$ ./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