\$ ./flagmatic --r 3 --n 6 --forbid 6:123145146156245246256345346356 --dir output/f33 flagmatic version 1.5 ============================================================================ Forbidding 6:123124125136146156236246256345 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 2073 admissible graphs. Approximate floating-point bound is 0.75000000 \$ sage -python scripts/find_sharp_graphs.py --dir output/f33 Floating point bound is 0.750000000005298650. 4 members of H are sharp. 0.749999999988901989 : graph 1 (6:) 0.750000000002609357 : graph 893 (6:123124125126134135136145146156) 0.750000000004601763 : graph 2062 (6:123124125126134135136145146156234235236245246256) 0.750000000005298650 : graph 2073 (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/f33 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/f33 Floating point bound is 0.750000000005298650. Type 1: smallest eigenvalue is 0.146799685707613203 Type 2: smallest eigenvalue is 0.011991617846940628 Type 3: smallest eigenvalue is 0.155908406063160310 Type 4: smallest eigenvalue is 0.120139061460082408 Type 5: smallest eigenvalue is 0.076085170410836178 Type 6: smallest eigenvalue is 0.071798381955376578 Type 7: smallest eigenvalue is 0.073414097350843227 Written r.py Written qdashf.py \$ sage -python scripts/make_exact_qdash.py '3/4' --denominator 72 --dir output/f33 --diagonalize Type 1: smallest eigenvalue is 0.146167708155777953 Type 2: smallest eigenvalue is 0.012874859183707104 Type 3: smallest eigenvalue is 0.152777777777777762 Type 4: smallest eigenvalue is 0.121814306492300045 Type 5: smallest eigenvalue is 0.062366158906262958 Type 6: smallest eigenvalue is 0.037785336649562531 Type 7: smallest eigenvalue is 0.042795646224669831 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py \$ sage -python scripts/verify_bound.py --dir output/f33 Written q.py Floating point bound (non-sharp graphs) is 0.745375780736357907 Exact bound (just sharp graphs) is 3/4 Bound (all graphs) is 3/4 \$ sage -python scripts/make_certificate.py --dir output/f33 Written certificate to cert.js