', 'c_{4}', 'm_{10}', 'm_{12}'], ['s_{5}', 's_{6}']),
        (['m_{4}', 'm_{11}'], ['c_{3}'], ['s_{7}', 's_{8}']),
        (['s_{5}', 's_{6}', 's_{9}', 's_{10}'], ['c_{8}', 'm_{13}', 'm_{8}', 'c_{14}'], ['m_{5}', 'm_{10}']),
        (['m_{4}', 'c_{3}', 'm_{13}', 'c_{6}'], ['s_{5}', 's_{6}'], ['m_{5}', 'm_{10}']),
        (['m_{4}', 'm_{11}'], ['s_{7}', 's_{8}'], ['m_{1}', 'c_{13}', 'm_{7}']),
        (['m_{4}', 'm_{11}'], ['m_{4}', 'm_{11}'], ['s_{9}', 's_{10}']),
        (['m_{4}', 'm_{11}'], ['t_{5}', 't_{6}'], ['c_{7}', 'c_{3}']),
        (['m_{4}', 'm_{11}'], ['m_{8}', 'm_{7}'], ['s_{9}', 's_{10}']),
        (['t_{5}', 't_{6}'], ['c_{3}', 'c_{7}'], ['m_{4}', 'm_{11}']),
        (['m_{8}', 'm_{7}'], ['s_{9}', 's_{10}'], ['m_{4}', 'm_{11}']),
        (['m_{8}', 'm_{7}'], ['c_{14}', 'c_{13}'], ['t_{1}', 't_{2}']),
        (['m_{4}', 'm_{11}'], ['s_{8}'], ['c_{13}', 'c_{14}']),
        (['m_{4}', 'm_{11}'], ['c_{4}', 'c_{8}'], ['s_{6}']),
        (['s_{8}'], ['c_{6}', 'c_{10}'], ['m_{5}', 'm_{10}']),
        (['c_{6}', 'c_{10}'], ['s_{8}'], ['m_{5}', 'm_{10}']),
        (['m_{4}', 'm_{11}'], ['s_{9}', 's_{10}'], ['m_{5}', 'm_{10}']),
        (['m_{4}', 'm_{11}'], ['c_{3}', 'c_{7}'], ['s_{6}', 's_{8}']),
        (['m_{4}', 'm_{11}'], ['c_{7}', 'c_{3}'], ['t_{5}', 't_{6}']),
        (['s_{5}', 's_{6}', 's_{9}', 's_{10}'], ['m_{6}', 'm_{9}'], ['m_{4}', 'm_{11}']),
        (['c_{6}', 'c_{10}'], ['t_{5}', 't_{6}'], ['m_{4}', 'm_{11}']),
        (['c_{10}', 'c_{6}'], ['m_{7}', 'm_{8}'], ['t_{1}', 't_{2}'])
    ]
}

g3 = chain_map_mod(expand_map_all(g3))

nabla_g3_computed = {k: [(l, m, r) for (l, m, r) in derivative(v, BR_C) if l and m and r] for k, v in g3.iteritems() if v}
nabla_g3_computed = chain_map_mod(expand_map_all(nabla_g3_computed))
print "\nNabla(g^3) (computed) =", nabla_g3_computed

# (g x g x g) Delta3
gxgxg_delta3 = {}
for h, chain in delta3.iteritems():
    gxgxg_delta3[h] = [g_tensor(hxhxh) for hxhxh in chain]
gxgxg_delta3 = chain_map_mod(expand_map_all(gxgxg_delta3))
print u"\n(g " + OTIMES + " g " + OTIMES + " g)" + DELTA + "_3 =", format_morphism(gxgxg_delta3)

should_be_zero = reduce(add_maps_mod_2, [nabla_g3_computed, gxgxg_delta3, phi_1], {})
print "\nNabla(g^3) + (g x g x g) Delta_3 + phi_1 =", format_morphism(should_be_zero)

should_be_zero_cyc = {h: factorize_cycles(chain, BR_C) for h, chain in should_be_zero.iteritems()}
print "\nNabla(g^3) + (g x g x g) Delta_3 + phi_1  (factored)=", format_morphism(should_be_zero_cyc)

should_be_zero_fd = {h: [(t, tuple(map(f_BR, list(t)))) for t in cycles] for h, cycles in should_be_zero_cyc.iteritems()}
print "(f x f x f)(remainder) =", format_morphism(should_be_zero_fd)