$ ./flagmatic --r 2 --n 7 --induced-density 4:1223241314 --max-flags 32 --verbose --dir output/k112 flagmatic version 1.5 ============================================================================ Optimizing for density of 4:1213142324. Using directory output/k112 Using admissible graphs of order 7. Generating types and flags... Generated 1 type of order 1, with 20 flags of order 4. Generated 4 types of order 3, with [72, 72, 72, 72] flags of order 5. Generated 34 types of order 5, with [32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32] flags of order 6. 4 types removed; remaining types have [20, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32] flags. Generating admissible graphs... Generated 1044 admissible graphs. Written flags.py Computing flag densities... Written flags.dat-s and flags.rat Running: ./csdp output/k112/flags.dat-s output/k112/flags.out ============================================================================ Iter: 0 Ap: 0.00e+00 Pobj: -1.4762358e+04 Ad: 0.00e+00 Dobj: 0.0000000e+00 Iter: 1 Ap: 1.00e+00 Pobj: -1.8404547e+04 Ad: 9.13e-01 Dobj: -1.2219419e-01 Iter: 2 Ap: 7.12e-01 Pobj: -1.7634160e+04 Ad: 9.55e-01 Dobj: -1.1154757e-01 Iter: 3 Ap: 1.00e+00 Pobj: -1.1838364e+04 Ad: 9.43e-01 Dobj: -1.0382559e-01 Iter: 4 Ap: 2.36e-01 Pobj: -1.0120128e+04 Ad: 8.12e-01 Dobj: -1.0343935e-01 Iter: 5 Ap: 7.68e-01 Pobj: -3.7507141e+03 Ad: 5.87e-01 Dobj: -1.0346821e-01 Iter: 6 Ap: 8.41e-01 Pobj: -1.4740935e+03 Ad: 7.83e-01 Dobj: -1.0393183e-01 Iter: 7 Ap: 7.65e-01 Pobj: -7.0322603e+02 Ad: 7.95e-01 Dobj: -1.0545982e-01 Iter: 8 Ap: 1.00e+00 Pobj: -1.6504516e+02 Ad: 1.00e+00 Dobj: -1.0597345e-01 Iter: 9 Ap: 9.88e-01 Pobj: -9.1554904e+00 Ad: 1.00e+00 Dobj: -1.0616636e-01 Iter: 10 Ap: 1.00e+00 Pobj: -1.0787489e+00 Ad: 1.00e+00 Dobj: -1.0950569e-01 Iter: 11 Ap: 1.00e+00 Pobj: -7.1585915e-01 Ad: 1.00e+00 Dobj: -1.5387642e-01 Iter: 12 Ap: 7.04e-01 Pobj: -7.1001187e-01 Ad: 9.49e-01 Dobj: -2.9770923e-01 Iter: 13 Ap: 5.72e-01 Pobj: -6.9397059e-01 Ad: 9.57e-01 Dobj: -4.0155200e-01 Iter: 14 Ap: 1.00e+00 Pobj: -6.1384906e-01 Ad: 4.93e-01 Dobj: -4.3949714e-01 Iter: 15 Ap: 6.39e-01 Pobj: -5.9922767e-01 Ad: 8.05e-01 Dobj: -4.9393823e-01 Iter: 16 Ap: 9.07e-01 Pobj: -5.8156391e-01 Ad: 1.00e+00 Dobj: -5.3278928e-01 Iter: 17 Ap: 6.96e-01 Pobj: -5.7760689e-01 Ad: 1.00e+00 Dobj: -5.6169473e-01 Iter: 18 Ap: 4.67e-01 Pobj: -5.7680399e-01 Ad: 9.48e-01 Dobj: -5.7016222e-01 Iter: 19 Ap: 8.76e-01 Pobj: -5.7613357e-01 Ad: 1.00e+00 Dobj: -5.7273241e-01 Iter: 20 Ap: 9.93e-01 Pobj: -5.7601620e-01 Ad: 1.00e+00 Dobj: -5.7504068e-01 Iter: 21 Ap: 8.90e-01 Pobj: -5.7600737e-01 Ad: 1.00e+00 Dobj: -5.7562279e-01 Iter: 22 Ap: 7.78e-01 Pobj: -5.7600395e-01 Ad: 1.00e+00 Dobj: -5.7584006e-01 Iter: 23 Ap: 8.79e-01 Pobj: -5.7600184e-01 Ad: 1.00e+00 Dobj: -5.7592544e-01 Iter: 24 Ap: 1.00e+00 Pobj: -5.7600074e-01 Ad: 1.00e+00 Dobj: -5.7597200e-01 Iter: 25 Ap: 1.00e+00 Pobj: -5.7600022e-01 Ad: 9.30e-01 Dobj: -5.7599753e-01 Iter: 26 Ap: 2.31e-01 Pobj: -5.7600021e-01 Ad: 6.11e-01 Dobj: -5.7599808e-01 Iter: 27 Ap: 1.09e-01 Pobj: -5.7600021e-01 Ad: 3.79e-01 Dobj: -5.7599569e-01 Iter: 28 Ap: 4.97e-01 Pobj: -5.7600017e-01 Ad: 8.52e-01 Dobj: -5.7599735e-01 Iter: 29 Ap: 8.56e-01 Pobj: -5.7600010e-01 Ad: 1.00e+00 Dobj: -5.7599870e-01 Iter: 30 Ap: 1.00e+00 Pobj: -5.7600003e-01 Ad: 1.00e+00 Dobj: -5.7599993e-01 Iter: 31 Ap: 1.00e+00 Pobj: -5.7600000e-01 Ad: 1.00e+00 Dobj: -5.7600000e-01 Iter: 32 Ap: 1.00e+00 Pobj: -5.7600000e-01 Ad: 9.95e-01 Dobj: -5.7600000e-01 Success: SDP solved Primal objective value: -5.7600000e-01 Dual objective value: -5.7600000e-01 Relative primal infeasibility: 3.76e-14 Relative dual infeasibility: 9.77e-10 Real Relative Gap: 3.21e-10 XZ Relative Gap: 8.56e-09 DIMACS error measures: 1.34e-13 0.00e+00 4.84e-09 0.00e+00 3.21e-10 8.56e-09 Elements time: 7.234951 Factor time: 0.561715 Other time: 1.336795 Total time: 9.133462 ============================================================================ Return code is 0 Approximate floating-point bound is 0.57600000 $ sage -python scripts/find_sharp_graphs.py --dir output/k112 Floating point bound is 0.576000000286327696. 13 members of H are sharp. 0.575999750412030997 : graph 1 (7:) 0.575999991409799628 : graph 41 (7:121314151617) 0.575999997360547411 : graph 433 (7:12131415162737475767) 0.575999999344119051 : graph 523 (7:1213141516172324252627) 0.575999998550704162 : graph 801 (7:121314152627363746475657) 0.576000000137562362 : graph 917 (7:1213141516172324252637475767) 0.576000000038364823 : graph 964 (7:121314151617232425262734353637) 0.576000000038372262 : graph 984 (7:121314151617232425363746475657) 0.576000000137540269 : graph 1025 (7:12131415162324252736374647565767) 0.576000000286327696 : graph 1031 (7:1213141516172324252627343536475767) 0.576000000038375926 : graph 1036 (7:121314151617232425262734353637454647) 0.576000000236721710 : graph 1040 (7:121314151617232425263435374647565767) 0.576000000236736920 : graph 1042 (7:12131415161723242526273435363745465767) Written sharp graphs to flags.py $ sage -python scripts/check_construction.py --n 7 --r 2 --induced-density 4:1223241314 --vertex-transitive 5:12131415232425343545 Density of 4:1223241314 is 72/125. 13 graphs of order 7 occur as induced subgraphs of the blow-up: 7: has density 1/15625 (0.000064) 7:121314151617 has density 28/15625 (0.001792) 7:12131415162737475767 has density 84/15625 (0.005376) 7:1213141516172324252627 has density 252/15625 (0.016128) 7:121314152627363746475657 has density 28/3125 (0.008960) 7:1213141516172324252637475767 has density 252/3125 (0.080640) 7:121314151617232425262734353637 has density 168/3125 (0.053760) 7:121314151617232425363746475657 has density 168/3125 (0.053760) 7:12131415162324252736374647565767 has density 252/3125 (0.080640) 7:1213141516172324252627343536475767 has density 1008/3125 (0.322560) 7:121314151617232425263435374647565767 has density 504/3125 (0.161280) 7:121314151617232425262734353637454647 has density 168/3125 (0.053760) 7:12131415161723242526273435363745465767 has density 504/3125 (0.161280) $ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 5:12131415232425343545 --dir output/k112 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 1 out of 1 zero eigenvectors for type 2. Constructed 0 out of 0 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 0 out of 0 zero eigenvectors for type 6. Constructed 0 out of 0 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 1 out of 1 zero eigenvectors for type 10. Constructed 0 out of 0 zero eigenvectors for type 11. Constructed 0 out of 0 zero eigenvectors for type 12. Constructed 0 out of 0 zero eigenvectors for type 13. Constructed 0 out of 0 zero eigenvectors for type 14. Constructed 0 out of 0 zero eigenvectors for type 15. Constructed 0 out of 0 zero eigenvectors for type 16. Constructed 0 out of 0 zero eigenvectors for type 17. Constructed 0 out of 0 zero eigenvectors for type 18. Constructed 0 out of 0 zero eigenvectors for type 19. Constructed 0 out of 0 zero eigenvectors for type 20. Constructed 0 out of 0 zero eigenvectors for type 21. Constructed 0 out of 0 zero eigenvectors for type 22. Constructed 0 out of 0 zero eigenvectors for type 23. Constructed 0 out of 0 zero eigenvectors for type 24. Constructed 0 out of 0 zero eigenvectors for type 25. Constructed 0 out of 0 zero eigenvectors for type 26. Constructed 1 out of 1 zero eigenvectors for type 27. Constructed 1 out of 1 zero eigenvectors for type 28. Constructed 0 out of 0 zero eigenvectors for type 29. Constructed 0 out of 0 zero eigenvectors for type 30. Constructed 0 out of 0 zero eigenvectors for type 31. Constructed 0 out of 0 zero eigenvectors for type 32. Constructed 1 out of 1 zero eigenvectors for type 33. Constructed 1 out of 1 zero eigenvectors for type 34. Constructed 1 out of 1 zero eigenvectors for type 35. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/k112 Floating point bound is 0.576000000286327696. Type 1: smallest eigenvalue is 0.008188551453348136 Type 2: smallest eigenvalue is 0.087440464672576060 Type 3: smallest eigenvalue is 0.181785997679569267 Type 4: smallest eigenvalue is 0.185495866559327038 Type 5: smallest eigenvalue is 0.185327962956105097 Type 6: smallest eigenvalue is 0.185037445185957355 Type 7: smallest eigenvalue is 0.180545276554447381 Type 8: smallest eigenvalue is 0.186763620910660011 Type 9: smallest eigenvalue is 0.185966892704718417 Type 10: smallest eigenvalue is 0.150366176809807572 Type 11: smallest eigenvalue is 0.186538817256012762 Type 12: smallest eigenvalue is 0.186528013424546724 Type 13: smallest eigenvalue is 0.180634898252160531 Type 14: smallest eigenvalue is 0.185229401490750928 Type 15: smallest eigenvalue is 0.186805032504184954 Type 16: smallest eigenvalue is 0.175830240491250650 Type 17: smallest eigenvalue is 0.185539763398088114 Type 18: smallest eigenvalue is 0.186668494722349032 Type 19: smallest eigenvalue is 0.186580081000483344 Type 20: smallest eigenvalue is 0.186154806179158611 Type 21: smallest eigenvalue is 0.185224633793169530 Type 22: smallest eigenvalue is 0.184620853935081569 Type 23: smallest eigenvalue is 0.180872496476581018 Type 24: smallest eigenvalue is 0.182093832013891954 Type 25: smallest eigenvalue is 0.186279258824005867 Type 26: smallest eigenvalue is 0.186298296258496060 Type 27: smallest eigenvalue is 0.131827535118360761 Type 28: smallest eigenvalue is 0.170269752299925164 Type 29: smallest eigenvalue is 0.184959190322237843 Type 30: smallest eigenvalue is 0.184077151299231689 Type 31: smallest eigenvalue is 0.180799436211102782 Type 32: smallest eigenvalue is 0.172221772643889992 Type 33: smallest eigenvalue is 0.183149048317012370 Type 34: smallest eigenvalue is 0.034031478600712588 Type 35: smallest eigenvalue is 0.152685493794362748 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '72/125' --denominator 2400 --dir output/k112 --diagonalize Type 1: smallest eigenvalue is 0.008094195210908463 Type 2: smallest eigenvalue is 0.130246124329936042 Type 3: smallest eigenvalue is 0.181965950132680937 Type 4: smallest eigenvalue is 0.185944615415292946 Type 5: smallest eigenvalue is 0.185481479062961141 Type 6: smallest eigenvalue is 0.185148942612728989 Type 7: smallest eigenvalue is 0.180175996745506717 Type 8: smallest eigenvalue is 0.187744077682344523 Type 9: smallest eigenvalue is 0.186402037903488083 Type 10: smallest eigenvalue is 0.149967508654708120 Type 11: smallest eigenvalue is 0.187417211981868309 Type 12: smallest eigenvalue is 0.187659152504687565 Type 13: smallest eigenvalue is 0.180563761054876093 Type 14: smallest eigenvalue is 0.185159084347364389 Type 15: smallest eigenvalue is 0.187659152504687482 Type 16: smallest eigenvalue is 0.175650697114031057 Type 17: smallest eigenvalue is 0.185891865254743605 Type 18: smallest eigenvalue is 0.187499999999999944 Type 19: smallest eigenvalue is 0.187659152504687510 Type 20: smallest eigenvalue is 0.186666666666666675 Type 21: smallest eigenvalue is 0.185416666666666646 Type 22: smallest eigenvalue is 0.185002309006567445 Type 23: smallest eigenvalue is 0.181081524606802352 Type 24: smallest eigenvalue is 0.181889857388841586 Type 25: smallest eigenvalue is 0.187264163374506409 Type 26: smallest eigenvalue is 0.187119904508964846 Type 27: smallest eigenvalue is 0.131901732933775717 Type 28: smallest eigenvalue is 0.170159949474648353 Type 29: smallest eigenvalue is 0.185181861426413352 Type 30: smallest eigenvalue is 0.184304865075358509 Type 31: smallest eigenvalue is 0.180797557100554951 Type 32: smallest eigenvalue is 0.172332260093899542 Type 33: smallest eigenvalue is 0.183230518902435607 Type 34: smallest eigenvalue is 0.033905824889582922 Type 35: smallest eigenvalue is 0.152458573191020186 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/k112 Written q.py Floating point bound (non-sharp graphs) is 0.556616385078479547 Exact bound (just sharp graphs) is 72/125 Bound (all graphs) is 72/125 $ sage -python scripts/make_certificate.py --dir output/k112 Written certificate to cert.js