$ ./flagmatic --n 6 --r 3 --induced-density 5.7  --dir output/max57
flagmatic version 1.5
============================================================================
Optimizing for density of 5.7.
Using admissible graphs of order 6.
Generated 1 type of order 0, with 2 flags of order 3.
Generated 1 type of order 2, with 12 flags of order 4.
Generated 5 types of order 4, with [64, 64, 64, 64, 64] flags of order 5.
Generated 2136 admissible graphs.
Approximate floating-point bound is 0.74074074

$ sage -python scripts/find_sharp_graphs.py --dir output/max57
Floating point bound is 0.740740740756017813.
9 members of H are sharp.
0.740740740746019033 : graph 392 (6:123124125126345346356456)
0.740740740726846592 : graph 1085 (6:123124125134135145234235245345)
0.740740740749246118 : graph 1294 (6:123124125126134135136234235236456)
0.740740740756017813 : graph 1821 (6:123124125126134135136145146234256356456)
0.740740740752403148 : graph 1969 (6:123124125126134135136145146156234235245345)
0.740740740755759242 : graph 2044 (6:123124125126134135136245246256345346356456)
0.740740740752734772 : graph 2060 (6:123124125134135146156236245246256345346356)
0.740740740746152926 : graph 2110 (6:123124125126134135136145146234235236245246345346)
0.740740740731381964 : graph 2136 (6:123124125126134135136145146156234235236245246256345346356456)
Written sharp graphs to flags.py

$ sage -python scripts/check_construction.py --n 6 --r 3 --induced-density 5.7 --vertex-transitive 3:123111222333112223331
Density of 5.7 is 20/27.
9 graphs of order 6 occur as induced subgraphs of the blow-up:
6:123124125126345346356456 has density 5/81 (0.061728)
6:123124125134135145234235245345 has density 2/81 (0.024691)
6:123124125126134135136234235236456 has density 20/243 (0.082305)
6:123124125126134135136145146234256356456 has density 20/81 (0.246914)
6:123124125126134135136145146156234235245345 has density 10/81 (0.123457)
6:123124125126134135136245246256345346356456 has density 20/81 (0.246914)
6:123124125134135146156236245246256345346356 has density 10/81 (0.123457)
6:123124125126134135136145146234235236245246345346 has density 5/81 (0.061728)
6:123124125126134135136145146156234235236245246256345346356456 has density 7/243 (0.028807)

$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 3:123111222333112223331 --dir output/max57
Constructed 1 out of 1 zero eigenvectors for type 1.
Constructed 3 out of 3 zero eigenvectors for type 2.
Constructed 0 out of 0 zero eigenvectors for type 3.
Constructed 1 out of 1 zero eigenvectors for type 4.
Constructed 1 out of 1 zero eigenvectors for type 5.
Constructed 3 out of 3 zero eigenvectors for type 6.
Constructed 5 out of 5 zero eigenvectors for type 7.
Written zev.py
Written field to flags.py

$ sage -python scripts/factor_approximate_q.py --dir output/max57
Floating point bound is 0.740740740756017590.
Type 1: smallest eigenvalue is 0.061074480552149077
Type 2: smallest eigenvalue is 0.040485725517051326
Type 3: smallest eigenvalue is 0.089521848808056151
Type 4: smallest eigenvalue is 0.150790757504811079
Type 5: smallest eigenvalue is 0.110239088323947645
Type 6: smallest eigenvalue is 0.116850811926848638
Type 7: smallest eigenvalue is 0.108574542442330779
Written r.py
Written qdashf.py

$ sage -python scripts/make_exact_qdash.py '20/27' --denominator 240 --dir output/max57 --diagonalize
Type 1: smallest eigenvalue is 0.059461624612066784
Type 2: smallest eigenvalue is 0.041715621319877771
Type 3: smallest eigenvalue is 0.086726368275631155
Type 4: smallest eigenvalue is 0.150988446888949718
Type 5: smallest eigenvalue is 0.109549845480245836
Type 6: smallest eigenvalue is 0.116869179692866171
Type 7: smallest eigenvalue is 0.106887792614515267
Diagonalizing matrices...
Written qdash.py
Written r.py
Added exact bound to flags.py

$ sage -python scripts/verify_bound.py --dir output/max57
Written q.py
Floating point bound (non-sharp graphs) is 0.736063156247989014
Exact bound (just sharp graphs) is 20/27
Bound (all graphs) is 20/27

$ sage -python scripts/make_certificate.py --dir output/max57
Written certificate to cert.js