\$ ./flagmatic --r 3 --n 5 --induced-density 4.2 --dir output/max42 flagmatic version 1.5 ============================================================================ Optimizing for density of 4.2. Using admissible graphs of order 5. Generated 1 type of order 1, with 2 flags of order 3. Generated 2 types of order 3, with [8, 8] flags of order 4. Generated 34 admissible graphs. Approximate floating-point bound is 0.75000000 \$ sage -python scripts/find_sharp_graphs.py --dir output/max42 Floating point bound is 0.750000000252714183. 7 members of H are sharp. 0.749999998145788327 : graph 1 (5:) 0.750000000101430753 : graph 5 (5:123124125) 0.750000000252714183 : graph 13 (5:123124135145) 0.750000000153896340 : graph 20 (5:123124135245345) 0.750000000251879961 : graph 24 (5:123124125134234345) 0.750000000099826813 : graph 28 (5:123124125134135234235) 0.749999998144634139 : graph 34 (5:123124125134135145234235245345) Written sharp graphs to flags.py \$ sage -python scripts/make_zero_eigenvectors.py max42 --dir output/max42 [?1034hConstructed 1 out of 1 zero eigenvectors for type 1. Constructed 1 out of 1 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Written zev.py Written field to flags.py \$ sage -python scripts/factor_approximate_q.py --dir output/max42 [?1034hFloating point bound is 0.750000000252714072. Type 1: smallest eigenvalue is 0.947891659130927766 Type 2: smallest eigenvalue is 0.410621247130690259 Type 3: smallest eigenvalue is 0.410621247408612833 Written r.py Written qdashf.py \$ sage -python scripts/make_exact_qdash.py '3/4' --denominator 3 --dir output/max42 --diagonalize [?1034hType 1: smallest eigenvalue is 0.925925925925925819 Type 2: smallest eigenvalue is 0.289062177380972229 Type 3: smallest eigenvalue is 0.289062177380971896 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py \$ sage -python scripts/verify_bound.py --dir output/max42 [?1034hWritten q.py Floating point bound (non-sharp graphs) is 0.650000000000000022 Exact bound (just sharp graphs) is 3/4 Bound (all graphs) is 3/4 \$ sage -python scripts/make_certificate.py --dir output/max42 Written certificate to cert.js