$ ./flagmatic --r 3 --n 7 --forbid-k4- --forbid-induced 5.1 --verbose --dir output/baber flagmatic version 1.5 ============================================================================ Using directory output/baber Forbidding 4.3 Forbidding 5.1 as an induced subgraph. Using admissible graphs of order 7. Generating types and flags... Generated 1 type of order 1, with 5 flags of order 4. Generated 2 types of order 3, with [89, 46] flags of order 5. Generated 10 types of order 5, with [183, 115, 110, 94, 93, 95, 78, 77, 81, 72] flags of order 6. Generating admissible graphs... Generated 1406 admissible graphs. Written flags.py Computing flag densities... Written flags.dat-s and flags.rat Running: ./csdp output/baber/flags.dat-s output/baber/flags.out ============================================================================ Iter: 0 Ap: 0.00e+00 Pobj: -1.4634501e+04 Ad: 0.00e+00 Dobj: 0.0000000e+00 Iter: 1 Ap: 1.00e+00 Pobj: -1.9529095e+04 Ad: 9.51e-01 Dobj: -2.0829104e-01 Iter: 2 Ap: 9.27e-01 Pobj: -1.8657316e+04 Ad: 9.00e-01 Dobj: -2.9380397e-01 Iter: 3 Ap: 1.00e+00 Pobj: -2.0230864e+04 Ad: 2.47e-01 Dobj: -2.9500315e-01 Iter: 4 Ap: 1.52e-01 Pobj: -1.8100938e+04 Ad: 4.37e-01 Dobj: -2.6430814e-01 Iter: 5 Ap: 4.91e-01 Pobj: -1.5579018e+04 Ad: 3.42e-01 Dobj: -2.6117020e-01 Iter: 6 Ap: 2.04e-01 Pobj: -1.4768958e+04 Ad: 4.79e-01 Dobj: -2.5493823e-01 Iter: 7 Ap: 5.17e-01 Pobj: -1.0945146e+04 Ad: 4.37e-01 Dobj: -2.5243419e-01 Iter: 8 Ap: 4.98e-01 Pobj: -8.2666737e+03 Ad: 3.18e-01 Dobj: -2.5215801e-01 Iter: 9 Ap: 3.56e-01 Pobj: -7.4873250e+03 Ad: 4.87e-01 Dobj: -2.4177445e-01 Iter: 10 Ap: 2.69e-01 Pobj: -6.2962006e+03 Ad: 3.70e-01 Dobj: -2.3777073e-01 Iter: 11 Ap: 4.95e-01 Pobj: -4.7260062e+03 Ad: 4.86e-01 Dobj: -2.2743546e-01 Iter: 12 Ap: 3.51e-01 Pobj: -3.7053711e+03 Ad: 4.43e-01 Dobj: -2.2220578e-01 Iter: 13 Ap: 3.77e-01 Pobj: -2.8591053e+03 Ad: 4.94e-01 Dobj: -2.1522721e-01 Iter: 14 Ap: 2.91e-01 Pobj: -2.3508699e+03 Ad: 4.74e-01 Dobj: -2.1171716e-01 Iter: 15 Ap: 2.72e-01 Pobj: -1.9009620e+03 Ad: 4.42e-01 Dobj: -2.0732773e-01 Iter: 16 Ap: 3.52e-01 Pobj: -1.4136515e+03 Ad: 4.66e-01 Dobj: -2.0403218e-01 Iter: 17 Ap: 3.83e-01 Pobj: -1.0052371e+03 Ad: 4.35e-01 Dobj: -2.0184700e-01 Iter: 18 Ap: 2.29e-01 Pobj: -8.6556026e+02 Ad: 4.20e-01 Dobj: -1.9820094e-01 Iter: 19 Ap: 3.51e-01 Pobj: -6.2342105e+02 Ad: 4.08e-01 Dobj: -1.9861443e-01 Iter: 20 Ap: 2.18e-01 Pobj: -5.1283457e+02 Ad: 4.29e-01 Dobj: -1.9589089e-01 Iter: 21 Ap: 3.23e-01 Pobj: -3.6273680e+02 Ad: 4.41e-01 Dobj: -1.9931340e-01 Iter: 22 Ap: 4.52e-01 Pobj: -2.3497538e+02 Ad: 5.43e-01 Dobj: -1.9891862e-01 Iter: 23 Ap: 6.57e-01 Pobj: -1.1763439e+02 Ad: 7.17e-01 Dobj: -2.0272057e-01 Iter: 24 Ap: 7.58e-01 Pobj: -5.1368755e+01 Ad: 9.98e-01 Dobj: -2.0250602e-01 Iter: 25 Ap: 9.43e-01 Pobj: -5.1290416e+00 Ad: 1.00e+00 Dobj: -2.0278650e-01 Iter: 26 Ap: 9.50e-01 Pobj: -8.5608603e-01 Ad: 1.00e+00 Dobj: -2.0562312e-01 Iter: 27 Ap: 1.00e+00 Pobj: -4.8418475e-01 Ad: 9.43e-01 Dobj: -2.2564047e-01 Iter: 28 Ap: 7.57e-01 Pobj: -4.4573058e-01 Ad: 1.00e+00 Dobj: -2.4198037e-01 Iter: 29 Ap: 5.81e-01 Pobj: -3.9978119e-01 Ad: 1.00e+00 Dobj: -2.4622528e-01 Iter: 30 Ap: 1.00e+00 Pobj: -3.3796651e-01 Ad: 9.98e-01 Dobj: -2.5487852e-01 Iter: 31 Ap: 1.00e+00 Pobj: -3.0189067e-01 Ad: 1.00e+00 Dobj: -2.6156393e-01 Iter: 32 Ap: 1.00e+00 Pobj: -2.9065388e-01 Ad: 1.00e+00 Dobj: -2.6755358e-01 Iter: 33 Ap: 1.00e+00 Pobj: -2.8250038e-01 Ad: 1.00e+00 Dobj: -2.7070609e-01 Iter: 34 Ap: 1.00e+00 Pobj: -2.8031746e-01 Ad: 1.00e+00 Dobj: -2.7352510e-01 Iter: 35 Ap: 9.61e-01 Pobj: -2.7884385e-01 Ad: 1.00e+00 Dobj: -2.7484815e-01 Iter: 36 Ap: 1.00e+00 Pobj: -2.7838320e-01 Ad: 1.00e+00 Dobj: -2.7583353e-01 Iter: 37 Ap: 1.00e+00 Pobj: -2.7803551e-01 Ad: 1.00e+00 Dobj: -2.7659409e-01 Iter: 38 Ap: 1.00e+00 Pobj: -2.7790426e-01 Ad: 9.08e-01 Dobj: -2.7706927e-01 Iter: 39 Ap: 9.93e-01 Pobj: -2.7784920e-01 Ad: 1.00e+00 Dobj: -2.7739301e-01 Iter: 40 Ap: 9.82e-01 Pobj: -2.7780714e-01 Ad: 1.00e+00 Dobj: -2.7758691e-01 Iter: 41 Ap: 1.00e+00 Pobj: -2.7779210e-01 Ad: 1.00e+00 Dobj: -2.7766430e-01 Iter: 42 Ap: 8.68e-01 Pobj: -2.7778441e-01 Ad: 1.00e+00 Dobj: -2.7773984e-01 Iter: 43 Ap: 1.00e+00 Pobj: -2.7778125e-01 Ad: 1.00e+00 Dobj: -2.7775492e-01 Iter: 44 Ap: 1.00e+00 Pobj: -2.7777943e-01 Ad: 1.00e+00 Dobj: -2.7777266e-01 Iter: 45 Ap: 9.17e-01 Pobj: -2.7777868e-01 Ad: 1.00e+00 Dobj: -2.7778037e-01 Iter: 46 Ap: 9.37e-01 Pobj: -2.7777839e-01 Ad: 1.00e+00 Dobj: -2.7778288e-01 Iter: 47 Ap: 1.00e+00 Pobj: -2.7777817e-01 Ad: 1.00e+00 Dobj: -2.7778488e-01 Iter: 48 Ap: 1.00e+00 Pobj: -2.7777796e-01 Ad: 1.00e+00 Dobj: -2.7778694e-01 Iter: 49 Ap: 1.00e+00 Pobj: -2.7777789e-01 Ad: 1.00e+00 Dobj: -2.7778398e-01 Iter: 50 Ap: 1.00e+00 Pobj: -2.7777781e-01 Ad: 1.00e+00 Dobj: -2.7778002e-01 Iter: 51 Ap: 1.00e+00 Pobj: -2.7777778e-01 Ad: 9.56e-01 Dobj: -2.7777814e-01 Iter: 52 Ap: 1.00e+00 Pobj: -2.7777778e-01 Ad: 9.82e-01 Dobj: -2.7777780e-01 Iter: 53 Ap: 9.56e-01 Pobj: -2.7777778e-01 Ad: 9.54e-01 Dobj: -2.7777778e-01 Success: SDP solved Primal objective value: -2.7777778e-01 Dual objective value: -2.7777778e-01 Relative primal infeasibility: 5.39e-12 Relative dual infeasibility: 9.68e-11 Real Relative Gap: -1.17e-09 XZ Relative Gap: 8.41e-10 DIMACS error measures: 4.76e-11 0.00e+00 2.99e-10 0.00e+00 -1.17e-09 8.41e-10 Elements time: 308.266075 Factor time: 1.885658 Other time: 11.292427 Total time: 321.444161 ============================================================================ Return code is 0 Approximate floating-point bound is 0.27777778 $ sage -python scripts/find_sharp_graphs.py --dir output/baber Floating point bound is 0.277777777795206071. 9 members of H are sharp. 0.277777777791013536 : graph 1 (7:) 0.277777777791524461 : graph 3 (7:123124125126127) 0.277777777795066683 : graph 14 (7:123124125126137147157167) 0.277777777793446035 : graph 50 (7:123124125136137146147156157) 0.277777777791042291 : graph 540 (7:123124125126137147157267367467567) 0.277777777795206071 : graph 1052 (7:123124125126137147257267357367457467) 0.277777777794480984 : graph 1124 (7:123124125136146156237247257367467567) 0.277777777794823155 : graph 1334 (7:123124125136137146147256257356357456457) 0.277777777788862423 : graph 1406 (7:123124125136146157167237247256267356357456457) Written sharp graphs to flags.py $ sage -python scripts/check_construction.py --n 7 --r 3 --vertex-transitive 6:123234345451512136246356256146 Density is 5/18. 9 graphs of order 7 occur as induced subgraphs of the blow-up: 7: has density 1663/23328 (0.071288) 7:123124125126127 has density 35/486 (0.072016) 7:123124125126137147157167 has density 175/864 (0.202546) 7:123124125136137146147156157 has density 1225/11664 (0.105024) 7:123124125126137147157267367467567 has density 175/1944 (0.090021) 7:123124125136146156237247257367467567 has density 175/1296 (0.135031) 7:123124125126137147257267357367457467 has density 175/1296 (0.135031) 7:123124125136137146147256257356357456457 has density 175/1296 (0.135031) 7:123124125136146157167237247256267356357456457 has density 35/648 (0.054012) $ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 6:123234345451512136246356256146 --dir output/baber Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 5 out of 5 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Constructed 16 out of 16 zero eigenvectors for type 4. Constructed 0 out of 0 zero eigenvectors for type 5. Constructed 0 out of 0 zero eigenvectors for type 6. Constructed 4 out of 4 zero eigenvectors for type 7. Constructed 0 out of 0 zero eigenvectors for type 8. Constructed 0 out of 0 zero eigenvectors for type 9. Constructed 0 out of 0 zero eigenvectors for type 10. Constructed 3 out of 3 zero eigenvectors for type 11. Constructed 0 out of 0 zero eigenvectors for type 12. Constructed 1 out of 1 zero eigenvectors for type 13. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/baber Floating point bound is 0.277777777795206071. Type 1: smallest eigenvalue is 0.000650072220474367 Type 2: smallest eigenvalue is 0.004497651309552819 Type 3: smallest eigenvalue is 0.004725387421772387 Type 4: smallest eigenvalue is 0.025445872073286378 Type 5: smallest eigenvalue is 0.019677954888816140 Type 6: smallest eigenvalue is 0.090547555541224747 Type 7: smallest eigenvalue is 0.045156162911131108 Type 8: smallest eigenvalue is 0.043503055408100552 Type 9: smallest eigenvalue is 0.100783629619847742 Type 10: smallest eigenvalue is 0.064188624079928466 Type 11: smallest eigenvalue is 0.066505109334299775 Type 12: smallest eigenvalue is 0.049966553737149998 Type 13: smallest eigenvalue is 0.036426401399882319 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '5/18' --denominator 1440 --dir output/baber --diagonalize Type 1: smallest eigenvalue is 0.000501684356358334 Type 2: smallest eigenvalue is 0.004078226188348272 Type 3: smallest eigenvalue is 0.005943674764063559 Type 4: smallest eigenvalue is 0.026880385923329631 Type 5: smallest eigenvalue is 0.020098888351166796 Type 6: smallest eigenvalue is 0.089780422777689703 Type 7: smallest eigenvalue is 0.044497027973117921 Type 8: smallest eigenvalue is 0.043650626792347547 Type 9: smallest eigenvalue is 0.101075951541384018 Type 10: smallest eigenvalue is 0.062958686982791126 Type 11: smallest eigenvalue is 0.066097066808917651 Type 12: smallest eigenvalue is 0.050269824995033782 Type 13: smallest eigenvalue is 0.035869859660939432 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/baber Written q.py Floating point bound (non-sharp graphs) is 0.277633885247563605 Exact bound (just sharp graphs) is 5/18 Bound (all graphs) is 5/18 $ sage -python scripts/make_certificate.py --dir output/baber Written certificate to cert.js