$ ./flagmatic --r 3 --n 6 --forbid-f32 --forbid 6:123124125126134135136145146156 --dir output/638 flagmatic version 1.5 ============================================================================ Forbidding 6:123124125126134135136145146156 Forbidding 5:123124125345 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, 56, 41, 24, 23] flags of order 5. Generated 425 admissible graphs. Approximate floating-point bound is 0.37500000 $ sage -python scripts/find_sharp_graphs.py --dir output/638 Floating point bound is 0.375000000225258145. 6 members of H are sharp. 0.375000000113248078 : graph 1 (6:) 0.375000000106213316 : graph 13 (6:123124125126) 0.375000000225258145 : graph 108 (6:123124125136146156) 0.375000000106621434 : graph 339 (6:123124135145236246356456) 0.375000000145704449 : graph 397 (6:123124125126134135136234235236) 0.375000000212319828 : graph 424 (6:123124125126134135146156234235246256) Written sharp graphs to flags.py $ sage -python scripts/check_construction.py --n 6 --r 3 --vertex-transitive 4:123124134234 Density is 3/8. 6 graphs of order 6 occur as induced subgraphs of the blow-up: 6: has density 47/512 (0.091797) 6:123124125126 has density 45/512 (0.087891) 6:123124125136146156 has density 45/128 (0.351562) 6:123124135145236246356456 has density 45/512 (0.087891) 6:123124125126134135136234235236 has density 15/128 (0.117188) 6:123124125126134135146156234235246256 has density 135/512 (0.263672) $ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 4:123124134234 --dir output/638 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 2 out of 2 zero eigenvectors for type 2. Constructed 8 out of 8 zero eigenvectors for type 3. Constructed 0 out of 0 zero eigenvectors for type 4. Constructed 1 out of 1 zero eigenvectors for type 5. Constructed 0 out of 0 zero eigenvectors for type 6. Constructed 1 out of 1 zero eigenvectors for type 7. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/638 Floating point bound is 0.375000000225258145. Type 1: smallest eigenvalue is 0.537727896311312237 Type 2: smallest eigenvalue is 0.002149795057319506 Type 3: smallest eigenvalue is 0.049609851310472741 Type 4: smallest eigenvalue is 0.042221567357168928 Type 5: smallest eigenvalue is 0.031127539377521423 Type 6: smallest eigenvalue is 0.049059433604750805 Type 7: smallest eigenvalue is 0.073439602208200727 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '3/8' --denominator 120 --dir output/638 --diagonalize Type 1: smallest eigenvalue is 0.540800452439082480 Type 2: smallest eigenvalue is 0.000539661762513981 Type 3: smallest eigenvalue is 0.048546824131814062 Type 4: smallest eigenvalue is 0.037812516093399938 Type 5: smallest eigenvalue is 0.029470090166058428 Type 6: smallest eigenvalue is 0.051840542146373195 Type 7: smallest eigenvalue is 0.055820561903746561 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/638 Written q.py Floating point bound (non-sharp graphs) is 0.373320837489178159 Exact bound (just sharp graphs) is 3/8 Bound (all graphs) is 3/8 $ sage -python scripts/make_certificate.py --dir output/638 Written certificate to cert.js