$ ./flagmatic --r 3 --n 6 --forbid 5:123124345 --dir output/ff83 flagmatic version 1.5 ============================================================================ Forbidding 5:123124345 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, 20, 14, 8, 1] flags of order 5. Generated 55 admissible graphs. Approximate floating-point bound is 0.22222222 $ sage -python scripts/find_sharp_graphs.py --dir output/ff83 Floating point bound is 0.222222222415343590. 4 members of H are sharp. 0.222222222389998059 : graph 1 (6:) 0.222222222331379948 : graph 12 (6:123124125126) 0.222222222415343590 : graph 42 (6:123124125136146156) 0.222222222331365321 : graph 53 (6:123124135145236246356456) Written sharp graphs to flags.py $ sage -python scripts/check_construction.py --n 6 --r 3 --vertex-transitive 3:123 Density is 2/9. 4 graphs of order 6 occur as induced subgraphs of the blow-up: 6: has density 7/27 (0.259259) 6:123124125126 has density 10/81 (0.123457) 6:123124125136146156 has density 40/81 (0.493827) 6:123124135145236246356456 has density 10/81 (0.123457) $ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 3:123 --dir output/ff83 [?1034hConstructed 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 0 out of 0 zero eigenvectors for type 7. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/ff83 [?1034hFloating point bound is 0.222222222415343590. Type 1: smallest eigenvalue is 8.115279296689324795 Type 2: smallest eigenvalue is 0.023165438839369144 Type 3: smallest eigenvalue is 0.119086043013336668 Type 4: smallest eigenvalue is 0.153549379724598034 Type 5: smallest eigenvalue is 0.230298702647167147 Type 6: smallest eigenvalue is 0.287170651140673527 Type 7: smallest eigenvalue is 0.161539776443277827 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '2/9' --denominator 24 --dir output/ff83 --diagonalize [?1034hType 1: smallest eigenvalue is 8.191762584136386138 Type 2: smallest eigenvalue is 0.044252525385156637 Type 3: smallest eigenvalue is 0.120835314676039016 Type 4: smallest eigenvalue is 0.155544201123217762 Type 5: smallest eigenvalue is 0.248411029825574725 Type 6: smallest eigenvalue is 0.291666666666666630 Type 7: smallest eigenvalue is 0.166666666666666657 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/ff83 [?1034hWritten q.py Floating point bound (non-sharp graphs) is 0.208316802716087796 Exact bound (just sharp graphs) is 2/9 Bound (all graphs) is 2/9 $ sage -python scripts/make_certificate.py --dir output/ff83 Written certificate to cert.js