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y_radius, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, x_level, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, x_level^3, x_level^4, x_level^7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level, x_level^2, x_level^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, y_radius^2, 0, y_radius^2, 0, x_level*y_radius^2, x_level^3*y_radius^2, x_level^4*y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, x_level^3, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, x_level*y_radius, x_level^2*y_radius, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, x_level*y_radius, x_level^2*y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level^4, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}", "chain_complex": "ChainComplex{...6...}", "d_squared_zero": true, "derived_category_maps": { "Ext_modules": { "H0_Ext0": "image matrix {{1}, {x_level}, {x_level^2}, {x_level^3}, {x_level^4}, {x_level^5}, {x_level^6}, {x_level^7}, {x_level^8}, {x_level^9}, {x_level^10}, {x_level^11}}", "H0_Ext1": "cokernel matrix {{y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4}}", "H1_Ext0": "image matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}", "H1_Ext1": "R^0", "H2_Ext0": "R^25", "H2_Ext1": "R^0" }, "Tor_residue_modules": { "H0_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^4*y_radius^4, x_level^6*y_radius^3, x_level^8*y_radius^4, x_level^10*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^4*y_radius^3, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^2, x_level^5*y_radius^3, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^3, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^4, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0}}", "H0_Tor1": "cokernel matrix {{0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level}}", "H1_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 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0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level}})", "H2_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius}}", "H2_Tor1": "R^0" }, "chain_identity_map": "ChainComplexMap{...7...}", "chain_identity_mapping_cone": "ChainComplex{...7...}", "chain_identity_mapping_cone_homology_pruned": { "H0": "R^0", "H1": "R^0", "H2": "R^0" }, "homology_resolution_identity_cone_homology_pruned": { "H0": { "H0": "R^0", "H1": "R^0" }, "H1": { "H0": "R^0", "H1": "R^0" }, "H2": { "H0": "R^0", "H1": "R^0" } }, "homology_resolution_identity_maps": { "H0": "ChainComplexMap{...8...}", "H1": "ChainComplexMap{...7...}", "H2": "ChainComplexMap{...6...}" } }, "homogeneous_d1": true, "homogeneous_d2": true, "homology_and_resolutions": { "H0_betti": "new BettiTally from {(0,{0, 0},0) => 1, (0,{1, 0},1) => 1, (0,{2, 0},2) => 1, (0,{3, 0},3) => 1, (0,{4, 0},4) => 1, (0,{5, 0},5) => 1, (0,{6, 0},6) => 1, (0,{7, 0},7) => 1, (0,{8, 0},8) => 1, (0,{9, 0},9) => 1, (0,{10, 0},10) => 1, (0,{11, 0},11) => 1, (1,{1, 4},5) => 1, (1,{2, 4},6) => 1, (1,{3, 3},6) => 1, (1,{4, 4},8) => 1, (1,{5, 4},9) => 1, (1,{6, 3},9) => 1, (1,{7, 2},9) => 1, (1,{7, 3},10) => 2, (1,{8, 3},11) => 1, (1,{9, 4},13) => 1, (1,{10, 4},14) => 1, (1,{11, 4},15) => 1, (2,{7, 4},11) => 2}", "H0_module": "cokernel matrix {{x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^4, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^4*y_radius^4, x_level^6*y_radius^3, x_level^8*y_radius^4, x_level^10*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^4*y_radius^3, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^4, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^2, x_level^5*y_radius^3, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^3, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^4, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0}}", "H0_presentation": "matrix {{x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^4, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^4*y_radius^4, x_level^6*y_radius^3, x_level^8*y_radius^4, x_level^10*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^4*y_radius^3, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^4, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^2, x_level^5*y_radius^3, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^3, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^4, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0}}", "H0_resolution": "ChainComplex{...9...}", "H1_betti": "new BettiTally from {(0,{2, 4},6) => 1, (0,{3, 4},7) => 2, (0,{4, 4},8) => 2, (0,{5, 4},9) => 3, (0,{6, 4},10) => 2, (0,{7, 3},10) => 1, (0,{7, 4},11) => 4, (0,{8, 4},12) => 4, (0,{9, 4},13) => 5, (0,{10, 4},14) => 2, (0,{11, 4},15) => 4, (1,{2, 4},6) => 1, (1,{3, 4},7) => 2, (1,{4, 4},8) => 2, (1,{5, 4},9) => 3, (1,{6, 4},10) => 2, (1,{7, 3},10) => 1, (1,{7, 4},11) => 4, (1,{8, 4},12) => 4, (1,{9, 4},13) => 5, (1,{10, 4},14) => 2, (1,{11, 4},15) => 4}", "H1_module": "subquotient(matrix {{x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius, 0, 0, x_level^2*y_radius, 0, 0, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 1, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, x_level^2*y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, x_level, x_level, x_level}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, x_level, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, y_radius, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, x_level^4, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, x_level, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, x_level, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, x_level, x_level}},matrix {{x_level, x_level^2, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, x_level, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 1, 0, x_level, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, x_level, x_level^5, x_level^7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, x_level^2*y_radius, x_level^4, x_level^8*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level^2, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 1, 0, y_radius, 0, x_level^2*y_radius, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, x_level^3, x_level^4, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level^3, x_level^4, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, x_level, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, x_level^3, x_level^4, x_level^7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level, x_level^2, x_level^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, y_radius^2, 0, y_radius^2, 0, x_level*y_radius^2, x_level^3*y_radius^2, x_level^4*y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, x_level^3, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, x_level*y_radius, x_level^2*y_radius, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, x_level*y_radius, x_level^2*y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, x_level^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, x_level^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}", "H2_presentation": "matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}", "H2_resolution": "ChainComplex{...7...}" }, "kind": "macaulay2_bigraded_persistence_resolution", "macaulay2_stdout_tail": "ius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^4, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, x_level*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0}}\", \"H0_betti\": \"new BettiTally from {(0,{0, 0},0) => 1, (0,{1, 0},1) => 1, (0,{2, 0},2) => 1, (0,{3, 0},3) => 1, (0,{4, 0},4) => 1, (0,{5, 0},5) => 1, (0,{6, 0},6) => 1, (0,{7, 0},7) => 1, (0,{8, 0},8) => 1, (0,{9, 0},9) => 1, (0,{10, 0},10) => 1, (0,{11, 0},11) => 1, (1,{1, 4},5) => 1, (1,{2, 4},6) => 1, (1,{3, 3},6) => 1, (1,{4, 4},8) => 1, (1,{5, 4},9) => 1, (1,{6, 3},9) => 1, (1,{7, 2},9) => 1, (1,{7, 3},10) => 2, (1,{8, 3},11) => 1, (1,{9, 4},13) => 1, (1,{10, 4},14) => 1, (1,{11, 4},15) => 1, (2,{7, 4},11) => 2}\", \"H2_presentation\": \"matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}\"}, \"homogeneous_d2\": true}\nTORICGT_JSON_END\n", "module_language": "F2[x_level,y_radius]-graded chain complex", "num_C0_generators": 12, "num_C1_generators": 41, "num_C2_generators": 55, "ring": "GF(2)[x_level,y_radius]", "script": "needsPackage \"JSON\"\nR = GF(2)[x_level,y_radius, Degrees=>{{1,0},{0,1}}]\nC0 = R^{{0,0},{-1,0},{-2,0},{-3,0},{-4,0},{-5,0},{-6,0},{-7,0},{-8,0},{-9,0},{-10,0},{-11,0}}\nC1 = R^{{-1,-4},{-2,-4},{-3,-4},{-4,-4},{-5,-4},{-2,-4},{-3,-3},{-5,-4},{-7,-3},{-9,-4},{-11,-4},{-3,-4},{-4,-4},{-6,-3},{-7,-4},{-8,-4},{-9,-4},{-4,-4},{-5,-4},{-6,-4},{-7,-2},{-8,-3},{-10,-4},{-11,-4},{-5,-4},{-7,-3},{-8,-4},{-9,-4},{-11,-4},{-6,-4},{-7,-3},{-8,-4},{-9,-4},{-7,-4},{-11,-4},{-8,-4},{-9,-4},{-10,-4},{-11,-4},{-9,-4},{-10,-4}}\nC2 = R^{{-2,-4},{-3,-4},{-5,-4},{-3,-4},{-4,-4},{-4,-4},{-5,-4},{-5,-4},{-3,-4},{-7,-4},{-9,-4},{-5,-4},{-7,-3},{-11,-4},{-7,-4},{-9,-4},{-9,-4},{-11,-4},{-4,-4},{-6,-4},{-7,-4},{-8,-4},{-7,-4},{-8,-4},{-9,-4},{-7,-4},{-8,-4},{-9,-4},{-9,-4},{-5,-4},{-7,-4},{-8,-4},{-11,-4},{-6,-4},{-7,-4},{-8,-4},{-7,-4},{-11,-4},{-8,-4},{-10,-4},{-11,-4},{-7,-4},{-8,-4},{-9,-4},{-8,-4},{-9,-4},{-11,-4},{-9,-4},{-7,-4},{-8,-4},{-9,-4},{-9,-4},{-11,-4},{-9,-4},{-10,-4}}\nd1 = map(C0,C1,matrix{{x_level*y_radius^4,x_level^2*y_radius^4,x_level^3*y_radius^4,x_level^4*y_radius^4,x_level^5*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{y_radius^4,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^2*y_radius^3,x_level^4*y_radius^4,x_level^6*y_radius^3,x_level^8*y_radius^4,x_level^10*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^2*y_radius^4,x_level^4*y_radius^3,x_level^5*y_radius^4,x_level^6*y_radius^4,x_level^7*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^2*y_radius^4,x_level^3*y_radius^4,x_level^4*y_radius^2,x_level^5*y_radius^3,x_level^7*y_radius^4,x_level^8*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^3*y_radius^3,x_level^4*y_radius^4,x_level^5*y_radius^4,x_level^7*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^2*y_radius^3,x_level^3*y_radius^4,x_level^4*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,x_level*y_radius^4,x_level^5*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,y_radius^4,0_R,x_level*y_radius^4,x_level^2*y_radius^4,x_level^3*y_radius^4,x_level^4*y_radius^4,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,x_level*y_radius^4,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R,y_radius^4,x_level*y_radius^4},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,y_radius^4},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R}})\nd2 = map(C1,C2,matrix{{x_level,x_level^2,x_level^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{1_R,0_R,0_R,x_level,x_level^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,1_R,0_R,1_R,0_R,x_level,x_level^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,1_R,1_R,0_R,x_level,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,1_R,0_R,0_R,0_R,1_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level,x_level^5,x_level^7,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,x_level^2*y_radius,x_level^4,x_level^8*y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,x_level^2,x_level^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,1_R,0_R,y_radius,0_R,x_level^2*y_radius,x_level^4*y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level,x_level^3,x_level^4,x_level^5,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,x_level^3,x_level^4,x_level^5,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,0_R,x_level*y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,1_R,0_R,0_R,1_R,x_level,x_level^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,1_R,0_R,0_R,1_R,0_R,x_level,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,1_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level,x_level^3,x_level^4,x_level^7,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,x_level,x_level^2,x_level^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,x_level,x_level^5,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,y_radius^2,0_R,y_radius^2,0_R,x_level*y_radius^2,x_level^3*y_radius^2,x_level^4*y_radius^2,0_R,0_R,0_R,0_R,0_R,0_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= chainComplex({d1,d2})\nH0 = HH_0 C\nH1 = HH_1 C\nH2 = HH_2 C\nRH0 = res H0\nRH1 = res H1\nRH2 = res H2\nIdC = id_C\nConeIdC = try cone IdC else null\nConeIdRH0 = try cone id_RH0 else null\nConeIdRH1 = try cone id_RH1 else null\nConeIdRH2 = try cone id_RH2 else null\nresolutionSummary = hashTable {\n \"H0_module\" => toString H0,\n \"H1_module\" => toString H1,\n \"H2_module\" => toString H2,\n \"H0_presentation\" => toString presentation H0,\n \"H1_presentation\" => toString presentation H1,\n \"H2_presentation\" => toString presentation H2,\n \"H0_betti\" => toString betti RH0,\n \"H1_betti\" => toString betti RH1,\n \"H2_betti\" => toString betti RH2,\n \"H0_resolution\" => toString RH0,\n \"H1_resolution\" => toString RH1,\n \"H2_resolution\" => toString RH2\n}\nderivedSummary = hashTable {\n \"chain_identity_map\" => toString IdC,\n \"chain_identity_mapping_cone\" => toString ConeIdC,\n \"chain_identity_mapping_cone_homology_pruned\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdC else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdC else \"\"),\n \"H2\" => toString (try prune HH_2 ConeIdC else \"\")\n },\n \"homology_resolution_identity_maps\" => hashTable {\n \"H0\" => toString (try id_RH0 else \"\"),\n \"H1\" => toString (try id_RH1 else \"\"),\n \"H2\" => toString (try id_RH2 else \"\")\n },\n \"homology_resolution_identity_cone_homology_pruned\" => hashTable {\n \"H0\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH0 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH0 else \"\")\n },\n \"H1\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH1 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH1 else \"\")\n },\n \"H2\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH2 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH2 else \"\")\n }\n },\n \"Ext_modules\" => hashTable {\n \"H0_Ext0\" => toString (try Ext^0(H0,R) else \"\"),\n \"H0_Ext1\" => toString (try Ext^1(H0,R) else \"\"),\n \"H1_Ext0\" => toString (try Ext^0(H1,R) else \"\"),\n \"H1_Ext1\" => toString (try Ext^1(H1,R) else \"\"),\n \"H2_Ext0\" => toString (try Ext^0(H2,R) else \"\"),\n \"H2_Ext1\" => toString (try Ext^1(H2,R) else \"\")\n },\n \"Tor_residue_modules\" => hashTable {\n \"H0_Tor0\" => toString (try Tor_0(H0,coker vars R) else \"\"),\n \"H0_Tor1\" => toString (try Tor_1(H0,coker vars R) else \"\"),\n \"H1_Tor0\" => toString (try Tor_0(H1,coker vars R) else \"\"),\n \"H1_Tor1\" => toString (try Tor_1(H1,coker vars R) else \"\"),\n \"H2_Tor0\" => toString (try Tor_0(H2,coker vars R) else \"\"),\n \"H2_Tor1\" => toString (try Tor_1(H2,coker vars R) else \"\")\n }\n}\nout = hashTable {\n \"kind\" => \"macaulay2_bigraded_persistence_resolution\",\n \"ring\" => \"GF(2)[x_level,y_radius]\",\n \"module_language\" => \"F2[x_level,y_radius]-graded chain complex\",\n \"num_C0_generators\" => rank C0,\n \"num_C1_generators\" => rank C1,\n \"num_C2_generators\" => rank C2,\n \"homogeneous_d1\" => isHomogeneous d1,\n \"homogeneous_d2\" => isHomogeneous d2,\n \"d_squared_zero\" => d1*d2 == 0,\n \"chain_complex\" => toString C,\n \"boundary_d1\" => toString d1,\n \"boundary_d2\" => toString d2,\n \"homology_and_resolutions\" => resolutionSummary,\n \"derived_category_maps\" => derivedSummary\n}\nprint \"TORICGT_JSON_BEGIN\"\nprint toJSON out\nprint \"TORICGT_JSON_END\"\n" }, "max_radius": 31.096457807654783, "ph_retrieval_candidates": [ { "candidate_signature_norm": 388.4135317990799, "exact_internal_simplicial_map_score": 1.0, "ph_signature_cosine": 0.9385684484455362, "record_id": "tok_emb_weight", "retrieval_score": 0.9557692828807861, "source_signature_norm": 452.6482560295248 }, { "candidate_signature_norm": 431.2156845738476, "exact_internal_simplicial_map_score": 1.0, "ph_signature_cosine": 0.9285480861311269, "record_id": "fineweb_tokengt_edge_source_class_emb_weight", "retrieval_score": 0.9485546220144114, "source_signature_norm": 452.6482560295248 } ], "ph_retrieval_signature": { "exact_internal_simplicial_map_valid_fraction": 1.0, "provenance": "exact_gudhi_vectorizers_and_exact_simplicial_map_audits", "schema": "toricgt.gudhi_ph_retrieval_signature.v1", "signature_length": 2139, "signature_norm": 452.6482560295248, "top_k": 2 }, "points": 12, "radii": [ 6.219291561530957, 12.438583123061914, 18.65787468459287, 24.877166246123828, 31.096457807654783 ], "record_id": "fineweb_tokengt_position_bucket_emb_weight", "simplex_tree": { "dimension": 2, "num_simplices": 108, "num_vertices": 12 }, "staircase_visualization": { "adjacent_lcm_outer_corners": [ [ 3, 4 ], [ 7, 3 ] ], "bounded_window": { "x_level_max": 11, "y_radius_max": 4 }, "higher_syzygy_corners": [ [ 2, 4 ], [ 7, 3 ] ], "ideal_chain_degree": "C1", "inner_corners": [ [ 1, 4 ], [ 3, 3 ], [ 7, 2 ] ], "layer_height_offsets_px": { "C0": 0, "C1": -7, "C2": -14, "adjacent_lcm": -21, "syzygy_edge": -17 }, "quotient_lattice_points": [ [ 0, 0 ], [ 0, 1 ], [ 0, 2 ], [ 0, 3 ], [ 0, 4 ], [ 1, 0 ], [ 1, 1 ], [ 1, 2 ], [ 1, 3 ], [ 2, 0 ], [ 2, 1 ], [ 2, 2 ], [ 2, 3 ], [ 3, 0 ], [ 3, 1 ], [ 3, 2 ], [ 4, 0 ], [ 4, 1 ], [ 4, 2 ], [ 5, 0 ], [ 5, 1 ], [ 5, 2 ], [ 6, 0 ], [ 6, 1 ], [ 6, 2 ], [ 7, 0 ], [ 7, 1 ], [ 8, 0 ], [ 8, 1 ], [ 9, 0 ], [ 9, 1 ], [ 10, 0 ], [ 10, 1 ], [ 11, 0 ], [ 11, 1 ] ], "ring": "F2[x_level,y_radius]", "schema": "toricgt.miller_sturmfels_staircase_visualization.v1", "staircase_thresholds_by_x_level": [ [ 0, 5 ], [ 1, 4 ], [ 2, 4 ], [ 3, 3 ], [ 4, 3 ], [ 5, 3 ], [ 6, 3 ], [ 7, 2 ], [ 8, 2 ], [ 9, 2 ], [ 10, 2 ], [ 11, 2 ] ] }, "two_parameter_module": { "chain_generators_c0": [ [ 2, 2, 2, 2, 2 ], [ 4, 4, 4, 4, 4 ], [ 7, 7, 7, 7, 7 ], [ 10, 10, 10, 10, 10 ], [ 12, 12, 12, 12, 12 ] ], "chain_generators_c1": [ [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 6 ], [ 0, 0, 0, 2, 16 ], [ 0, 0, 1, 7, 33 ], [ 0, 0, 1, 7, 41 ] ], "chain_generators_c2": [ [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 14 ], [ 0, 0, 0, 1, 46 ], [ 0, 0, 0, 1, 55 ] ], 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0, y_radius, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, x_level^3*y_radius, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 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"H0_Ext0": "image matrix {{1}, {x_level}, {x_level^2}, {x_level^3}, {x_level^4}, {x_level^5}, {x_level^6}, {x_level^7}, {x_level^8}, {x_level^9}, {x_level^10}, {x_level^11}}", "H0_Ext1": "cokernel matrix {{0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0}, {0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0}, {0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0}}", "H1_Ext0": "image matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}", "H1_Ext1": "R^0", "H2_Ext0": "R^39", "H2_Ext1": "R^0" }, "Tor_residue_modules": { "H0_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^2, x_level^3*y_radius^3, x_level^4*y_radius^3, x_level^5*y_radius^3, x_level^6*y_radius^2, x_level^7*y_radius^3, x_level^8, x_level^9*y_radius^3, x_level^10*y_radius^3, x_level^11*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^2, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^3, x_level^6*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^3, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, x_level^2*y_radius^2, x_level^3*y_radius^3, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^4*y_radius^4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, y_radius^2, 0, 0, y_radius^3, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^3, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^3, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, y_radius^3, 0}}", "H0_Tor1": "subquotient(matrix {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}},matrix {{y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level}})", "H1_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 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0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius}}", "H2_Tor1": "R^0" }, "chain_identity_map": "ChainComplexMap{...7...}", "chain_identity_mapping_cone": "ChainComplex{...7...}", "chain_identity_mapping_cone_homology_pruned": { "H0": "R^0", "H1": "R^0", "H2": "R^0" }, "homology_resolution_identity_cone_homology_pruned": { "H0": { "H0": "R^0", "H1": "R^0" }, "H1": { "H0": "R^0", "H1": "R^0" }, "H2": { "H0": "R^0", "H1": "R^0" } }, "homology_resolution_identity_maps": { "H0": "ChainComplexMap{...7...}", "H1": "ChainComplexMap{...7...}", "H2": "ChainComplexMap{...6...}" } }, "homogeneous_d1": true, "homogeneous_d2": true, "homology_and_resolutions": { "H0_betti": "new BettiTally from {(0,{0, 0},0) => 1, (0,{1, 0},1) => 1, (0,{2, 0},2) => 1, (0,{3, 0},3) => 1, (0,{4, 0},4) => 1, (0,{5, 0},5) => 1, (0,{6, 0},6) => 1, (0,{7, 0},7) => 1, (0,{8, 0},8) => 1, (0,{9, 0},9) => 1, (0,{10, 0},10) => 1, (0,{11, 0},11) => 1, (1,{1, 4},5) => 1, (1,{2, 2},4) => 1, (1,{3, 3},6) => 1, (1,{4, 3},7) => 1, (1,{5, 3},8) => 1, (1,{6, 2},8) => 1, (1,{7, 3},10) => 1, (1,{8, 0},8) => 1, (1,{9, 3},12) => 1, (1,{10, 3},13) => 1, (1,{11, 3},14) => 1}", "H0_module": "cokernel matrix {{x_level*y_radius^4, x_level^2*y_radius^2, x_level^3*y_radius^3, x_level^4*y_radius^3, x_level^5*y_radius^3, x_level^6*y_radius^2, x_level^7*y_radius^3, x_level^8, x_level^9*y_radius^3, x_level^10*y_radius^3, x_level^11*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^2, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^3, x_level^6*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^3, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, x_level^2*y_radius^2, x_level^3*y_radius^3, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^4*y_radius^4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, y_radius^2, 0, 0, y_radius^3, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^3, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^3, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, y_radius^3, 0}}", "H0_presentation": "matrix {{x_level*y_radius^4, x_level^2*y_radius^2, x_level^3*y_radius^3, x_level^4*y_radius^3, x_level^5*y_radius^3, x_level^6*y_radius^2, x_level^7*y_radius^3, x_level^8, x_level^9*y_radius^3, x_level^10*y_radius^3, x_level^11*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^2, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^3, x_level^6*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^3, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, x_level^2*y_radius^2, x_level^3*y_radius^3, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^4*y_radius^4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, y_radius^2, 0, 0, y_radius^3, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^3, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^3, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, y_radius^3, 0}}", "H0_resolution": "ChainComplex{...8...}", "H1_betti": "new BettiTally from {(0,{3, 4},7) => 1, (0,{4, 4},8) => 2, (0,{6, 4},10) => 4, (0,{7, 4},11) => 3, (0,{8, 2},10) => 2, (0,{8, 3},11) => 4, (0,{8, 4},12) => 1, (0,{9, 3},12) => 3, (0,{9, 4},13) => 3, (0,{10, 3},13) => 1, (0,{10, 4},14) => 2, (0,{11, 3},14) => 1, (0,{11, 4},15) => 3, (1,{3, 4},7) => 1, (1,{4, 4},8) => 2, (1,{6, 4},10) => 4, (1,{7, 4},11) => 3, (1,{8, 2},10) => 2, (1,{8, 3},11) => 4, (1,{8, 4},12) => 1, (1,{9, 3},12) => 3, (1,{9, 4},13) => 3, (1,{10, 3},13) => 1, (1,{10, 4},14) => 2, (1,{11, 3},14) => 1, (1,{11, 4},15) => 3}", "H1_module": "subquotient(matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {x_level*y_radius^2, 0, 0, x_level^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius, 0, 0, x_level^2*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, x_level^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^2, 0, 0, y_radius^2, x_level^2, x_level*y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, x_level, x_level, x_level, x_level, x_level*y_radius, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, x_level, 0, x_level*y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, x_level, y_radius, 0, x_level*y_radius, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, y_radius, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, x_level, x_level, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, x_level, x_level, x_level}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, y_radius, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, y_radius, y_radius, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, x_level, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, x_level, x_level}},matrix {{x_level^7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, x_level*y_radius^2, x_level^2*y_radius^2, x_level^4*y_radius^2, x_level^5*y_radius^2, x_level^6, x_level^7*y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius, 0, 0, 0, 0, 0, x_level*y_radius, x_level^3*y_radius, x_level^4*y_radius, x_level^5, x_level^6*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, x_level^2*y_radius, x_level^3*y_radius, x_level^4, x_level^5*y_radius, x_level^6*y_radius, x_level^7*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius, x_level^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, y_radius^2, 0, x_level^2, x_level^3*y_radius, x_level^5*y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius, 0, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, x_level^2, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^4, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, y_radius^2, 0, 0, y_radius^3, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, y_radius, 0, 0, y_radius, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, x_level^3, x_level^4, x_level^5, x_level^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level^2, x_level^3, x_level^4, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 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"ChainComplex{...8...}", "H2_betti": "new BettiTally from {(0,{4, 4},8) => 1, (0,{6, 4},10) => 3, (0,{7, 4},11) => 3, (0,{8, 4},12) => 10, (0,{9, 3},12) => 2, (0,{9, 4},13) => 12, (0,{10, 4},14) => 3, (0,{11, 4},15) => 5}", "H2_module": "image matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, x_level, x_level, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, x_level, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, x_level^2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, x_level^2, 0, x_level^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, x_level, 0, 0, x_level, x_level}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, x_level, x_level, x_level, x_level}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius, y_radius, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, x_level, x_level}}", "H2_presentation": "matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}", "H2_resolution": "ChainComplex{...7...}" }, "kind": "macaulay2_bigraded_persistence_resolution", "macaulay2_stdout_tail": "y_radius^4, x_level^3*y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^4, 0, x_level^2*y_radius^2, x_level^3*y_radius^3, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^4*y_radius^4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^3, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^3, y_radius^2, 0, 0, y_radius^3, 0, 0, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^3, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, y_radius^3, 0, 0, y_radius^3, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, y_radius^3, 0}}\", \"H0_betti\": \"new BettiTally from {(0,{0, 0},0) => 1, (0,{1, 0},1) => 1, (0,{2, 0},2) => 1, (0,{3, 0},3) => 1, (0,{4, 0},4) => 1, (0,{5, 0},5) => 1, (0,{6, 0},6) => 1, (0,{7, 0},7) => 1, (0,{8, 0},8) => 1, (0,{9, 0},9) => 1, (0,{10, 0},10) => 1, (0,{11, 0},11) => 1, (1,{1, 4},5) => 1, (1,{2, 2},4) => 1, (1,{3, 3},6) => 1, (1,{4, 3},7) => 1, (1,{5, 3},8) => 1, (1,{6, 2},8) => 1, (1,{7, 3},10) => 1, (1,{8, 0},8) => 1, (1,{9, 3},12) => 1, (1,{10, 3},13) => 1, (1,{11, 3},14) => 1}\", \"H2_presentation\": \"matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}\"}, \"homogeneous_d2\": true}\nTORICGT_JSON_END\n", "module_language": "F2[x_level,y_radius]-graded chain complex", "num_C0_generators": 12, "num_C1_generators": 41, "num_C2_generators": 69, "ring": "GF(2)[x_level,y_radius]", "script": "needsPackage \"JSON\"\nR = GF(2)[x_level,y_radius, Degrees=>{{1,0},{0,1}}]\nC0 = R^{{0,0},{-1,0},{-2,0},{-3,0},{-4,0},{-5,0},{-6,0},{-7,0},{-8,0},{-9,0},{-10,0},{-11,0}}\nC1 = R^{{-1,-4},{-2,-2},{-3,-3},{-4,-3},{-5,-3},{-6,-2},{-7,-3},{-8,0},{-9,-3},{-10,-3},{-11,-3},{-8,-4},{-3,-4},{-4,-4},{-6,-4},{-7,-4},{-8,-2},{-9,-4},{-4,-4},{-6,-4},{-7,-4},{-8,-3},{-9,-4},{-6,-4},{-7,-4},{-8,-3},{-9,-4},{-10,-4},{-11,-4},{-6,-4},{-8,-3},{-8,-2},{-9,-3},{-11,-4},{-8,-3},{-9,-3},{-11,-4},{-9,-3},{-10,-3},{-11,-3},{-10,-4}}\nC2 = R^{{-8,-4},{-3,-4},{-4,-4},{-6,-4},{-7,-4},{-8,-2},{-9,-4},{-4,-4},{-6,-4},{-7,-4},{-8,-3},{-9,-4},{-6,-4},{-7,-4},{-8,-3},{-9,-4},{-10,-4},{-11,-4},{-6,-4},{-8,-3},{-8,-2},{-9,-3},{-11,-4},{-8,-3},{-9,-3},{-11,-4},{-9,-3},{-10,-3},{-11,-3},{-10,-4},{-4,-4},{-6,-4},{-7,-4},{-8,-4},{-9,-4},{-6,-4},{-7,-4},{-8,-4},{-9,-4},{-8,-4},{-9,-4},{-8,-4},{-9,-4},{-9,-4},{-6,-4},{-7,-4},{-8,-4},{-9,-4},{-8,-4},{-9,-4},{-8,-4},{-9,-4},{-9,-4},{-8,-4},{-9,-4},{-11,-4},{-8,-4},{-9,-4},{-11,-4},{-9,-4},{-10,-4},{-11,-4},{-10,-4},{-8,-4},{-9,-3},{-11,-4},{-9,-3},{-11,-4},{-10,-4}}\nd1 = map(C0,C1,matrix{{x_level*y_radius^4,x_level^2*y_radius^2,x_level^3*y_radius^3,x_level^4*y_radius^3,x_level^5*y_radius^3,x_level^6*y_radius^2,x_level^7*y_radius^3,x_level^8,x_level^9*y_radius^3,x_level^10*y_radius^3,x_level^11*y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^7*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,y_radius^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^2*y_radius^4,x_level^4*y_radius^4,x_level^5*y_radius^4,x_level^6*y_radius^2,x_level^7*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^3*y_radius^4,x_level^4*y_radius^4,x_level^5*y_radius^3,x_level^6*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,x_level^2*y_radius^4,x_level^3*y_radius^4,x_level^4*y_radius^3,x_level^5*y_radius^4,x_level^6*y_radius^4,x_level^7*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^3*y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,x_level^2*y_radius^2,x_level^3*y_radius^3,x_level^5*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^3,x_level^2*y_radius^3,x_level^4*y_radius^4,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,y_radius^3,y_radius^2,0_R,0_R,y_radius^3,0_R,0_R,x_level*y_radius^3,x_level^2*y_radius^3,x_level^3*y_radius^3,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,y_radius^3,0_R,y_radius^3,0_R,0_R,x_level*y_radius^4},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,y_radius^4},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,y_radius^4,0_R,0_R,y_radius^3,0_R}})\nd2 = 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= chainComplex({d1,d2})\nH0 = HH_0 C\nH1 = HH_1 C\nH2 = HH_2 C\nRH0 = res H0\nRH1 = res H1\nRH2 = res H2\nIdC = id_C\nConeIdC = try cone IdC else null\nConeIdRH0 = try cone id_RH0 else null\nConeIdRH1 = try cone id_RH1 else null\nConeIdRH2 = try cone id_RH2 else null\nresolutionSummary = hashTable {\n \"H0_module\" => toString H0,\n \"H1_module\" => toString H1,\n \"H2_module\" => toString H2,\n \"H0_presentation\" => toString presentation H0,\n \"H1_presentation\" => toString presentation H1,\n \"H2_presentation\" => toString presentation H2,\n \"H0_betti\" => toString betti RH0,\n \"H1_betti\" => toString betti RH1,\n \"H2_betti\" => toString betti RH2,\n \"H0_resolution\" => toString RH0,\n \"H1_resolution\" => toString RH1,\n \"H2_resolution\" => toString RH2\n}\nderivedSummary = hashTable {\n \"chain_identity_map\" => toString IdC,\n \"chain_identity_mapping_cone\" => toString ConeIdC,\n \"chain_identity_mapping_cone_homology_pruned\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdC else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdC else \"\"),\n \"H2\" => toString (try prune HH_2 ConeIdC else \"\")\n },\n \"homology_resolution_identity_maps\" => hashTable {\n \"H0\" => toString (try id_RH0 else \"\"),\n \"H1\" => toString (try id_RH1 else \"\"),\n \"H2\" => toString (try id_RH2 else \"\")\n },\n \"homology_resolution_identity_cone_homology_pruned\" => hashTable {\n \"H0\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH0 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH0 else \"\")\n },\n \"H1\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH1 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH1 else \"\")\n },\n \"H2\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH2 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH2 else \"\")\n }\n },\n \"Ext_modules\" => hashTable {\n \"H0_Ext0\" => toString (try Ext^0(H0,R) else \"\"),\n \"H0_Ext1\" => toString (try Ext^1(H0,R) else \"\"),\n \"H1_Ext0\" => toString (try Ext^0(H1,R) else \"\"),\n \"H1_Ext1\" => toString (try Ext^1(H1,R) else \"\"),\n \"H2_Ext0\" => toString (try Ext^0(H2,R) else \"\"),\n \"H2_Ext1\" => toString (try Ext^1(H2,R) else \"\")\n },\n \"Tor_residue_modules\" => hashTable {\n \"H0_Tor0\" => toString (try Tor_0(H0,coker vars R) else \"\"),\n \"H0_Tor1\" => toString (try Tor_1(H0,coker vars R) else \"\"),\n \"H1_Tor0\" => toString (try Tor_0(H1,coker vars R) else \"\"),\n \"H1_Tor1\" => toString (try Tor_1(H1,coker vars R) else \"\"),\n \"H2_Tor0\" => toString (try Tor_0(H2,coker vars R) else \"\"),\n \"H2_Tor1\" => toString (try Tor_1(H2,coker vars R) else \"\")\n }\n}\nout = hashTable {\n \"kind\" => \"macaulay2_bigraded_persistence_resolution\",\n \"ring\" => \"GF(2)[x_level,y_radius]\",\n \"module_language\" => \"F2[x_level,y_radius]-graded chain complex\",\n \"num_C0_generators\" => rank C0,\n \"num_C1_generators\" => rank C1,\n \"num_C2_generators\" => rank C2,\n \"homogeneous_d1\" => isHomogeneous d1,\n \"homogeneous_d2\" => isHomogeneous d2,\n \"d_squared_zero\" => d1*d2 == 0,\n \"chain_complex\" => toString C,\n \"boundary_d1\" => toString d1,\n \"boundary_d2\" => toString d2,\n \"homology_and_resolutions\" => resolutionSummary,\n \"derived_category_maps\" => derivedSummary\n}\nprint \"TORICGT_JSON_BEGIN\"\nprint toJSON out\nprint \"TORICGT_JSON_END\"\n" }, "max_radius": 34.80647759904382, "ph_retrieval_candidates": [ { "candidate_signature_norm": 452.6482560295248, "exact_internal_simplicial_map_score": 1.0, "ph_signature_cosine": 0.9385684484455362, "record_id": "fineweb_tokengt_position_bucket_emb_weight", "retrieval_score": 0.9557692828807861, "source_signature_norm": 388.4135317990799 }, { "candidate_signature_norm": 431.2156845738476, "exact_internal_simplicial_map_score": 1.0, "ph_signature_cosine": 0.9232210305369433, "record_id": "fineweb_tokengt_edge_source_class_emb_weight", "retrieval_score": 0.9447191419865991, "source_signature_norm": 388.4135317990799 } ], "ph_retrieval_signature": { "exact_internal_simplicial_map_valid_fraction": 1.0, "provenance": "exact_gudhi_vectorizers_and_exact_simplicial_map_audits", "schema": "toricgt.gudhi_ph_retrieval_signature.v1", "signature_length": 2139, "signature_norm": 388.4135317990799, "top_k": 2 }, "points": 12, "radii": [ 6.961295519808765, 13.92259103961753, 20.883886559426294, 27.84518207923506, 34.80647759904382 ], "record_id": "tok_emb_weight", "simplex_tree": { "dimension": 2, "num_simplices": 122, "num_vertices": 12 }, "staircase_visualization": { "adjacent_lcm_outer_corners": [ [ 2, 4 ], [ 8, 2 ] ], "bounded_window": { "x_level_max": 11, "y_radius_max": 4 }, "higher_syzygy_corners": [ [ 3, 4 ], [ 8, 2 ] ], "ideal_chain_degree": "C1", "inner_corners": [ [ 1, 4 ], [ 2, 2 ], [ 8, 0 ] ], "layer_height_offsets_px": { "C0": 0, "C1": -7, "C2": -14, "adjacent_lcm": -21, "syzygy_edge": -17 }, "quotient_lattice_points": [ [ 0, 0 ], [ 0, 1 ], [ 0, 2 ], [ 0, 3 ], [ 0, 4 ], [ 1, 0 ], [ 1, 1 ], [ 1, 2 ], [ 1, 3 ], [ 2, 0 ], [ 2, 1 ], [ 3, 0 ], [ 3, 1 ], [ 4, 0 ], [ 4, 1 ], [ 5, 0 ], [ 5, 1 ], [ 6, 0 ], [ 6, 1 ], [ 7, 0 ], [ 7, 1 ] ], "ring": "F2[x_level,y_radius]", "schema": "toricgt.miller_sturmfels_staircase_visualization.v1", "staircase_thresholds_by_x_level": [ [ 0, 5 ], [ 1, 4 ], [ 2, 2 ], [ 3, 2 ], [ 4, 2 ], [ 5, 2 ], [ 6, 2 ], [ 7, 2 ], [ 8, 0 ], [ 9, 0 ], [ 10, 0 ], [ 11, 0 ] ] }, "two_parameter_module": { "chain_generators_c0": [ [ 2, 2, 2, 2, 2 ], [ 4, 4, 4, 4, 4 ], [ 7, 7, 7, 7, 7 ], [ 10, 10, 10, 10, 10 ], [ 12, 12, 12, 12, 12 ] ], "chain_generators_c1": [ [ 0, 0, 0, 0, 1 ], [ 0, 0, 1, 2, 4 ], [ 0, 0, 2, 5, 13 ], [ 1, 1, 5, 17, 32 ], [ 1, 1, 5, 21, 41 ] ], "chain_generators_c2": [ [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 11 ], [ 0, 0, 2, 11, 54 ], [ 0, 0, 2, 13, 69 ] ], "commutative_square_chain_residuals_by_dimension": { "0": 0, "1": 0, "2": 0 }, "commutative_square_residual": 0.0, "commutative_squares_checked": 16, "hilbert_h0": [ [ 2, 2, 2, 2, 1 ], [ 4, 4, 3, 2, 1 ], [ 7, 7, 5, 2, 1 ], [ 9, 9, 7, 2, 1 ], [ 11, 11, 9, 2, 1 ] ], "hilbert_h1": [ [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], "levels": [ 2, 4, 7, 10, 12 ], "nodes": [ { "betti0": 2, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 2, "num_triangles": 0, "x_level": 0, "x_prefix_points": 2, "y_radius": 6.961295519808765, "y_radius_index": 0 }, { "betti0": 2, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 2, "num_triangles": 0, "x_level": 0, "x_prefix_points": 2, "y_radius": 13.92259103961753, "y_radius_index": 1 }, { "betti0": 2, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 2, "num_triangles": 0, "x_level": 0, "x_prefix_points": 2, "y_radius": 20.883886559426294, "y_radius_index": 2 }, { "betti0": 2, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 2, "num_triangles": 0, "x_level": 0, "x_prefix_points": 2, "y_radius": 27.84518207923506, "y_radius_index": 3 }, { "betti0": 1, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 1, "num_simplices": 3, "num_triangles": 0, "x_level": 0, "x_prefix_points": 2, "y_radius": 34.80647759904382, "y_radius_index": 4 }, { "betti0": 4, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 4, "num_triangles": 0, "x_level": 1, "x_prefix_points": 4, "y_radius": 6.961295519808765, "y_radius_index": 0 }, { "betti0": 4, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 4, "num_triangles": 0, "x_level": 1, "x_prefix_points": 4, "y_radius": 13.92259103961753, "y_radius_index": 1 }, { "betti0": 3, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 1, "num_simplices": 5, "num_triangles": 0, "x_level": 1, "x_prefix_points": 4, "y_radius": 20.883886559426294, "y_radius_index": 2 }, { "betti0": 2, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 2, "num_simplices": 6, "num_triangles": 0, "x_level": 1, "x_prefix_points": 4, "y_radius": 27.84518207923506, "y_radius_index": 3 }, { "betti0": 1, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 4, "num_simplices": 9, "num_triangles": 1, "x_level": 1, "x_prefix_points": 4, "y_radius": 34.80647759904382, "y_radius_index": 4 }, { "betti0": 7, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 7, "num_triangles": 0, "x_level": 2, "x_prefix_points": 7, "y_radius": 6.961295519808765, "y_radius_index": 0 }, { "betti0": 7, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 0, "num_simplices": 7, "num_triangles": 0, "x_level": 2, "x_prefix_points": 7, "y_radius": 13.92259103961753, "y_radius_index": 1 }, { "betti0": 5, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 2, "num_simplices": 9, "num_triangles": 0, "x_level": 2, "x_prefix_points": 7, "y_radius": 20.883886559426294, "y_radius_index": 2 }, { "betti0": 2, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 5, "num_simplices": 12, "num_triangles": 0, "x_level": 2, "x_prefix_points": 7, "y_radius": 27.84518207923506, "y_radius_index": 3 }, { "betti0": 1, "betti1": 0, "betti2": 4, "d_squared_residual": 0, "num_edges": 13, "num_simplices": 31, "num_triangles": 11, "x_level": 2, "x_prefix_points": 7, "y_radius": 34.80647759904382, "y_radius_index": 4 }, { "betti0": 9, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 1, "num_simplices": 11, "num_triangles": 0, "x_level": 3, "x_prefix_points": 10, "y_radius": 6.961295519808765, "y_radius_index": 0 }, { "betti0": 9, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 1, "num_simplices": 11, "num_triangles": 0, "x_level": 3, "x_prefix_points": 10, "y_radius": 13.92259103961753, "y_radius_index": 1 }, { "betti0": 7, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 5, "num_simplices": 17, "num_triangles": 2, "x_level": 3, "x_prefix_points": 10, "y_radius": 20.883886559426294, "y_radius_index": 2 }, { "betti0": 2, "betti1": 0, "betti2": 2, "d_squared_residual": 0, "num_edges": 17, "num_simplices": 38, "num_triangles": 11, "x_level": 3, "x_prefix_points": 10, "y_radius": 27.84518207923506, "y_radius_index": 3 }, { "betti0": 1, "betti1": 0, "betti2": 31, "d_squared_residual": 0, "num_edges": 32, "num_simplices": 96, "num_triangles": 54, "x_level": 3, "x_prefix_points": 10, "y_radius": 34.80647759904382, "y_radius_index": 4 }, { "betti0": 11, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 1, "num_simplices": 13, "num_triangles": 0, "x_level": 4, "x_prefix_points": 12, "y_radius": 6.961295519808765, "y_radius_index": 0 }, { "betti0": 11, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 1, "num_simplices": 13, "num_triangles": 0, "x_level": 4, "x_prefix_points": 12, "y_radius": 13.92259103961753, "y_radius_index": 1 }, { "betti0": 9, "betti1": 0, "betti2": 0, "d_squared_residual": 0, "num_edges": 5, "num_simplices": 19, "num_triangles": 2, "x_level": 4, "x_prefix_points": 12, "y_radius": 20.883886559426294, "y_radius_index": 2 }, { "betti0": 2, "betti1": 0, "betti2": 2, "d_squared_residual": 0, "num_edges": 21, "num_simplices": 46, "num_triangles": 13, "x_level": 4, "x_prefix_points": 12, "y_radius": 27.84518207923506, "y_radius_index": 3 }, { "betti0": 1, "betti1": 0, "betti2": 39, "d_squared_residual": 0, "num_edges": 41, "num_simplices": 122, "num_triangles": 69, "x_level": 4, "x_prefix_points": 12, "y_radius": 34.80647759904382, "y_radius_index": 4 } ], "radii": [ 6.961295519808765, 13.92259103961753, 20.883886559426294, 27.84518207923506, 34.80647759904382 ], "ring": "F2[x_level,y_radius]", "structure_map_summary": { "all_simplicial_maps_valid": true, "map_count": 40, "mean_simplicial_map_valid_fraction": 1.0, "min_simplicial_map_valid_fraction": 1.0, "x_level_map_count": 20, "y_radius_map_count": 20 }, "structure_maps": [ { "from": [ 0, 0 ], "h0_rank": 2, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 1, 0 ] }, { "from": [ 0, 0 ], "h0_rank": 2, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 0, 1 ] }, { "from": [ 0, 1 ], "h0_rank": 2, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 1, 1 ] }, { "from": [ 0, 1 ], "h0_rank": 2, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 0, 2 ] }, { "from": [ 0, 2 ], "h0_rank": 2, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 1, 2 ] }, { "from": [ 0, 2 ], "h0_rank": 2, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 0, 3 ] }, { "from": [ 0, 3 ], "h0_rank": 2, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 1, 3 ] }, { "from": [ 0, 3 ], "h0_rank": 1, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 0, 4 ] }, { "from": [ 0, 4 ], "h0_rank": 1, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 1.0, "dim1_valid": 1.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 1, 4 ] }, { "from": [ 1, 0 ], "h0_rank": 4, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 2, 0 ] }, { "from": [ 1, 0 ], "h0_rank": 4, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 0.0, "dim1_valid": 0.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 0.0, "dim2_valid": 0.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 1, 1 ] }, { 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level^2, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, y_radius^2, 0, y_radius^2, x_level*y_radius^2, x_level^2*y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^5, x_level^6, x_level^7, x_level^8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^4*y_radius, x_level^5*y_radius, x_level^6, x_level^7*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, x_level^4, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, x_level^2*y_radius, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, y_radius, 0, y_radius, x_level, x_level^2*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 1, 0, 0, 0, y_radius, 0, 0, 0, 1, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, x_level^3, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, x_level, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius, x_level^3*y_radius, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, x_level, x_level^2, x_level^3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, y_radius, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, x_level, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, x_level^2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, y_radius, 0, 0, y_radius, 0, x_level*y_radius}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1}}", "chain_complex": "ChainComplex{...6...}", "d_squared_zero": true, "derived_category_maps": { "Ext_modules": { "H0_Ext0": "image matrix {{1}, {x_level}, {x_level^2}, {x_level^3}, {x_level^4}, {x_level^5}, {x_level^6}, {x_level^7}, {x_level^8}, {x_level^9}, {x_level^10}, {x_level^11}}", "H0_Ext1": "cokernel matrix {{y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^3}}", "H1_Ext0": "image matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}", "H1_Ext1": "cokernel matrix {{x_level^2}}", "H2_Ext0": "R^30", "H2_Ext1": "R^0" }, "Tor_residue_modules": { "H0_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^3*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, x_level^8*y_radius^2, x_level^9*y_radius^4, x_level^10*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^3*y_radius^4, x_level^5*y_radius^3, x_level^6*y_radius^4, x_level^7*y_radius^3, x_level^8*y_radius^3, x_level^9*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, x_level^3*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius^3, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^3, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, 0, x_level^2*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, y_radius^4, 0, y_radius^3, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0}}", "H0_Tor1": "cokernel matrix {{0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level}}", "H1_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, x_level}})", "H2_Tor0": "cokernel matrix {{x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, y_radius}}", "H2_Tor1": "R^0" }, "chain_identity_map": "ChainComplexMap{...7...}", "chain_identity_mapping_cone": "ChainComplex{...7...}", "chain_identity_mapping_cone_homology_pruned": { "H0": "R^0", "H1": "R^0", "H2": "R^0" }, "homology_resolution_identity_cone_homology_pruned": { "H0": { "H0": "R^0", "H1": "R^0" }, "H1": { "H0": "R^0", "H1": "R^0" }, "H2": { "H0": "R^0", "H1": "R^0" } }, "homology_resolution_identity_maps": { "H0": "ChainComplexMap{...8...}", "H1": "ChainComplexMap{...7...}", "H2": "ChainComplexMap{...6...}" } }, "homogeneous_d1": true, "homogeneous_d2": true, "homology_and_resolutions": { "H0_betti": "new BettiTally from {(0,{0, 0},0) => 1, (0,{1, 0},1) => 1, (0,{2, 0},2) => 1, (0,{3, 0},3) => 1, (0,{4, 0},4) => 1, (0,{5, 0},5) => 1, (0,{6, 0},6) => 1, (0,{7, 0},7) => 1, (0,{8, 0},8) => 1, (0,{9, 0},9) => 1, (0,{10, 0},10) => 1, (0,{11, 0},11) => 1, (1,{1, 4},5) => 1, (1,{2, 4},6) => 1, (1,{3, 3},6) => 1, (1,{4, 4},8) => 1, (1,{5, 3},8) => 1, (1,{6, 3},9) => 1, (1,{7, 4},11) => 1, (1,{8, 2},10) => 1, (1,{8, 3},11) => 2, (1,{9, 3},12) => 1, (1,{10, 3},13) => 1, (1,{11, 4},15) => 1, (2,{8, 4},12) => 2}", "H0_module": "cokernel matrix {{x_level*y_radius^4, x_level^3*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, x_level^8*y_radius^2, x_level^9*y_radius^4, x_level^10*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^4, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^3*y_radius^4, x_level^5*y_radius^3, x_level^6*y_radius^4, x_level^7*y_radius^3, x_level^8*y_radius^3, x_level^9*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, x_level^3*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius^3, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^3, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, 0, x_level^2*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, y_radius^4, 0, y_radius^3, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0}}", "H0_presentation": "matrix {{x_level*y_radius^4, x_level^3*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, x_level^8*y_radius^2, x_level^9*y_radius^4, x_level^10*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius^4, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^3, x_level^3*y_radius^4, x_level^5*y_radius^3, x_level^6*y_radius^4, x_level^7*y_radius^3, x_level^8*y_radius^3, x_level^9*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, x_level^3*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^4, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius^3, x_level^4*y_radius^4, x_level^5*y_radius^4, x_level^6*y_radius^3, x_level^7*y_radius^4, x_level^8*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius^4, x_level^4*y_radius^4, x_level^5*y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, 0, x_level^2*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, y_radius^4, 0, y_radius^3, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0}}", "H0_resolution": "ChainComplex{...9...}", "H1_betti": "new BettiTally from {(0,{3, 4},7) => 1, (0,{5, 4},9) => 2, (0,{6, 4},10) => 3, (0,{7, 4},11) => 4, (0,{8, 4},12) => 7, (0,{9, 3},12) => 2, (0,{9, 4},13) => 4, (0,{10, 4},14) => 6, (0,{11, 4},15) => 1, (1,{3, 4},7) => 1, (1,{5, 4},9) => 1, (1,{6, 4},10) => 3, (1,{7, 4},11) => 5, (1,{8, 4},12) => 7, (1,{9, 3},12) => 2, (1,{9, 4},13) => 4, (1,{10, 4},14) => 6, (1,{11, 4},15) => 1}", "H1_module": "subquotient(matrix {{x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, x_level, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, x_level, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, x_level, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, x_level^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius, 0, x_level^2*y_radius, 0, 0, x_level^3*y_radius, 0, 0, 0, 0, x_level^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius, 0, y_radius, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, y_radius, y_radius, 0, 0, x_level*y_radius, 0, 0, x_level^2*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, x_level}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius, y_radius, y_radius, y_radius, y_radius, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, y_radius, y_radius, y_radius, y_radius, 0, 0, 0, 0, 0, x_level*y_radius, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, y_radius, x_level*y_radius}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0}},matrix {{x_level^2, x_level^5, x_level^6, x_level^7, x_level^8, x_level^9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, x_level^2, x_level^4, x_level^5, x_level^6, x_level^7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, x_level^2, x_level^3, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, x_level^2, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, y_radius^2, 0, y_radius^2, x_level*y_radius^2, x_level^2*y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^5, x_level^6, x_level^7, x_level^8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^4*y_radius, x_level^5*y_radius, x_level^6, x_level^7*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, x_level^4, x_level^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, x_level^2*y_radius, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, 0, 0, y_radius, 0, y_radius, 0, y_radius, x_level, x_level^2*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 1, 0, 0, 0, y_radius, 0, 0, 0, 1, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, x_level^3, x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, x_level, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2*y_radius, x_level^3*y_radius, x_level^4*y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, x_level, x_level^2, x_level^3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, y_radius, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, x_level, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, x_level, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, x_level^2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, y_radius, 0, 0, y_radius, 0, x_level*y_radius}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1}})", "H1_presentation": "matrix {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}", "H1_resolution": "ChainComplex{...8...}", "H2_betti": "new BettiTally from {(0,{7, 4},11) => 2, (0,{8, 4},12) => 10, (0,{9, 4},13) => 8, (0,{10, 4},14) => 10}", "H2_module": "image matrix {{x_level^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level^2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius, 0, y_radius, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level*y_radius, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, x_level, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_level}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}}", "H2_presentation": "matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}", "H2_resolution": "ChainComplex{...7...}" }, "kind": "macaulay2_bigraded_persistence_resolution", "macaulay2_stdout_tail": "x_level*y_radius^4, x_level^2*y_radius^4, x_level^3*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^4, 0, 0, 0, x_level^2*y_radius^4, x_level^4*y_radius^4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, x_level*y_radius^3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, y_radius^4, 0, y_radius^3, x_level*y_radius^3, x_level^2*y_radius^3, x_level^3*y_radius^4, 0}, {0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^3, 0, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^4, 0, 0, 0, y_radius^3, 0, 0, x_level*y_radius^4}, {0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, y_radius^3, 0, y_radius^4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^4, 0}}\", \"H0_betti\": \"new BettiTally from {(0,{0, 0},0) => 1, (0,{1, 0},1) => 1, (0,{2, 0},2) => 1, (0,{3, 0},3) => 1, (0,{4, 0},4) => 1, (0,{5, 0},5) => 1, (0,{6, 0},6) => 1, (0,{7, 0},7) => 1, (0,{8, 0},8) => 1, (0,{9, 0},9) => 1, (0,{10, 0},10) => 1, (0,{11, 0},11) => 1, (1,{1, 4},5) => 1, (1,{2, 4},6) => 1, (1,{3, 3},6) => 1, (1,{4, 4},8) => 1, (1,{5, 3},8) => 1, (1,{6, 3},9) => 1, (1,{7, 4},11) => 1, (1,{8, 2},10) => 1, (1,{8, 3},11) => 2, (1,{9, 3},12) => 1, (1,{10, 3},13) => 1, (1,{11, 4},15) => 1, (2,{8, 4},12) => 2}\", \"H2_presentation\": \"matrix {{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}\"}, \"homogeneous_d2\": true}\nTORICGT_JSON_END\n", "module_language": "F2[x_level,y_radius]-graded chain complex", "num_C0_generators": 12, "num_C1_generators": 41, "num_C2_generators": 60, "ring": "GF(2)[x_level,y_radius]", "script": "needsPackage \"JSON\"\nR = GF(2)[x_level,y_radius, Degrees=>{{1,0},{0,1}}]\nC0 = R^{{0,0},{-1,0},{-2,0},{-3,0},{-4,0},{-5,0},{-6,0},{-7,0},{-8,0},{-9,0},{-10,0},{-11,0}}\nC1 = R^{{-1,-4},{-3,-4},{-5,-4},{-6,-4},{-7,-4},{-8,-2},{-9,-4},{-10,-4},{-2,-4},{-3,-3},{-4,-4},{-6,-3},{-7,-4},{-8,-3},{-9,-3},{-10,-4},{-5,-4},{-7,-4},{-8,-4},{-9,-4},{-10,-4},{-5,-3},{-7,-4},{-8,-4},{-9,-3},{-10,-4},{-11,-4},{-6,-4},{-8,-4},{-9,-4},{-6,-4},{-7,-4},{-8,-4},{-9,-4},{-8,-4},{-10,-4},{-8,-3},{-9,-3},{-10,-3},{-11,-4},{-10,-4}}\nC2 = R^{{-3,-4},{-6,-4},{-7,-4},{-8,-4},{-9,-4},{-10,-4},{-5,-4},{-7,-4},{-8,-4},{-9,-4},{-10,-4},{-6,-4},{-7,-4},{-8,-4},{-9,-4},{-8,-4},{-10,-4},{-8,-4},{-9,-4},{-10,-4},{-10,-4},{-7,-4},{-8,-4},{-9,-4},{-10,-4},{-7,-4},{-8,-4},{-9,-3},{-10,-4},{-6,-4},{-8,-4},{-9,-4},{-8,-4},{-10,-4},{-8,-4},{-9,-3},{-10,-4},{-10,-4},{-7,-4},{-8,-4},{-9,-4},{-8,-4},{-9,-4},{-10,-4},{-10,-4},{-7,-4},{-8,-4},{-9,-4},{-8,-4},{-9,-4},{-10,-4},{-11,-4},{-10,-4},{-8,-4},{-9,-4},{-8,-4},{-8,-4},{-9,-4},{-10,-4},{-10,-4}}\nd1 = map(C0,C1,matrix{{x_level*y_radius^4,x_level^3*y_radius^4,x_level^5*y_radius^4,x_level^6*y_radius^4,x_level^7*y_radius^4,x_level^8*y_radius^2,x_level^9*y_radius^4,x_level^10*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^2*y_radius^3,x_level^3*y_radius^4,x_level^5*y_radius^3,x_level^6*y_radius^4,x_level^7*y_radius^3,x_level^8*y_radius^3,x_level^9*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^3*y_radius^4,x_level^5*y_radius^4,x_level^6*y_radius^4,x_level^7*y_radius^4,x_level^8*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^2*y_radius^3,x_level^4*y_radius^4,x_level^5*y_radius^4,x_level^6*y_radius^3,x_level^7*y_radius^4,x_level^8*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^2*y_radius^4,x_level^4*y_radius^4,x_level^5*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level*y_radius^4,x_level^2*y_radius^4,x_level^3*y_radius^4,x_level^4*y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,y_radius^4,0_R,0_R,0_R,x_level^2*y_radius^4,x_level^4*y_radius^4,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,x_level*y_radius^3,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,y_radius^4,0_R,y_radius^3,x_level*y_radius^3,x_level^2*y_radius^3,x_level^3*y_radius^4,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^3,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,y_radius^3,0_R,0_R,x_level*y_radius^4},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,y_radius^3,0_R,y_radius^4},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius^4,0_R}})\nd2 = map(C1,C2,matrix{{x_level^2,x_level^5,x_level^6,x_level^7,x_level^8,x_level^9,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{1_R,0_R,0_R,0_R,0_R,0_R,x_level^2,x_level^4,x_level^5,x_level^6,x_level^7,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,x_level,x_level^2,x_level^3,x_level^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,x_level^2,x_level^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,x_level,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,0_R,y_radius^2,0_R,0_R,0_R,0_R,y_radius^2,0_R,y_radius^2,0_R,y_radius^2,x_level*y_radius^2,x_level^2*y_radius^2,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,1_R,0_R,x_level,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,1_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^5,x_level^6,x_level^7,x_level^8,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^4*y_radius,x_level^5*y_radius,x_level^6,x_level^7*y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^2,x_level^4,x_level^5,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,x_level^2*y_radius,x_level^4*y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,y_radius,0_R,y_radius,0_R,y_radius,x_level,x_level^2*y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,1_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,1_R,0_R,x_level*y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,1_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level^2,x_level^3,x_level^4,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,x_level,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,1_R,x_level,x_level^2,0_R,0_R,0_R,0_R,0_R,0_R,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,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,y_radius,y_radius},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,0_R,0_R,0_R,1_R}})\nC = chainComplex({d1,d2})\nH0 = HH_0 C\nH1 = HH_1 C\nH2 = HH_2 C\nRH0 = res H0\nRH1 = res H1\nRH2 = res H2\nIdC = id_C\nConeIdC = try cone IdC else null\nConeIdRH0 = try cone id_RH0 else null\nConeIdRH1 = try cone id_RH1 else null\nConeIdRH2 = try cone id_RH2 else null\nresolutionSummary = hashTable {\n \"H0_module\" => toString H0,\n \"H1_module\" => toString H1,\n \"H2_module\" => toString H2,\n \"H0_presentation\" => toString presentation H0,\n \"H1_presentation\" => toString presentation H1,\n \"H2_presentation\" => toString presentation H2,\n \"H0_betti\" => toString betti RH0,\n \"H1_betti\" => toString betti RH1,\n \"H2_betti\" => toString betti RH2,\n \"H0_resolution\" => toString RH0,\n \"H1_resolution\" => toString RH1,\n \"H2_resolution\" => toString RH2\n}\nderivedSummary = hashTable {\n \"chain_identity_map\" => toString IdC,\n \"chain_identity_mapping_cone\" => toString ConeIdC,\n \"chain_identity_mapping_cone_homology_pruned\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdC else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdC else \"\"),\n \"H2\" => toString (try prune HH_2 ConeIdC else \"\")\n },\n \"homology_resolution_identity_maps\" => hashTable {\n \"H0\" => toString (try id_RH0 else \"\"),\n \"H1\" => toString (try id_RH1 else \"\"),\n \"H2\" => toString (try id_RH2 else \"\")\n },\n \"homology_resolution_identity_cone_homology_pruned\" => hashTable {\n \"H0\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH0 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH0 else \"\")\n },\n \"H1\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH1 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH1 else \"\")\n },\n \"H2\" => hashTable {\n \"H0\" => toString (try prune HH_0 ConeIdRH2 else \"\"),\n \"H1\" => toString (try prune HH_1 ConeIdRH2 else \"\")\n }\n },\n \"Ext_modules\" => hashTable {\n \"H0_Ext0\" => toString (try Ext^0(H0,R) else \"\"),\n \"H0_Ext1\" => toString (try Ext^1(H0,R) else \"\"),\n \"H1_Ext0\" => toString (try Ext^0(H1,R) else \"\"),\n \"H1_Ext1\" => toString (try Ext^1(H1,R) else \"\"),\n \"H2_Ext0\" => toString (try Ext^0(H2,R) else \"\"),\n \"H2_Ext1\" => toString (try Ext^1(H2,R) else \"\")\n },\n \"Tor_residue_modules\" => hashTable {\n \"H0_Tor0\" => toString (try Tor_0(H0,coker vars R) else \"\"),\n \"H0_Tor1\" => toString (try Tor_1(H0,coker vars R) else \"\"),\n \"H1_Tor0\" => toString (try Tor_0(H1,coker vars R) else \"\"),\n \"H1_Tor1\" => toString (try Tor_1(H1,coker vars R) else \"\"),\n \"H2_Tor0\" => toString (try Tor_0(H2,coker vars R) else \"\"),\n \"H2_Tor1\" => toString (try Tor_1(H2,coker vars R) else \"\")\n }\n}\nout = hashTable {\n \"kind\" => \"macaulay2_bigraded_persistence_resolution\",\n \"ring\" => \"GF(2)[x_level,y_radius]\",\n \"module_language\" => \"F2[x_level,y_radius]-graded chain complex\",\n \"num_C0_generators\" => rank C0,\n \"num_C1_generators\" => rank C1,\n \"num_C2_generators\" => rank C2,\n \"homogeneous_d1\" => isHomogeneous d1,\n \"homogeneous_d2\" => isHomogeneous d2,\n \"d_squared_zero\" => d1*d2 == 0,\n \"chain_complex\" => toString C,\n \"boundary_d1\" => toString d1,\n \"boundary_d2\" => toString d2,\n \"homology_and_resolutions\" => resolutionSummary,\n \"derived_category_maps\" => derivedSummary\n}\nprint \"TORICGT_JSON_BEGIN\"\nprint toJSON out\nprint \"TORICGT_JSON_END\"\n" }, "max_radius": 30.936045960411082, "ph_retrieval_candidates": [ { "candidate_signature_norm": 452.6482560295248, "exact_internal_simplicial_map_score": 1.0, "ph_signature_cosine": 0.9285480861311269, "record_id": "fineweb_tokengt_position_bucket_emb_weight", "retrieval_score": 0.9485546220144114, "source_signature_norm": 431.2156845738476 }, { "candidate_signature_norm": 388.4135317990799, "exact_internal_simplicial_map_score": 1.0, "ph_signature_cosine": 0.9232210305369433, "record_id": "tok_emb_weight", "retrieval_score": 0.9447191419865991, "source_signature_norm": 431.2156845738476 } ], 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