$ ./flagmatic --r 3 --n 6 --forbid 6:234135145245126146346256356456 --dir output/baber-s4 flagmatic version 1.5 ============================================================================ Forbidding 6:123124125134136156235236246345 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 2033 admissible graphs. Approximate floating-point bound is 0.75000000 $ sage -python scripts/find_sharp_graphs.py --dir output/baber-s4 Floating point bound is 0.750000000038139936. 4 members of H are sharp. 0.749999999923071425 : graph 1 (6:) 0.750000000027018388 : graph 893 (6:123124125126134135136145146156) 0.750000000038139936 : graph 2024 (6:123124125126134135136145146156234235236245246256) 0.750000000034218850 : graph 2033 (6:123124125126134135136145146235236245246256345346356456) Written sharp graphs to flags.py $ sage -python scripts/check_construction.py --n 6 --r 3 --vertex-transitive 2:112122 Density is 3/4. 4 graphs of order 6 occur as induced subgraphs of the blow-up: 6: has density 1/32 (0.031250) 6:123124125126134135136145146156 has density 3/16 (0.187500) 6:123124125126134135136145146156234235236245246256 has density 15/32 (0.468750) 6:123124125126134135136145146235236245246256345346356456 has density 5/16 (0.312500) $ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 2:112122 --dir output/baber-s4 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 2 out of 2 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Constructed 0 out of 0 zero eigenvectors for type 4. Constructed 0 out of 0 zero eigenvectors for type 5. Constructed 1 out of 1 zero eigenvectors for type 6. Constructed 3 out of 3 zero eigenvectors for type 7. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/baber-s4 Floating point bound is 0.750000000038139714. Type 1: smallest eigenvalue is 0.147196628703973903 Type 2: smallest eigenvalue is 0.012266092443444534 Type 3: smallest eigenvalue is 0.137340388600938695 Type 4: smallest eigenvalue is 0.109905788764465537 Type 5: smallest eigenvalue is 0.089727430012715284 Type 6: smallest eigenvalue is 0.090333598840075371 Type 7: smallest eigenvalue is 0.081439819187158188 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '3/4' --denominator 120 --dir output/baber-s4 --diagonalize Type 1: smallest eigenvalue is 0.148654276091508997 Type 2: smallest eigenvalue is 0.007681571036184952 Type 3: smallest eigenvalue is 0.143816773247367580 Type 4: smallest eigenvalue is 0.109847563161811157 Type 5: smallest eigenvalue is 0.083097673961186239 Type 6: smallest eigenvalue is 0.097467782555681629 Type 7: smallest eigenvalue is 0.084083251533811409 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/baber-s4 Written q.py Floating point bound (non-sharp graphs) is 0.743942098811089525 Exact bound (just sharp graphs) is 3/4 Bound (all graphs) is 3/4 $ sage -python scripts/make_certificate.py --dir output/baber-s4 Written certificate to cert.js