{ "bigraded_chain_presentation": { "boundary_matrices": { "1": [ [ "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" ] ], "2": [ [ "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", "0_R", "0_R", "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^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_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "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", "x_level^3*y_radius", "x_level^4*y_radius", "x_level^5", "x_level^6*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", "y_radius", "0_R", "0_R", "0_R", "0_R", "y_radius", "0_R", "0_R", "0_R", "0_R", "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_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R" ], [ "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "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", "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", "0_R", "0_R", "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", "y_radius^2", "0_R", "0_R", "0_R", "0_R", "0_R", "y_radius^2", "0_R", "x_level^2", "x_level^3*y_radius", "x_level^5*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", "0_R", "0_R" ], [ "0_R", "0_R", "0_R", "0_R", "y_radius", "0_R", "0_R", "0_R", "0_R", "y_radius", "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", "x_level", "x_level^2", "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" ], [ "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", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "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", "y_radius", "0_R", "0_R", "0_R", "y_radius", "0_R", "0_R", "0_R", "0_R", "0_R", "1_R", "0_R", "0_R", "1_R", "0_R", "1_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", "0_R" ], [ "0_R", "0_R", "0_R", "0_R", "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", "1_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", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R" ], [ "0_R", "0_R", "0_R", "0_R", "0_R", "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", "y_radius", "0_R", "0_R", "y_radius", "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", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "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", "x_level", "x_level^3", "x_level^4", "x_level^5", "x_level^6", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "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", "1_R", "0_R", "0_R", "0_R", "0_R", "x_level^2", "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", "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", "1_R", "0_R", "0_R", "0_R", "1_R", "0_R", "0_R", "0_R", "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", "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", "1_R", "0_R", "0_R", "0_R", "1_R", "0_R", "0_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", "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", "y_radius^2", "0_R", "0_R", "0_R", "y_radius^2", "0_R", "y_radius^2", "0_R", "y_radius^2", "0_R", "x_level*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", "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", "1_R", "0_R", "0_R", "0_R", "1_R", "0_R", "1_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", "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", "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", "x_level^2", "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", "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", "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", "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", "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", "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", "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", "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", "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", "y_radius", "0_R", "y_radius", "0_R", "y_radius", "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", "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", "1_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", "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", "1_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", "x_level^2", "x_level^3", "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", "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", "1_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^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", "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", "y_radius", "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", "y_radius", "0_R", "0_R", "x_level*y_radius", "x_level^2*y_radius", "x_level^3*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", "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", "1_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", "1_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", "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", "1_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", "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", "1_R", "0_R", "0_R", "1_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", "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", "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", "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", "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", "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", "y_radius^2", "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", "0_R", "0_R", "0_R", "0_R", "0_R", "y_radius^2", "x_level*y_radius", "x_level^3*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", "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", "y_radius", "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", "y_radius", "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", "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", "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" ], [ "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "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", "y_radius", "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", "y_radius", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "x_level", "x_level^3*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", "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", "y_radius", "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", "y_radius", "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", "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", "1_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", "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", "y_radius", "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", "0_R", "0_R", "1_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", "0_R", "0_R", "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" ], [ "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "0_R", "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", "0_R", "0_R", "0_R", "0_R", "y_radius", "0_R", "0_R", "0_R", "y_radius", "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", "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", "1_R", "0_R", "0_R", "0_R", "0_R", "0_R", "1_R" ] ] }, "field": "GF(2)", "generators": { "0": [ { "degree": [ 0, 0 ], "diameter": 0.0, "simplex": [ 0 ] }, { "degree": [ 1, 0 ], "diameter": 0.0, "simplex": [ 1 ] }, { "degree": [ 2, 0 ], "diameter": 0.0, "simplex": [ 2 ] }, { "degree": [ 3, 0 ], "diameter": 0.0, "simplex": [ 3 ] }, { "degree": [ 4, 0 ], "diameter": 0.0, "simplex": [ 4 ] }, { "degree": [ 5, 0 ], "diameter": 0.0, "simplex": [ 5 ] }, { "degree": [ 6, 0 ], "diameter": 0.0, "simplex": [ 6 ] }, { "degree": [ 7, 0 ], "diameter": 0.0, "simplex": [ 7 ] }, { "degree": [ 8, 0 ], "diameter": 0.0, "simplex": [ 8 ] }, { "degree": [ 9, 0 ], "diameter": 0.0, "simplex": [ 9 ] }, { "degree": [ 10, 0 ], "diameter": 0.0, "simplex": [ 10 ] }, { "degree": [ 11, 0 ], "diameter": 0.0, "simplex": [ 11 ] } ], "1": [ { "degree": [ 1, 4 ], "diameter": 28.08542453614254, "simplex": [ 0, 1 ] }, { "degree": [ 2, 2 ], "diameter": 20.682708935503946, "simplex": [ 0, 2 ] }, { "degree": [ 3, 3 ], "diameter": 23.99427674762746, "simplex": [ 0, 3 ] }, { "degree": [ 4, 3 ], "diameter": 20.96747171639442, "simplex": [ 0, 4 ] }, { "degree": [ 5, 3 ], "diameter": 24.565089567020852, "simplex": [ 0, 5 ] }, { "degree": [ 6, 2 ], "diameter": 20.78994333074983, "simplex": [ 0, 6 ] }, { "degree": [ 7, 3 ], "diameter": 22.403622981304064, "simplex": [ 0, 7 ] }, { "degree": [ 8, 0 ], "diameter": 1.2893192064157897, "simplex": [ 0, 8 ] }, { "degree": [ 9, 3 ], "diameter": 22.84563937199988, "simplex": [ 0, 9 ] }, { "degree": [ 10, 3 ], "diameter": 26.036372235747926, "simplex": [ 0, 10 ] }, { "degree": [ 11, 3 ], "diameter": 22.54935007763261, "simplex": [ 0, 11 ] }, { "degree": [ 8, 4 ], "diameter": 27.90519749913889, "simplex": [ 1, 8 ] }, { "degree": [ 3, 4 ], "diameter": 32.76352931435438, "simplex": [ 2, 3 ] }, { "degree": [ 4, 4 ], "diameter": 32.30265295810302, "simplex": [ 2, 4 ] }, { "degree": [ 6, 4 ], "diameter": 33.00394400876511, "simplex": [ 2, 6 ] }, { "degree": [ 7, 4 ], "diameter": 33.32458601067043, "simplex": [ 2, 7 ] }, { "degree": [ 8, 2 ], "diameter": 20.460695672673424, "simplex": [ 2, 8 ] }, { "degree": [ 9, 4 ], "diameter": 32.93934165335602, "simplex": [ 2, 9 ] }, { "degree": [ 4, 4 ], "diameter": 34.192388450323726, "simplex": [ 3, 4 ] }, { "degree": [ 6, 4 ], "diameter": 29.30165611942438, "simplex": [ 3, 6 ] }, { "degree": [ 7, 4 ], "diameter": 29.880233341877666, "simplex": [ 3, 7 ] }, { "degree": [ 8, 3 ], "diameter": 23.92937348892006, "simplex": [ 3, 8 ] }, { "degree": [ 9, 4 ], "diameter": 34.77329431600468, "simplex": [ 3, 9 ] }, { "degree": [ 6, 4 ], "diameter": 28.494717497867757, "simplex": [ 4, 6 ] }, { "degree": [ 7, 4 ], "diameter": 29.491522163907494, "simplex": [ 4, 7 ] }, { "degree": [ 8, 3 ], "diameter": 21.207568721750444, "simplex": [ 4, 8 ] }, { "degree": [ 9, 4 ], "diameter": 33.60463166480373, "simplex": [ 4, 9 ] }, { "degree": [ 10, 4 ], "diameter": 34.41735085369404, "simplex": [ 4, 10 ] }, { "degree": [ 11, 4 ], "diameter": 33.86682311374962, "simplex": [ 4, 11 ] }, { "degree": [ 6, 4 ], "diameter": 32.19680466754507, "simplex": [ 5, 6 ] }, { "degree": [ 8, 3 ], "diameter": 25.189591172502844, "simplex": [ 5, 8 ] }, { "degree": [ 8, 2 ], "diameter": 20.567491553470262, "simplex": [ 6, 8 ] }, { "degree": [ 9, 3 ], "diameter": 22.049879527739094, "simplex": [ 6, 9 ] }, { "degree": [ 11, 4 ], "diameter": 32.151854407854664, "simplex": [ 6, 11 ] }, { "degree": [ 8, 3 ], "diameter": 22.720289586720124, "simplex": [ 7, 8 ] }, { "degree": [ 9, 3 ], "diameter": 25.320311176369078, "simplex": [ 7, 9 ] }, { "degree": [ 11, 4 ], "diameter": 33.82954954297284, "simplex": [ 7, 11 ] }, { "degree": [ 9, 3 ], "diameter": 22.503874720518628, "simplex": [ 8, 9 ] }, { "degree": [ 10, 3 ], "diameter": 25.06836074496855, "simplex": [ 8, 10 ] }, { "degree": [ 11, 3 ], "diameter": 23.03642918944148, "simplex": [ 8, 11 ] }, { "degree": [ 10, 4 ], "diameter": 34.03699800134989, "simplex": [ 9, 10 ] } ], "2": [ { "degree": [ 8, 4 ], "diameter": 28.08542453614254, "simplex": [ 0, 1, 8 ] }, { "degree": [ 3, 4 ], "diameter": 32.76352931435438, "simplex": [ 0, 2, 3 ] }, { "degree": [ 4, 4 ], "diameter": 32.30265295810302, "simplex": [ 0, 2, 4 ] }, { "degree": [ 6, 4 ], "diameter": 33.00394400876511, "simplex": [ 0, 2, 6 ] }, { "degree": [ 7, 4 ], "diameter": 33.32458601067043, "simplex": [ 0, 2, 7 ] }, { "degree": [ 8, 2 ], "diameter": 20.682708935503946, "simplex": [ 0, 2, 8 ] }, { "degree": [ 9, 4 ], "diameter": 32.93934165335602, "simplex": [ 0, 2, 9 ] }, { "degree": [ 4, 4 ], "diameter": 34.192388450323726, "simplex": [ 0, 3, 4 ] }, { "degree": [ 6, 4 ], "diameter": 29.30165611942438, "simplex": [ 0, 3, 6 ] }, { "degree": [ 7, 4 ], "diameter": 29.880233341877666, "simplex": [ 0, 3, 7 ] }, { "degree": [ 8, 3 ], "diameter": 23.99427674762746, "simplex": [ 0, 3, 8 ] }, { "degree": [ 9, 4 ], "diameter": 34.77329431600468, "simplex": [ 0, 3, 9 ] }, { "degree": [ 6, 4 ], "diameter": 28.494717497867757, "simplex": [ 0, 4, 6 ] }, { "degree": [ 7, 4 ], "diameter": 29.491522163907494, "simplex": [ 0, 4, 7 ] }, { "degree": [ 8, 3 ], "diameter": 21.207568721750444, "simplex": [ 0, 4, 8 ] }, { "degree": [ 9, 4 ], "diameter": 33.60463166480373, "simplex": [ 0, 4, 9 ] }, { "degree": [ 10, 4 ], "diameter": 34.41735085369404, "simplex": [ 0, 4, 10 ] }, { "degree": [ 11, 4 ], "diameter": 33.86682311374962, "simplex": [ 0, 4, 11 ] }, { "degree": [ 6, 4 ], "diameter": 32.19680466754507, "simplex": [ 0, 5, 6 ] }, { "degree": [ 8, 3 ], "diameter": 25.189591172502844, "simplex": [ 0, 5, 8 ] }, { "degree": [ 8, 2 ], "diameter": 20.78994333074983, "simplex": [ 0, 6, 8 ] }, { "degree": [ 9, 3 ], "diameter": 22.84563937199988, "simplex": [ 0, 6, 9 ] }, { "degree": [ 11, 4 ], "diameter": 32.151854407854664, "simplex": [ 0, 6, 11 ] }, { "degree": [ 8, 3 ], "diameter": 22.720289586720124, "simplex": [ 0, 7, 8 ] }, { "degree": [ 9, 3 ], "diameter": 25.320311176369078, "simplex": [ 0, 7, 9 ] }, { "degree": [ 11, 4 ], "diameter": 33.82954954297284, "simplex": [ 0, 7, 11 ] }, { "degree": [ 9, 3 ], "diameter": 22.84563937199988, "simplex": [ 0, 8, 9 ] }, { "degree": [ 10, 3 ], "diameter": 26.036372235747926, "simplex": [ 0, 8, 10 ] }, { "degree": [ 11, 3 ], "diameter": 23.03642918944148, "simplex": [ 0, 8, 11 ] }, { "degree": [ 10, 4 ], "diameter": 34.03699800134989, "simplex": [ 0, 9, 10 ] }, { "degree": [ 4, 4 ], "diameter": 34.192388450323726, "simplex": [ 2, 3, 4 ] }, { "degree": [ 6, 4 ], "diameter": 33.00394400876511, "simplex": [ 2, 3, 6 ] }, { "degree": [ 7, 4 ], "diameter": 33.32458601067043, "simplex": [ 2, 3, 7 ] }, { "degree": [ 8, 4 ], "diameter": 32.76352931435438, "simplex": [ 2, 3, 8 ] }, { "degree": [ 9, 4 ], "diameter": 34.77329431600468, "simplex": [ 2, 3, 9 ] }, { "degree": [ 6, 4 ], "diameter": 33.00394400876511, "simplex": [ 2, 4, 6 ] }, { "degree": [ 7, 4 ], "diameter": 33.32458601067043, "simplex": [ 2, 4, 7 ] }, { "degree": [ 8, 4 ], "diameter": 32.30265295810302, "simplex": [ 2, 4, 8 ] }, { "degree": [ 9, 4 ], "diameter": 33.60463166480373, "simplex": [ 2, 4, 9 ] }, { "degree": [ 8, 4 ], "diameter": 33.00394400876511, "simplex": [ 2, 6, 8 ] }, { "degree": [ 9, 4 ], "diameter": 33.00394400876511, "simplex": [ 2, 6, 9 ] }, { "degree": [ 8, 4 ], "diameter": 33.32458601067043, "simplex": [ 2, 7, 8 ] }, { "degree": [ 9, 4 ], "diameter": 33.32458601067043, "simplex": [ 2, 7, 9 ] }, { "degree": [ 9, 4 ], "diameter": 32.93934165335602, "simplex": [ 2, 8, 9 ] }, { "degree": [ 6, 4 ], "diameter": 34.192388450323726, "simplex": [ 3, 4, 6 ] }, { "degree": [ 7, 4 ], "diameter": 34.192388450323726, "simplex": [ 3, 4, 7 ] }, { "degree": [ 8, 4 ], "diameter": 34.192388450323726, "simplex": [ 3, 4, 8 ] }, { "degree": [ 9, 4 ], "diameter": 34.77329431600468, "simplex": [ 3, 4, 9 ] }, { "degree": [ 8, 4 ], "diameter": 29.30165611942438, "simplex": [ 3, 6, 8 ] }, { "degree": [ 9, 4 ], "diameter": 34.77329431600468, "simplex": [ 3, 6, 9 ] }, { "degree": [ 8, 4 ], "diameter": 29.880233341877666, "simplex": [ 3, 7, 8 ] }, { "degree": [ 9, 4 ], "diameter": 34.77329431600468, "simplex": [ 3, 7, 9 ] }, { "degree": [ 9, 4 ], "diameter": 34.77329431600468, "simplex": [ 3, 8, 9 ] }, { "degree": [ 8, 4 ], "diameter": 28.494717497867757, "simplex": [ 4, 6, 8 ] }, { "degree": [ 9, 4 ], "diameter": 33.60463166480373, "simplex": [ 4, 6, 9 ] }, { "degree": [ 11, 4 ], "diameter": 33.86682311374962, "simplex": [ 4, 6, 11 ] }, { "degree": [ 8, 4 ], "diameter": 29.491522163907494, "simplex": [ 4, 7, 8 ] }, { "degree": [ 9, 4 ], "diameter": 33.60463166480373, "simplex": [ 4, 7, 9 ] }, { "degree": [ 11, 4 ], "diameter": 33.86682311374962, "simplex": [ 4, 7, 11 ] }, { "degree": [ 9, 4 ], "diameter": 33.60463166480373, "simplex": [ 4, 8, 9 ] }, { "degree": [ 10, 4 ], "diameter": 34.41735085369404, "simplex": [ 4, 8, 10 ] }, { "degree": [ 11, 4 ], "diameter": 33.86682311374962, "simplex": [ 4, 8, 11 ] }, { "degree": [ 10, 4 ], "diameter": 34.41735085369404, "simplex": [ 4, 9, 10 ] }, { "degree": [ 8, 4 ], "diameter": 32.19680466754507, "simplex": [ 5, 6, 8 ] }, { "degree": [ 9, 3 ], "diameter": 22.503874720518628, "simplex": [ 6, 8, 9 ] }, { "degree": [ 11, 4 ], "diameter": 32.151854407854664, "simplex": [ 6, 8, 11 ] }, { "degree": [ 9, 3 ], "diameter": 25.320311176369078, "simplex": [ 7, 8, 9 ] }, { "degree": [ 11, 4 ], "diameter": 33.82954954297284, "simplex": [ 7, 8, 11 ] }, { "degree": [ 10, 4 ], "diameter": 34.03699800134989, "simplex": [ 8, 9, 10 ] } ] }, "max_dimension": 2, "radii": [ 6.961295519808765, 13.92259103961753, 20.883886559426294, 27.84518207923506, 34.80647759904382 ], "ring": "F2[x_level,y_radius]", "variables": [ "x_level", "y_radius" ] }, "chain_complex": { "betti": { "0": 1, "1": 0, "2": 39 }, "boundary_ranks": { "0": 0, "1": 11, "2": 30 }, "d_squared_residual": 0, "num_edges": 41, "num_simplices": 122, "num_triangles": 69, "num_vertices": 12 }, "diagrams": { "0": [ [ 0.0, 1.2893192064157897 ], [ 0.0, 20.460695672673424 ], [ 0.0, 20.567491553470266 ], [ 0.0, 20.967471716394417 ], [ 0.0, 22.049879527739098 ], [ 0.0, 22.403622981304064 ], [ 0.0, 22.54935007763261 ], [ 0.0, 23.92937348892006 ], [ 0.0, 24.565089567020856 ], [ 0.0, 25.06836074496855 ], [ 0.0, 27.905197499138893 ], [ 0.0, Infinity ] ], "1": [], "2": [] }, "dimension": 8, "finite_field_chain_audit": { "buchsbaum_eisenbud_rank_condition_c1": true, "buchsbaum_eisenbud_rank_residual_c1": 0, "chain_dimensions": { "C0": 12, "C1": 41, "C2": 69 }, "d1d2_residual": 0, "d_squared_zero": true, "exact_at_c1": true, "field": "F2", "h1_dim": 0, "image_d2_dim": 30, "kernel_d1_dim": 30, "rank_d1": 11, "rank_d2": 30 }, "macaulay2_resolution": { "boundary_d1": "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}}", "boundary_d2": "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, 0, 0, 0, 0, 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, 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, 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, 1, 0, 0, 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, 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, y_radius^2, 0, 0, 0, y_radius^2, 0, y_radius^2, 0, y_radius^2, 0, 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, 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, 1, 0, 1, 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, 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, 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, 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, 1, 0, 0, 0, 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, 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, 1, 0, 0, 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, 1, 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, y_radius, 0, y_radius, 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, 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, 1, 0, 1, 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, 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, x_level^2, x_level^3, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 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, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, y_radius, 0, 0, x_level*y_radius, x_level^2*y_radius, 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, 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, 1, 0, 0, 0, 0, 0, 0, 1, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, x_level*y_radius, x_level^3*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, 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, 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, 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, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 1, 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, 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, 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, y_radius, 0, 0, 0, y_radius, 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, 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, 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 {{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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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}}", "H1_Tor1": "subquotient(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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 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}},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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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, 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, 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, 1, 0, 0, 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, 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, y_radius^2, 0, 0, 0, y_radius^2, 0, y_radius^2, 0, y_radius^2, 0, 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, 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, 1, 0, 1, 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, 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, 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, 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, 1, 0, 0, 0, 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, 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, 1, 0, 0, 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, 1, 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, y_radius, 0, y_radius, 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, 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, 1, 0, 1, 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, 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, x_level^2, x_level^3, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 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, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, y_radius, 0, 0, x_level*y_radius, x_level^2*y_radius, 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, 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, 1, 0, 0, 0, 0, 0, 0, 1, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, y_radius^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, y_radius^2, x_level*y_radius, x_level^3*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, 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, 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, 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, y_radius, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 0, 0, y_radius, 0, 0, 0, 0, 1, 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, 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, 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, y_radius, 0, 0, 0, y_radius, 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, 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, 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, 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, 0, 0, 0, 0}, {0, 0, 0, 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,{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, 0, 0, 0, 0, 0, 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, 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, x_level, 0, 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, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius, 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, 1, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, y_radius, y_radius, 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, 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, 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, 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, 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, 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, y_radius^2, y_radius^2, 0, 0, y_radius^2, 0, 0, 0, y_radius^2, 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, 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, y_radius, y_radius, 0, y_radius, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, y_radius, 0, 0, 0, 0, 0, 0, 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, 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, 0, y_radius, 0, y_radius, 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, 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, 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, 1, 1, 0, 0, x_level, x_level, 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, 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, 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, 0, 0, 0, 0, 0, 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, 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, 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, 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, 1, 1, 0, 0, 1, 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, 1, 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, 1, 0, 1, 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, 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 = map(C1,C2,matrix{{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,0_R,0_R,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^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_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,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,x_level^3*y_radius,x_level^4*y_radius,x_level^5,x_level^6*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,y_radius,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,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_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,0_R,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,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,0_R,0_R,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,y_radius^2,0_R,0_R,0_R,0_R,0_R,y_radius^2,0_R,x_level^2,x_level^3*y_radius,x_level^5*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,0_R,0_R},{0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,y_radius,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,x_level,x_level^2,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},{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,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,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,y_radius,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,0_R,0_R,1_R,0_R,0_R,1_R,0_R,1_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,0_R},{0_R,0_R,0_R,0_R,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,1_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,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R},{0_R,0_R,0_R,0_R,0_R,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,y_radius,0_R,0_R,y_radius,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,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,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,x_level,x_level^3,x_level^4,x_level^5,x_level^6,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,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,1_R,0_R,0_R,0_R,0_R,x_level^2,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,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,1_R,0_R,0_R,0_R,1_R,0_R,0_R,0_R,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,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,1_R,0_R,0_R,0_R,1_R,0_R,0_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,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,y_radius^2,0_R,0_R,0_R,y_radius^2,0_R,y_radius^2,0_R,y_radius^2,0_R,x_level*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,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,1_R,0_R,0_R,0_R,1_R,0_R,1_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,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,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,x_level^2,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,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,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,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,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,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,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,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,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,y_radius,0_R,y_radius,0_R,y_radius,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,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,1_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,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,1_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,x_level^2,x_level^3,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,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,1_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^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,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,y_radius,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,y_radius,0_R,0_R,x_level*y_radius,x_level^2*y_radius,x_level^3*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,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,1_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,1_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,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,1_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,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,1_R,0_R,0_R,1_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,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,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,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,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,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,y_radius^2,0_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,0_R,0_R,0_R,0_R,0_R,y_radius^2,x_level*y_radius,x_level^3*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,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,y_radius,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,y_radius,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,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,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},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,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,y_radius,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,y_radius,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,x_level,x_level^3*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,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,y_radius,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,y_radius,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,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,1_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,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,y_radius,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,0_R,0_R,1_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,0_R,0_R,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},{0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,0_R,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,0_R,0_R,0_R,0_R,y_radius,0_R,0_R,0_R,y_radius,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,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,1_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": 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 ] }, { "from": [ 1, 1 ], "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, 1 ] }, { "from": [ 1, 1 ], "h0_rank": 3, "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, 2 ] }, { "from": [ 1, 2 ], "h0_rank": 3, "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": [ 2, 2 ] }, { "from": [ 1, 2 ], "h0_rank": 2, "h1_rank": 0, "operator": "y_radius", "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, 3 ] }, { "from": [ 1, 3 ], "h0_rank": 2, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 2.0, "dim1_valid": 2.0, "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, 3 ] }, { "from": [ 1, 3 ], "h0_rank": 1, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 2.0, "dim1_valid": 2.0, "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, 4 ], "h0_rank": 1, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 4.0, "dim1_valid": 4.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 1.0, "dim2_valid": 1.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 2, 4 ] }, { "from": [ 2, 0 ], "h0_rank": 7, "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": [ 3, 0 ] }, { "from": [ 2, 0 ], "h0_rank": 7, "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": [ 2, 1 ] }, { "from": [ 2, 1 ], "h0_rank": 7, "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": [ 3, 1 ] }, { "from": [ 2, 1 ], "h0_rank": 5, "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": [ 2, 2 ] }, { "from": [ 2, 2 ], "h0_rank": 5, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 2.0, "dim1_valid": 2.0, "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": [ 3, 2 ] }, { "from": [ 2, 2 ], "h0_rank": 2, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 2.0, "dim1_valid": 2.0, "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, 3 ] }, { "from": [ 2, 3 ], "h0_rank": 2, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 5.0, "dim1_valid": 5.0, "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": [ 3, 3 ] }, { "from": [ 2, 3 ], "h0_rank": 1, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 5.0, "dim1_valid": 5.0, "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, 4 ] }, { "from": [ 2, 4 ], "h0_rank": 1, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 13.0, "dim1_valid": 13.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 11.0, "dim2_valid": 11.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 3, 4 ] }, { "from": [ 3, 0 ], "h0_rank": 9, "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": [ 4, 0 ] }, { "from": [ 3, 0 ], "h0_rank": 9, "h1_rank": 0, "operator": "y_radius", "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": [ 3, 1 ] }, { "from": [ 3, 1 ], "h0_rank": 9, "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": [ 4, 1 ] }, { "from": [ 3, 1 ], "h0_rank": 7, "h1_rank": 0, "operator": "y_radius", "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": [ 3, 2 ] }, { "from": [ 3, 2 ], "h0_rank": 7, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 5.0, "dim1_valid": 5.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 2.0, "dim2_valid": 2.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 4, 2 ] }, { "from": [ 3, 2 ], "h0_rank": 2, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 5.0, "dim1_valid": 5.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 2.0, "dim2_valid": 2.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 3, 3 ] }, { "from": [ 3, 3 ], "h0_rank": 2, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 17.0, "dim1_valid": 17.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 11.0, "dim2_valid": 11.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 4, 3 ] }, { "from": [ 3, 3 ], "h0_rank": 1, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 17.0, "dim1_valid": 17.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 11.0, "dim2_valid": 11.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 3, 4 ] }, { "from": [ 3, 4 ], "h0_rank": 1, "h1_rank": 0, "operator": "x_level", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 32.0, "dim1_valid": 32.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 54.0, "dim2_valid": 54.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 4, 4 ] }, { "from": [ 4, 0 ], "h0_rank": 11, "h1_rank": 0, "operator": "y_radius", "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": [ 4, 1 ] }, { "from": [ 4, 1 ], "h0_rank": 9, "h1_rank": 0, "operator": "y_radius", "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": [ 4, 2 ] }, { "from": [ 4, 2 ], "h0_rank": 2, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 5.0, "dim1_valid": 5.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 2.0, "dim2_valid": 2.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 4, 3 ] }, { "from": [ 4, 3 ], "h0_rank": 1, "h1_rank": 0, "operator": "y_radius", "simplicial": { "dim1_collapsed": 0.0, "dim1_simplices": 21.0, "dim1_valid": 21.0, "dim1_valid_fraction": 1.0, "dim2_collapsed": 0.0, "dim2_simplices": 13.0, "dim2_valid": 13.0, "dim2_valid_fraction": 1.0, "simplicial_map_valid": true, "simplicial_map_valid_fraction": 1.0 }, "to": [ 4, 4 ] } ] }, "vectorizations": { "0": { "count": 11, "entropy_vector": [ 0.01864269525120933, 0.01864269525120933, 0.01864269525120933, 0.01864269525120933, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.0184105749696445, 0.01496095879697435, 0.013213923302371262, 0.013213923302371262, 0.013213923302371262, 0.011415188589011744, 0.007777997950650838, 0.007777997950650838, 0.007777997950650838, 0.005893821310620672, 0.005893821310620672, 0.003981924605719423, 0.002048488391758311, 0.002048488391758311, 0.002048488391758311, 0.002048488391758311, 0.002048488391758311 ], "entropy_vector_norm": 0.13217311241217447, "landscape": [ 0.6071370579074153, 1.2142741158148307, 1.8214111737222458, 2.4285482316296614, 3.0356852895370765, 3.6428223474444916, 4.249959405351907, 4.857096463259323, 5.464233521166737, 6.071370579074154, 6.6785076369815695, 7.285644694888985, 7.892781752796401, 8.499918810703816, 9.10705586861123, 9.714192926518646, 10.321329984426061, 10.928467042333477, 11.535604100240894, 12.142741158148308, 12.749878216055723, 13.357015273963139, 13.964152331870554, 14.57128938977797, 15.178426447685386, 15.785563505592801, 16.392700563500217, 16.999837621407632, 17.606974679315048, 18.21411173722246, 18.821248795129875, 19.42838585303729, 19.42838585303729, 18.821248795129875, 18.21411173722246, 17.606974679315048, 16.999837621407632, 16.392700563500213, 15.785563505592798, 15.178426447685382, 14.571289389777967, 13.964152331870553, 13.357015273963137, 12.749878216055722, 12.142741158148306, 11.53560410024089, 10.928467042333475, 10.32132998442606, 9.714192926518646, 9.10705586861123, 8.499918810703814, 7.892781752796399, 7.285644694888983, 6.678507636981569, 6.071370579074153, 5.464233521166737, 4.857096463259323, 4.249959405351907, 3.6428223474444916, 3.0356852895370765, 2.4285482316296614, 1.8214111737222458, 1.2142741158148307, 0.6071370579074153, 0.6071370579074153, 1.2142741158148307, 1.8214111737222458, 2.4285482316296614, 3.0356852895370765, 3.6428223474444916, 4.249959405351907, 4.857096463259323, 5.464233521166737, 6.071370579074154, 6.6785076369815695, 7.285644694888985, 7.892781752796401, 8.499918810703816, 9.10705586861123, 9.714192926518646, 10.321329984426061, 10.928467042333477, 11.535604100240894, 12.142741158148308, 12.749878216055723, 13.357015273963139, 13.964152331870554, 14.57128938977797, 15.178426447685386, 15.785563505592801, 16.392700563500217, 16.999837621407632, 17.606974679315048, 17.23790401477337, 16.630766956865955, 16.02362989895854, 15.416492841051124, 14.809355783143708, 14.202218725236294, 13.595081667328879, 12.987944609421463, 12.380807551514046, 11.77367049360663, 11.166533435699215, 10.5593963777918, 9.952259319884384, 9.345122261976968, 8.737985204069554, 8.130848146162139, 7.523711088254723, 6.9165740303473076, 6.309436972439892, 5.702299914532477, 5.095162856625062, 4.488025798717646, 3.880888740810231, 3.273751682902816, 2.6666146249954004, 2.0594775670879852, 1.45234050918057, 0.8452034512731545, 0.23806639336573926, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.6071370579074153, 1.2142741158148307, 1.8214111737222458, 2.4285482316296614, 3.0356852895370765, 3.6428223474444916, 4.249959405351907, 4.857096463259323, 5.464233521166737, 6.071370579074154, 6.6785076369815695, 7.285644694888985, 7.892781752796401, 8.499918810703816, 9.10705586861123, 9.714192926518646, 10.321329984426061, 10.928467042333477, 11.535604100240894, 12.142741158148308, 12.749878216055723, 13.357015273963139, 13.964152331870554, 14.57128938977797, 15.178426447685386, 15.785563505592801, 16.392700563500217, 16.999837621407632, 17.13330814727567, 16.526171089368255, 15.919034031460841, 15.311896973553425, 14.70475991564601, 14.097622857738594, 13.490485799831179, 12.883348741923765, 12.27621168401635, 11.66907462610893, 11.061937568201516, 10.4548005102941, 9.847663452386685, 9.24052639447927, 8.633389336571854, 8.026252278664439, 7.419115220757024, 6.811978162849608, 6.204841104942194, 5.597704047034778, 4.9905669891273625, 4.383429931219947, 3.7762928733125323, 3.1691558154051167, 2.5620187574977016, 1.9548816995902862, 1.347744641682871, 0.7406075837754555, 0.13347052586804023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.6071370579074153, 1.2142741158148307, 1.8214111737222458, 2.4285482316296614, 3.0356852895370765, 3.6428223474444916, 4.249959405351907, 4.857096463259323, 5.464233521166737, 6.071370579074154, 6.6785076369815695, 7.285644694888985, 7.892781752796401, 8.499918810703816, 9.10705586861123, 9.714192926518646, 10.321329984426061, 10.928467042333477, 11.535604100240894, 12.142741158148308, 12.749878216055723, 13.357015273963139, 13.964152331870554, 14.57128938977797, 15.178426447685386, 15.785563505592801, 16.392700563500217, 16.841406905714308, 16.234269847806893, 15.627132789899477, 15.019995731992061, 14.412858674084646, 13.805721616177232, 13.198584558269816, 12.591447500362401, 11.984310442454985, 11.37717338454757, 10.770036326640152, 10.162899268732737, 9.555762210825321, 8.948625152917906, 8.34148809501049, 7.7343510371030755, 7.12721397919566, 6.520076921288245, 5.91293986338083, 5.305802805473414, 4.698665747565999, 4.091528689658584, 3.4843916317511683, 2.877254573843753, 2.270117515936338, 1.6629804580289227, 1.0558434001215073, 0.448706342214092, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.6071370579074153, 1.2142741158148307, 1.8214111737222458, 2.4285482316296614, 3.0356852895370765, 3.6428223474444916, 4.249959405351907, 4.857096463259323, 5.464233521166737, 6.071370579074154, 6.6785076369815695, 7.285644694888985, 7.892781752796401, 8.499918810703816, 9.10705586861123, 9.714192926518646, 10.321329984426061, 10.928467042333477, 11.535604100240894, 12.142741158148308, 12.749878216055723, 13.357015273963139, 13.964152331870554, 14.57128938977797, 15.178426447685386, 15.785563505592801, 15.496896138986628, 14.889759081079212, 14.282622023171797, 13.675484965264381, 13.068347907356966, 12.46121084944955, 11.854073791542136, 11.24693673363472, 10.639799675727305, 10.03266261781989, 9.425525559912474, 8.818388502005057, 8.211251444097641, 7.604114386190226, 6.996977328282811, 6.389840270375395, 5.78270321246798, 5.175566154560565, 4.56842909665315, 3.961292038745734, 3.354154980838319, 2.7470179229309037, 2.139880865023488, 1.532743807116073, 0.9256067492086577, 0.31846969130124236, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "landscape_norm": 173.42016121233587, "max_persistence": 27.905197499138893, "mean_persistence": 21.068713821425277, "persistence_entropy": 0.967372789987364, "persistence_image": [ 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 6.819261324710765e-68, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 5.36400210353007e-273, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 3.854247295525001e-222, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 9.018488272396512e-44, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 5.365502441162453, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 18.329666602070382, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 1.8057567340315257, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 4.9031628459433885e-24, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533, 15.915494309189533 ], "persistence_image_norm": 118.29670966064026, "silhouette": [ 0.6071370579074153, 1.159258159115891, 1.6560066610401398, 2.2077711196633283, 2.759713899579161, 3.311656679494992, 3.8635994594108256, 4.415542239326657, 4.967485019242488, 5.519427799158323, 6.071370579074154, 6.623313358989987, 7.175256138905818, 7.727198918821651, 8.279141698737483, 8.831084478653315, 9.383027258569147, 9.934970038484979, 10.486912818400814, 11.038855598316646, 11.590798378232476, 12.142741158148308, 12.694683938064138, 13.22275955940571, 13.489891588685072, 13.67540612480012, 13.604185763959627, 13.479394415640707, 13.215556709852612, 12.79564488531683, 12.354090661384165, 11.912536437451502, 11.415787935527252, 10.863845155611418, 10.311902375695587, 9.759959595779755, 9.208016815863921, 8.656074035948087, 8.104131256032257, 7.552188476116425, 7.000245696200592, 6.44830291628476, 5.896360136368927, 5.3444173564530955, 4.792474576537263, 4.240531796621431, 3.6885890167055995, 3.1605133953640303, 2.7277985321099183, 2.341438586168836, 1.9550786402277531, 1.6039812701379534, 1.3440359630289476, 1.123258851062615, 0.9024817390962819, 0.6961074194657058, 0.5305245854909562, 0.40800234533796786, 0.33116566794949925, 0.27597138995791604, 0.22077711196633282, 0.16558283397474963, 0.11038855598316641, 0.055194277991583204 ], "silhouette_norm": 61.93709538647199, "total_persistence": 231.75585203567803 }, "1": { "count": 0, "entropy_vector": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "entropy_vector_norm": 0.0, "landscape": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "landscape_norm": 0.0, "max_persistence": 0.0, "mean_persistence": 0.0, "persistence_entropy": 0.0, "persistence_image": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "persistence_image_norm": 0.0, "silhouette": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "silhouette_norm": 0.0, "total_persistence": 0.0 }, "2": { "count": 0, "entropy_vector": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "entropy_vector_norm": 0.0, "landscape": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "landscape_norm": 0.0, "max_persistence": 0.0, "mean_persistence": 0.0, "persistence_entropy": 0.0, "persistence_image": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "persistence_image_norm": 0.0, "silhouette": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "silhouette_norm": 0.0, "total_persistence": 0.0 } }, "xy_grid_module": { "bounded_window": { "x_level_max": 11, "y_radius_max": 4 }, "chain_degrees": { "0": { "adjacent_lcm_outer_corners": [], "adjacent_lcm_syzygies": [], "degree_counts": [ { "count": 1, "degree": [ 0, 0 ] }, { "count": 1, "degree": [ 1, 0 ] }, { "count": 1, "degree": [ 2, 0 ] }, { "count": 1, "degree": [ 3, 0 ] }, { "count": 1, "degree": [ 4, 0 ] }, { "count": 1, "degree": [ 5, 0 ] }, { "count": 1, "degree": [ 6, 0 ] }, { "count": 1, "degree": [ 7, 0 ] }, { "count": 1, "degree": [ 8, 0 ] }, { "count": 1, "degree": [ 9, 0 ] }, { "count": 1, "degree": [ 10, 0 ] }, { "count": 1, "degree": [ 11, 0 ] } ], "generator_count": 12, "minimal_inner_corners": [ [ 0, 0 ] ] }, "1": { "adjacent_lcm_outer_corners": [ [ 2, 4 ], [ 8, 2 ] ], "adjacent_lcm_syzygies": [ { "left_generator_degree": [ 1, 4 ], "left_multiplier": [ 1, 0 ], "outer_lcm_corner": [ 2, 4 ], "right_generator_degree": [ 2, 2 ], "right_multiplier": [ 0, 2 ] }, { "left_generator_degree": [ 2, 2 ], "left_multiplier": [ 6, 0 ], "outer_lcm_corner": [ 8, 2 ], "right_generator_degree": [ 8, 0 ], "right_multiplier": [ 0, 2 ] } ], "degree_counts": [ { "count": 1, "degree": [ 1, 4 ] }, { "count": 1, "degree": [ 2, 2 ] }, { "count": 1, "degree": [ 3, 3 ] }, { "count": 1, "degree": [ 3, 4 ] }, { "count": 1, "degree": [ 4, 3 ] }, { "count": 2, "degree": [ 4, 4 ] }, { "count": 1, "degree": [ 5, 3 ] }, { "count": 1, "degree": [ 6, 2 ] }, { "count": 4, "degree": [ 6, 4 ] }, { "count": 1, "degree": [ 7, 3 ] }, { "count": 3, "degree": [ 7, 4 ] }, { "count": 1, "degree": [ 8, 0 ] }, { "count": 2, "degree": [ 8, 2 ] }, { "count": 4, "degree": [ 8, 3 ] }, { "count": 1, "degree": [ 8, 4 ] }, { "count": 4, "degree": [ 9, 3 ] }, { "count": 3, "degree": [ 9, 4 ] }, { "count": 2, "degree": [ 10, 3 ] }, { "count": 2, "degree": [ 10, 4 ] }, { "count": 2, "degree": [ 11, 3 ] }, { "count": 3, "degree": [ 11, 4 ] } ], "generator_count": 41, "minimal_inner_corners": [ [ 1, 4 ], [ 2, 2 ], [ 8, 0 ] ] }, "2": { "adjacent_lcm_outer_corners": [ [ 8, 4 ] ], "adjacent_lcm_syzygies": [ { "left_generator_degree": [ 3, 4 ], "left_multiplier": [ 5, 0 ], "outer_lcm_corner": [ 8, 4 ], "right_generator_degree": [ 8, 2 ], "right_multiplier": [ 0, 2 ] } ], "degree_counts": [ { "count": 1, "degree": [ 3, 4 ] }, { "count": 3, "degree": [ 4, 4 ] }, { "count": 7, "degree": [ 6, 4 ] }, { "count": 6, "degree": [ 7, 4 ] }, { "count": 2, "degree": [ 8, 2 ] }, { "count": 4, "degree": [ 8, 3 ] }, { "count": 11, "degree": [ 8, 4 ] }, { "count": 5, "degree": [ 9, 3 ] }, { "count": 15, "degree": [ 9, 4 ] }, { "count": 1, "degree": [ 10, 3 ] }, { "count": 5, "degree": [ 10, 4 ] }, { "count": 1, "degree": [ 11, 3 ] }, { "count": 8, "degree": [ 11, 4 ] } ], "generator_count": 69, "minimal_inner_corners": [ [ 3, 4 ], [ 8, 2 ] ] } }, "kind": "miller_sturmfels_bivariate_grid_summary", "ring": "F2[x_level,y_radius]", "variables": [ "x_level", "y_radius" ] } }