$ ./flagmatic --r 3 --n 6 --forbid-f32 --forbid 5:123124125134135145 --dir output/38 flagmatic version 1.5 ============================================================================ Forbidding 5:123124125134135145 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 [63, 56, 41, 23, 23] flags of order 5. Generated 409 admissible graphs. Approximate floating-point bound is 0.37500000 $ sage -python scripts/find_sharp_graphs.py --dir output/38 Floating point bound is 0.375000000058043625. 6 members of H are sharp. 0.375000000029177882 : graph 1 (6:) 0.375000000027337244 : graph 13 (6:123124125126) 0.375000000058043625 : graph 107 (6:123124125136146156) 0.375000000027025493 : graph 332 (6:123124135145236246356456) 0.375000000037294445 : graph 385 (6:123124125126134135136234235236) 0.375000000054602878 : graph 409 (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/38 [?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 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/38 [?1034hFloating point bound is 0.375000000058043625. Type 1: smallest eigenvalue is 0.366516323757832996 Type 2: smallest eigenvalue is 0.003608000818081584 Type 3: smallest eigenvalue is 0.056575547731642389 Type 4: smallest eigenvalue is 0.050453511436363063 Type 5: smallest eigenvalue is 0.036119614079747175 Type 6: smallest eigenvalue is 0.075297924603222890 Type 7: smallest eigenvalue is 0.068602098381727775 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '3/8' --denominator 240 --dir output/38 --diagonalize [?1034hType 1: smallest eigenvalue is 0.368542960161406474 Type 2: smallest eigenvalue is 0.002048568640039072 Type 3: smallest eigenvalue is 0.050231104398987869 Type 4: smallest eigenvalue is 0.048175206007955218 Type 5: smallest eigenvalue is 0.038112950787247364 Type 6: smallest eigenvalue is 0.077356192475306784 Type 7: smallest eigenvalue is 0.061681054717883953 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/38 [?1034hWritten q.py Floating point bound (non-sharp graphs) is 0.373143871547453543 Exact bound (just sharp graphs) is 3/8 Bound (all graphs) is 3/8 $ sage -python scripts/make_certificate.py --dir output/38 [?1034hWritten certificate to cert.js