tok_emb_weight

Exact GUDHI simplex-tree persistence, vectorized PH, F2[x_level,y_radius] module maps, and Macaulay2 free-resolution output for a reasoning/radius trajectory filtration.

index record JSON Macaulay2 script PH feature JSON PH feature NPZ

Core Metrics

points12

ambient dimension8

max radius34.8065

GUDHI simplices122

Betti{'0': 1, '1': 0, '2': 39}

GF(2) d^2=0True

GF(2) exact at C1True

BE rank residual C10

simplicial maps valid fraction1

M2 homogeneous d1True

M2 homogeneous d2True

M2 d^2=0True

F2[x,y] C0/C1/C2(12, 41, 69)

Module

GF(2) d^2=0: PASSGF(2) exact at C1: PASSM2 homogeneous d1: PASSM2 homogeneous d2: PASSM2 d1*d2=0: PASS2-param square residual: PASSchain square residuals: PASS

Ring: F2[x_level,y_radius]

Commutative squares checked: 16

Square residual: 0.0

The xy-grid below follows the bivariate monomial-ideal convention: x is reasoning level, y is radius degree, shaded regions are shifted positive orthants from C1 monomial generators, white dots are quotient lattice points, and the orange line is the Miller-Sturmfels staircase boundary. Green corners are adjacent lcm corners computed from the emitted bidegrees.

F2[x_level,y_radius] Miller-Sturmfels Staircase Module View

chain	generators	minimal inner corners	outer lcm corners	adjacent syzygies
C0	12	((0, 0))	()	0
C1	41	((1, 4), (2, 2), (8, 0))	((2, 4), (8, 2))	2
C2	69	((3, 4), (8, 2))	((8, 4))	1

Hilbert H0 grid

x_level	y=0	y=1	y=2	y=3	y=4
x=0	2	2	2	2	1
x=1	4	4	3	2	1
x=2	7	7	5	2	1
x=3	9	9	7	2	1
x=4	11	11	9	2	1

Hilbert H1 grid

x_level	y=0	y=1	y=2	y=3	y=4
x=0	0	0	0	0	0
x=1	0	0	0	0	0
x=2	0	0	0	0	0
x=3	0	0	0	0	0
x=4	0	0	0	0	0

Chain generators C0

x_level	y=0	y=1	y=2	y=3	y=4
x=0	2	2	2	2	2
x=1	4	4	4	4	4
x=2	7	7	7	7	7
x=3	10	10	10	10	10
x=4	12	12	12	12	12

Chain generators C1

x_level	y=0	y=1	y=2	y=3	y=4
x=0	0	0	0	0	1
x=1	0	0	1	2	4
x=2	0	0	2	5	13
x=3	1	1	5	17	32
x=4	1	1	5	21	41

Chain generators C2

x_level	y=2	y=3	y=4
x=0	0	0	0
x=1	0	0	1
x=2	0	0	11
x=3	2	11	54
x=4	2	13	69

Readable Resolution And Differential Summary

Exact Module Maps And Derived Identity-Cones

The arrows below are the actual two-parameter inclusion maps. Macaulay2 then checks the bigraded differential and the identity mapping cone in the derived category. Acyclic identity cones are the expected sanity check for the emitted complex and its homology resolutions.

Identity Cone Acyclicity

chain identity cone H0R^0

chain identity cone H1R^0

chain identity cone H2R^0

Resolution-Level Identity Cones

resolution identity cone H0{'H0': 'R^0', 'H1': 'R^0'}

resolution identity cone H1{'H0': 'R^0', 'H1': 'R^0'}

resolution identity cone H2{'H0': 'R^0', 'H1': 'R^0'}

Vectorized Persistent-Homology Feature Dashboard

Exact GUDHI vectorizers for persistence landscapes, persistence images, silhouettes, entropy vectors, Betti curves, interval lifetimes, and feature norms. These are persisted for training and analogical-memory retrieval; they are not torch topology fallbacks.

homology	intervals	total persistence	landscape norm	image norm	silhouette norm	entropy-vector norm
H0	11	231.756	173.42	118.297	61.9371	0.132173
H1	0	0	0	0	0	0
H2	0	0	0	0	0	0

Analogical Memory PH Retrieval Panel

Candidate scores use persisted GUDHI vectorized PH features and exact internal simplicial-map validity from the reasoning/radius simplex-tree filtration. No torch-only topology proxy is used in this panel.

PH Retrieval Signature

provenanceexact_gudhi_vectorizers_and_exact_simplicial_map_audits

signature length2139

signature norm388.414

exact simplicial-map validity1

Top Candidates

rank	candidate	retrieval score	PH cosine	exact simplicial-map score
1	fineweb_tokengt_position_bucket_emb_weight	0.955769	0.938568	1
2	fineweb_tokengt_edge_source_class_emb_weight	0.944719	0.923221	1

Exact Chain And Simplicial-Map Audit

GF(2) chain exactness and Buchsbaum-Eisenbud-style rank check

{
  "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
}

Reasoning/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
}

Macaulay2 Homology Modules And Free Resolutions

Homology modules and free 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, 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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, 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  "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, 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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...}"
}

Derived maps, identity mapping cones, Ext, and Tor modules

{
  "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, 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    "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, 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    "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, 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    "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...}"
  }
}

Full Macaulay2 resolution payload

{
  "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, 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      "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, 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0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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    "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, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 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 = 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= chainComplex({d1,d2})\nH0 = HH_0 C\nH1 = HH_1 C\nH2 = HH_2 C\nRH0 = res H0\nRH1 = res H1\nRH2 = res H2\nIdC = id_C\nConeIdC = try cone IdC else null\nConeIdRH0 = try cone id_RH0 else null\nConeIdRH1 = try cone id_RH1 else null\nConeIdRH2 = try cone id_RH2 else null\nresolutionSummary = hashTable {\n  \"H0_module\" => toString H0,\n  \"H1_module\" => toString H1,\n  \"H2_module\" => toString H2,\n  \"H0_presentation\" => toString presentation H0,\n  \"H1_presentation\" => toString presentation H1,\n  \"H2_presentation\" => toString presentation H2,\n  \"H0_betti\" => toString betti RH0,\n  \"H1_betti\" => toString betti RH1,\n  \"H2_betti\" => toString betti RH2,\n  \"H0_resolution\" => toString RH0,\n  \"H1_resolution\" => toString RH1,\n  \"H2_resolution\" => toString RH2\n}\nderivedSummary = hashTable {\n  \"chain_identity_map\" => toString IdC,\n  \"chain_identity_mapping_cone\" => toString ConeIdC,\n  \"chain_identity_mapping_cone_homology_pruned\" => hashTable {\n    \"H0\" => toString (try prune HH_0 ConeIdC else \"\"),\n    \"H1\" => toString (try prune HH_1 ConeIdC else \"\"),\n    \"H2\" => toString (try prune HH_2 ConeIdC else \"\")\n  },\n  \"homology_resolution_identity_maps\" => hashTable {\n    \"H0\" => toString (try id_RH0 else \"\"),\n    \"H1\" => toString (try id_RH1 else \"\"),\n    \"H2\" => toString (try id_RH2 else \"\")\n  },\n  \"homology_resolution_identity_cone_homology_pruned\" => hashTable {\n    \"H0\" => hashTable {\n      \"H0\" => toString (try prune HH_0 ConeIdRH0 else \"\"),\n      \"H1\" => toString (try prune HH_1 ConeIdRH0 else \"\")\n    },\n    \"H1\" => hashTable {\n      \"H0\" => toString (try prune HH_0 ConeIdRH1 else \"\"),\n      \"H1\" => toString (try prune HH_1 ConeIdRH1 else \"\")\n    },\n    \"H2\" => hashTable {\n      \"H0\" => toString (try prune HH_0 ConeIdRH2 else \"\"),\n      \"H1\" => toString (try prune HH_1 ConeIdRH2 else \"\")\n    }\n  },\n  \"Ext_modules\" => hashTable {\n    \"H0_Ext0\" => toString (try Ext^0(H0,R) else \"\"),\n    \"H0_Ext1\" => toString (try Ext^1(H0,R) else \"\"),\n    \"H1_Ext0\" => toString (try Ext^0(H1,R) else \"\"),\n    \"H1_Ext1\" => toString (try Ext^1(H1,R) else \"\"),\n    \"H2_Ext0\" => toString (try Ext^0(H2,R) else \"\"),\n    \"H2_Ext1\" => toString (try Ext^1(H2,R) else \"\")\n  },\n  \"Tor_residue_modules\" => hashTable {\n    \"H0_Tor0\" => toString (try Tor_0(H0,coker vars R) else \"\"),\n    \"H0_Tor1\" => toString (try Tor_1(H0,coker vars R) else \"\"),\n    \"H1_Tor0\" => toString (try Tor_0(H1,coker vars R) else \"\"),\n    \"H1_Tor1\" => toString (try Tor_1(H1,coker vars R) else \"\"),\n    \"H2_Tor0\" => toString (try Tor_0(H2,coker vars R) else \"\"),\n    \"H2_Tor1\" => toString (try Tor_1(H2,coker vars R) else \"\")\n  }\n}\nout = hashTable {\n  \"kind\" => \"macaulay2_bigraded_persistence_resolution\",\n  \"ring\" => \"GF(2)[x_level,y_radius]\",\n  \"module_language\" => \"F2[x_level,y_radius]-graded chain complex\",\n  \"num_C0_generators\" => rank C0,\n  \"num_C1_generators\" => rank C1,\n  \"num_C2_generators\" => rank C2,\n  \"homogeneous_d1\" => isHomogeneous d1,\n  \"homogeneous_d2\" => isHomogeneous d2,\n  \"d_squared_zero\" => d1*d2 == 0,\n  \"chain_complex\" => toString C,\n  \"boundary_d1\" => toString d1,\n  \"boundary_d2\" => toString d2,\n  \"homology_and_resolutions\" => resolutionSummary,\n  \"derived_category_maps\" => derivedSummary\n}\nprint \"TORICGT_JSON_BEGIN\"\nprint toJSON out\nprint \"TORICGT_JSON_END\"\n"
}