Random timeout on CI for fusion_ring get_braid_generators

[user202729]

e.g.

https://github.com/sagemath/sage/actions/runs/13357347461/job/37301912535#step:10:8731

Example log:

2025-02-16T18:17:16.3576647Z sage -t --warn-long 5.0 --random-seed=233588306476208617699738222937140165961 src/sage/algebras/fusion_rings/fusion_ring.py  # [failed in baseline: unreported random timeouts]
2025-02-16T18:17:16.3586558Z     Timed out
2025-02-16T18:17:16.3608612Z **********************************************************************
2025-02-16T18:17:16.3609303Z 
2025-02-16T18:17:16.3609894Z Tests run before process (pid=47801) timed out:
2025-02-16T18:17:16.3614538Z sage: A22 = FusionRing("A2", 2) ## line 78 ##
2025-02-16T18:17:16.3615277Z sage: [f1, f2] = A22.fundamental_weights() ## line 79 ##
2025-02-16T18:17:16.3616137Z sage: M = [A22(x) for x in [0*f1, 2*f1, 2*f2, f1+f2, f2, f1]] ## line 80 ##
2025-02-16T18:17:16.3628156Z sage: [M[3] * x for x in M] ## line 81 ##
2025-02-16T18:17:16.3629175Z [A22(1,1),
2025-02-16T18:17:16.3629904Z  A22(0,1),
2025-02-16T18:17:16.3630596Z  A22(1,0),
2025-02-16T18:17:16.3631264Z  A22(0,0) + A22(1,1),
2025-02-16T18:17:16.3647156Z  A22(0,1) + A22(2,0),
2025-02-16T18:17:16.3647694Z  A22(1,0) + A22(0,2)]
2025-02-16T18:17:16.3648535Z sage: B22 = FusionRing("B2", 2) ## line 94 ##
2025-02-16T18:17:16.3649212Z sage: b = [B22(x) for x in B22.get_order()]; b ## line 95 ##
2025-02-16T18:17:16.3650157Z [B22(0,0), B22(1,0), B22(0,1), B22(2,0), B22(1,1), B22(0,2)]
2025-02-16T18:17:16.3652347Z sage: [x.weight() for x in b] ## line 97 ##
2025-02-16T18:17:16.3653012Z [(0, 0), (1, 0), (1/2, 1/2), (2, 0), (3/2, 1/2), (1, 1)]
2025-02-16T18:17:16.3654862Z sage: B22.fusion_labels(['I0', 'Y1', 'X', 'Z', 'Xp', 'Y2'], inject_variables=True) ## line 99 ##
2025-02-16T18:17:16.3655875Z sage: b = [B22(x) for x in B22.get_order()]; b ## line 100 ##
2025-02-16T18:17:16.3656662Z [I0, Y1, X, Z, Xp, Y2]
2025-02-16T18:17:16.3657203Z sage: [(x, x.weight()) for x in b] ## line 102 ##
2025-02-16T18:17:16.3658020Z [(I0, (0, 0)),
2025-02-16T18:17:16.3659409Z  (Y1, (1, 0)),
2025-02-16T18:17:16.3660817Z  (X, (1/2, 1/2)),
2025-02-16T18:17:16.3661941Z  (Z, (2, 0)),
2025-02-16T18:17:16.3662439Z  (Xp, (3/2, 1/2)),
2025-02-16T18:17:16.3662898Z  (Y2, (1, 1))]
2025-02-16T18:17:16.3663368Z sage: X * Y1 ## line 109 ##
2025-02-16T18:17:16.3663879Z X + Xp
2025-02-16T18:17:16.3680259Z sage: Z * Z ## line 111 ##
2025-02-16T18:17:16.3681179Z I0
2025-02-16T18:17:16.3682140Z sage: B22.set_order([x.weight() for x in [I0, Y1, Y2, X, Xp, Z]]) ## line 118 ##
2025-02-16T18:17:16.3683082Z sage: [B22(x) for x in B22.get_order()] ## line 119 ##
2025-02-16T18:17:16.3683735Z [I0, Y1, Y2, X, Xp, Z]
2025-02-16T18:17:16.3684244Z sage: B22.fusion_labels() ## line 124 ##
2025-02-16T18:17:16.3684890Z sage: [B22(x) for x in B22.get_order()] ## line 125 ##
2025-02-16T18:17:16.3685843Z [B22(0,0), B22(1,0), B22(0,2), B22(0,1), B22(1,1), B22(2,0)]
2025-02-16T18:17:16.3686640Z sage: B22.set_order(B22.basis().keys().list()) ## line 131 ##
2025-02-16T18:17:16.3687406Z sage: [B22(x) for x in B22.get_order()] ## line 132 ##
2025-02-16T18:17:16.3688410Z [B22(0,0), B22(1,0), B22(0,1), B22(2,0), B22(1,1), B22(0,2)]
2025-02-16T18:17:16.3689052Z sage: def V(i, j, k):
2025-02-16T18:17:16.3689593Z     R = i.parent()
2025-02-16T18:17:16.3690266Z     return sum(R.s_ij(i, l) * R.s_ij(j, l) * R.s_ij(k, l) / R.s_ij(R.one(), l)
2025-02-16T18:17:16.3691052Z                for l in R.basis()) ## line 188 ##
2025-02-16T18:17:16.3691882Z sage: def test_verlinde(R):
2025-02-16T18:17:16.3692408Z     b0 = R.one()
2025-02-16T18:17:16.3692907Z     c = R.global_q_dimension()
2025-02-16T18:17:16.3693576Z     return all(V(i, j, k) == c * R.N_ijk(i, j, k) for i in R.basis()
2025-02-16T18:17:16.3694384Z                for j in R.basis() for k in R.basis()) ## line 197 ##
2025-02-16T18:17:16.3695187Z sage: test_verlinde(FusionRing("A2", 1)) ## line 205 ##
2025-02-16T18:17:16.3695814Z True
2025-02-16T18:17:16.3696354Z sage: I = FusionRing("E8", 2, conjugate=True) ## line 219 ##
2025-02-16T18:17:16.3697182Z sage: I.fusion_labels(["i0", "p", "s"], inject_variables=True) ## line 220 ##
2025-02-16T18:17:16.3698252Z sage: b = I.basis().list(); b ## line 221 ##
2025-02-16T18:17:16.3698821Z [i0, p, s]
2025-02-16T18:17:16.3699251Z sage: [x.twist() for x in b] ## line 227 ##
2025-02-16T18:17:16.3699755Z [0, 1, 1/8]
2025-02-16T18:17:16.3700147Z sage: [x.ribbon() for x in b] ## line 229 ##
2025-02-16T18:17:16.3700722Z [1, -1, zeta128^8]
2025-02-16T18:17:16.3701577Z sage: [I.r_matrix(i, j, k) for (i, j, k) in [(s, s, i0), (p, p, i0), (p, s, s), (s, p, s), (s, s, p)]] ## line 231 ##
2025-02-16T18:17:16.3702519Z [-zeta128^56, -1, -zeta128^32, -zeta128^32, zeta128^24]
2025-02-16T18:17:16.3703301Z sage: I.r_matrix(s, s, i0) == I.root_of_unity(-1/8) ## line 233 ##
2025-02-16T18:17:16.3703938Z True
2025-02-16T18:17:16.3704408Z sage: I.global_q_dimension() ## line 235 ##
2025-02-16T18:17:16.3705028Z 4
2025-02-16T18:17:16.3705527Z sage: I.total_q_order() ## line 237 ##
2025-02-16T18:17:16.3706169Z 2
2025-02-16T18:17:16.3706678Z sage: [x.q_dimension()^2 for x in b] ## line 239 ##
2025-02-16T18:17:16.3708974Z [1, 1, 2]
2025-02-16T18:17:16.3709311Z sage: I.s_matrix() ## line 241 ##
2025-02-16T18:17:16.3709789Z [                       1                        1 -zeta128^48 + zeta128^16]
2025-02-16T18:17:16.3710321Z [                       1                        1  zeta128^48 - zeta128^16]
2025-02-16T18:17:16.3710951Z [-zeta128^48 + zeta128^16  zeta128^48 - zeta128^16                        0]
2025-02-16T18:17:16.3711626Z sage: I.s_matrix().apply_map(lambda x:x^2) ## line 245 ##
2025-02-16T18:17:16.3712116Z [1 1 2]
2025-02-16T18:17:16.3712368Z [1 1 2]
2025-02-16T18:17:16.3712615Z [2 2 0]
2025-02-16T18:17:16.3712932Z sage: R = FusionRing("G2", 1) ## line 288 ##
2025-02-16T18:17:16.3713464Z sage: S = R.s_matrix(unitary=True) ## line 289 ##
2025-02-16T18:17:16.3713969Z sage: T = R.twists_matrix() ## line 290 ##
2025-02-16T18:17:16.3714420Z sage: C = R.conj_matrix() ## line 291 ##
2025-02-16T18:17:16.3714909Z sage: c = R.virasoro_central_charge(); c ## line 292 ##
2025-02-16T18:17:16.3715371Z 14/5
2025-02-16T18:17:16.3715744Z sage: (S*T)^3 == R.root_of_unity(c/4) * S^2 ## line 294 ##
2025-02-16T18:17:16.3716224Z True
2025-02-16T18:17:16.3716515Z sage: S^2 == C ## line 296 ##
2025-02-16T18:17:16.3716860Z True
2025-02-16T18:17:16.3717130Z sage: C*T == T*C ## line 298 ##
2025-02-16T18:17:16.3717499Z True
2025-02-16T18:17:16.3718181Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 300 ##
2025-02-16T18:17:16.3718942Z 0
2025-02-16T18:17:16.3719256Z sage: F1 = FusionRing('B3', 2) ## line 308 ##
2025-02-16T18:17:16.3719795Z sage: F2 = FusionRing(CartanType('B3'), QQ(2), ZZ) ## line 309 ##
2025-02-16T18:17:16.3720558Z sage: F3 = FusionRing(CartanType('B3'), int(2), style='coroots') ## line 310 ##
2025-02-16T18:17:16.3721449Z sage: F1 is F2 and F2 is F3 ## line 311 ##
2025-02-16T18:17:16.3721906Z True
2025-02-16T18:17:16.3722252Z sage: A23 = FusionRing('A2', 3) ## line 314 ##
2025-02-16T18:17:16.3722744Z sage: TestSuite(A23).run() ## line 315 ##
2025-02-16T18:17:16.3723234Z sage: B22 = FusionRing('B2', 2) ## line 317 ##
2025-02-16T18:17:16.3723694Z sage: TestSuite(B22).run() ## line 318 ##
2025-02-16T18:17:16.3724162Z sage: C31 = FusionRing('C3', 1) ## line 320 ##
2025-02-16T18:17:16.3724617Z sage: TestSuite(C31).run() ## line 321 ##
2025-02-16T18:17:16.3725086Z sage: D41 = FusionRing('D4', 1) ## line 323 ##
2025-02-16T18:17:16.3725731Z sage: TestSuite(D41).run() ## line 324 ##
2025-02-16T18:17:16.3726219Z sage: G22 = FusionRing('G2', 2) ## line 326 ##
2025-02-16T18:17:16.3726696Z sage: TestSuite(G22).run() ## line 327 ##
2025-02-16T18:17:16.3727148Z sage: F41 = FusionRing('F4', 1) ## line 329 ##
2025-02-16T18:17:16.3727605Z sage: TestSuite(F41).run() ## line 330 ##
2025-02-16T18:17:16.3752149Z sage: E61 = FusionRing('E6', 1) ## line 332 ##
2025-02-16T18:17:16.3752702Z sage: TestSuite(E61).run() ## line 333 ##
2025-02-16T18:17:16.3753221Z sage: E71 = FusionRing('E7', 1) ## line 335 ##
2025-02-16T18:17:16.3753711Z sage: TestSuite(E71).run() ## line 336 ##
2025-02-16T18:17:16.3754171Z sage: E81 = FusionRing('E8', 1) ## line 338 ##
2025-02-16T18:17:16.3754631Z sage: TestSuite(E81).run() ## line 339 ##
2025-02-16T18:17:16.3755260Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 340 ##
2025-02-16T18:17:16.3755862Z 0
2025-02-16T18:17:16.3756179Z sage: G22 = FusionRing("G2", 2) ## line 354 ##
2025-02-16T18:17:16.3756664Z sage: G22._test_verlinde() ## line 355 ##
2025-02-16T18:17:16.3757289Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 356 ##
2025-02-16T18:17:16.3758127Z 0
2025-02-16T18:17:16.3758481Z sage: G22 = FusionRing("G2", 2) ## line 376 ##
2025-02-16T18:17:16.3758982Z sage: G22._test_total_q_order() ## line 377 ##
2025-02-16T18:17:16.3759648Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 378 ##
2025-02-16T18:17:16.3760246Z 0
2025-02-16T18:17:16.3760583Z sage: A21 = FusionRing("A2", 1) ## line 404 ##
2025-02-16T18:17:16.3761175Z sage: A21.test_braid_representation(max_strands=4) ## line 405 ##
2025-02-16T18:17:16.3761728Z True
2025-02-16T18:17:16.3762218Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 410 ##
2025-02-16T18:17:16.3762802Z 0
2025-02-16T18:17:16.3763143Z sage: A13 = FusionRing("A1", 3) ## line 460 ##
2025-02-16T18:17:16.3763647Z sage: A13.fusion_labels("x") ## line 461 ##
2025-02-16T18:17:16.3764172Z sage: fb = list(A13.basis()); fb ## line 462 ##
2025-02-16T18:17:16.3764627Z [x0, x1, x2, x3]
2025-02-16T18:17:16.3765102Z sage: Matrix([[x*y for y in A13.basis()] for x in A13.basis()]) ## line 464 ##
2025-02-16T18:17:16.3765692Z [     x0      x1      x2      x3]
2025-02-16T18:17:16.3766108Z [     x1 x0 + x2 x1 + x3      x2]
2025-02-16T18:17:16.3766502Z [     x2 x1 + x3 x0 + x2      x1]
2025-02-16T18:17:16.3766887Z [     x3      x2      x1      x0]
2025-02-16T18:17:16.3767410Z sage: A13.fusion_labels("y", inject_variables=True) ## line 473 ##
2025-02-16T18:17:16.3768175Z sage: y0 ## line 474 ##
2025-02-16T18:17:16.3768524Z y0
2025-02-16T18:17:16.3768850Z sage: y0.parent() is A13 ## line 476 ##
2025-02-16T18:17:16.3769268Z True
2025-02-16T18:17:16.3769575Z sage: A13.fusion_labels() ## line 481 ##
2025-02-16T18:17:16.3769998Z sage: fb ## line 482 ##
2025-02-16T18:17:16.3770343Z [A13(0), A13(1), A13(2), A13(3)]
2025-02-16T18:17:16.3770700Z sage: y0 ## line 484 ##
2025-02-16T18:17:16.3770997Z A13(0)
2025-02-16T18:17:16.3771493Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 486 ##
2025-02-16T18:17:16.3772274Z 0
2025-02-16T18:17:16.3772614Z sage: FusionRing("A2", 2).field() ## line 516 ##
2025-02-16T18:17:16.3773118Z Cyclotomic Field of order 60 and degree 16
2025-02-16T18:17:16.3773604Z sage: FusionRing("B2", 2).field() ## line 518 ##
2025-02-16T18:17:16.3774100Z Cyclotomic Field of order 40 and degree 16
2025-02-16T18:17:16.3774977Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 520 ##
2025-02-16T18:17:16.3775607Z 0
2025-02-16T18:17:16.3776122Z sage: A13 = FusionRing("A1", 3, fusion_labels='a', inject_variables=True) ## line 557 ##
2025-02-16T18:17:16.3776805Z sage: A13.fvars_field() ## line 558 ##
2025-02-16T18:17:16.3777281Z Cyclotomic Field of order 40 and degree 16
2025-02-16T18:17:16.3777744Z sage: A13.field() ## line 560 ##
2025-02-16T18:17:16.3808577Z Cyclotomic Field of order 40 and degree 16
2025-02-16T18:17:16.3809049Z sage: a2**4 ## line 562 ##
2025-02-16T18:17:16.3809557Z 2*a0 + 3*a2
2025-02-16T18:17:16.3809870Z sage: A13.field() ## line 569 ##
2025-02-16T18:17:16.3810333Z Cyclotomic Field of order 40 and degree 16
2025-02-16T18:17:16.3811020Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 576 ##
2025-02-16T18:17:16.3811621Z 0
2025-02-16T18:17:16.3811951Z sage: A11 = FusionRing("A1", 1) ## line 591 ##
2025-02-16T18:17:16.3812413Z sage: A11.field() ## line 592 ##
2025-02-16T18:17:16.3812862Z Cyclotomic Field of order 24 and degree 8
2025-02-16T18:17:16.3813316Z sage: for n in [1..7]:
2025-02-16T18:17:16.3813647Z     try:
2025-02-16T18:17:16.3813959Z         print(n, A11.root_of_unity(2/n))
2025-02-16T18:17:16.3814399Z     except ValueError as err:
2025-02-16T18:17:16.3814800Z         print(n, err) ## line 594 ##
2025-02-16T18:17:16.3815209Z 1 1
2025-02-16T18:17:16.3815479Z 2 -1
2025-02-16T18:17:16.3815764Z 3 zeta24^4 - 1
2025-02-16T18:17:16.3816090Z 4 zeta24^6
2025-02-16T18:17:16.3816405Z 5 not a root of unity in the field
2025-02-16T18:17:16.3816790Z 6 zeta24^4
2025-02-16T18:17:16.3817098Z 7 not a root of unity in the field
2025-02-16T18:17:16.3817672Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 606 ##
2025-02-16T18:17:16.3818499Z 0
2025-02-16T18:17:16.3818844Z sage: A15 = FusionRing("A1", 5) ## line 623 ##
2025-02-16T18:17:16.3819328Z sage: w = A15.get_order(); w ## line 624 ##
2025-02-16T18:17:16.3819834Z [(0, 0), (1/2, -1/2), (1, -1), (3/2, -3/2), (2, -2), (5/2, -5/2)]
2025-02-16T18:17:16.3820440Z sage: A15.set_order([w[k] for k in [0, 4, 1, 3, 5, 2]]) ## line 626 ##
2025-02-16T18:17:16.3821093Z sage: [A15(x) for x in A15.get_order()] ## line 627 ##
2025-02-16T18:17:16.3821615Z [A15(0), A15(4), A15(1), A15(3), A15(5), A15(2)]
2025-02-16T18:17:16.3822252Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 637 ##
2025-02-16T18:17:16.3822844Z 0
2025-02-16T18:17:16.3823157Z sage: D41 = FusionRing('D4', 1) ## line 648 ##
2025-02-16T18:17:16.3823662Z sage: D41.some_elements() ## line 649 ##
2025-02-16T18:17:16.3824139Z [D41(1,0,0,0), D41(0,0,1,0), D41(0,0,0,1)]
2025-02-16T18:17:16.3824749Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 651 ##
2025-02-16T18:17:16.3825334Z 0
2025-02-16T18:17:16.3825635Z sage: B22 = FusionRing('B2', 2) ## line 661 ##
2025-02-16T18:17:16.3826103Z sage: B22.fusion_level() ## line 662 ##
2025-02-16T18:17:16.3826528Z 2
2025-02-16T18:17:16.3827035Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 664 ##
2025-02-16T18:17:16.3827663Z 0
2025-02-16T18:17:16.3828184Z sage: B22 = FusionRing('B2', 2) ## line 680 ##
2025-02-16T18:17:16.3828692Z sage: B22.fusion_l() ## line 681 ##
2025-02-16T18:17:16.3829098Z 10
2025-02-16T18:17:16.3829422Z sage: D52 = FusionRing('D5', 2) ## line 683 ##
2025-02-16T18:17:16.3829890Z sage: D52.fusion_l() ## line 684 ##
2025-02-16T18:17:16.3830289Z 10
2025-02-16T18:17:16.3830775Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 686 ##
2025-02-16T18:17:16.3831370Z 0
2025-02-16T18:17:16.3831834Z sage: R = FusionRing("A1", 2) ## line 717 ##
2025-02-16T18:17:16.3832384Z sage: c = R.virasoro_central_charge(); c ## line 718 ##
2025-02-16T18:17:16.3832880Z 3/2
2025-02-16T18:17:16.3833213Z sage: Dp = R.D_plus(); Dp ## line 720 ##
2025-02-16T18:17:16.3833650Z 2*zeta32^6
2025-02-16T18:17:16.3833967Z sage: Dm = R.D_minus(); Dm ## line 722 ##
2025-02-16T18:17:16.3834410Z -2*zeta32^10
2025-02-16T18:17:16.3835012Z sage: Dp / Dm == R.root_of_unity(c/2) ## line 724 ##
2025-02-16T18:17:16.3835499Z True
2025-02-16T18:17:16.3835978Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 726 ##
2025-02-16T18:17:16.3836603Z 0
2025-02-16T18:17:16.3836980Z sage: FusionRing("A2", 1).conj_matrix() ## line 737 ##
2025-02-16T18:17:16.3837466Z [1 0 0]
2025-02-16T18:17:16.3837754Z [0 0 1]
2025-02-16T18:17:16.3838205Z [0 1 0]
2025-02-16T18:17:16.3838693Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 741 ##
2025-02-16T18:17:16.3839434Z 0
2025-02-16T18:17:16.3839734Z sage: B21=FusionRing("B2", 1) ## line 752 ##
2025-02-16T18:17:16.3840267Z sage: [x.twist() for x in B21.basis().list()] ## line 753 ##
2025-02-16T18:17:16.3840746Z [0, 1, 5/8]
2025-02-16T18:17:16.3841223Z sage: [B21.root_of_unity(x.twist()) for x in B21.basis().list()] ## line 755 ##
2025-02-16T18:17:16.3841856Z [1, -1, zeta32^10]
2025-02-16T18:17:16.3842212Z sage: B21.twists_matrix() ## line 757 ##
2025-02-16T18:17:16.3842655Z [        1         0         0]
2025-02-16T18:17:16.3843003Z [        0        -1         0]
2025-02-16T18:17:16.3843350Z [        0         0 zeta32^10]
2025-02-16T18:17:16.3843897Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 761 ##
2025-02-16T18:17:16.3844459Z 0
2025-02-16T18:17:16.3844780Z sage: G23 = FusionRing("G2", 3) ## line 781 ##
2025-02-16T18:17:16.3845240Z sage: G23.fusion_labels("g") ## line 782 ##
2025-02-16T18:17:16.3845696Z sage: b = G23.basis().list(); b ## line 783 ##
2025-02-16T18:17:16.3846141Z [g0, g1, g2, g3, g4, g5]
2025-02-16T18:17:16.3846660Z sage: [(x, y, z) for x in b for y in b for z in b if G23.N_ijk(x, y, z) > 1] ## line 785 ##
2025-02-16T18:17:16.3847295Z [(g3, g3, g3), (g3, g3, g4), (g3, g4, g3), (g4, g3, g3)]
2025-02-16T18:17:16.3888432Z sage: all(G23.N_ijk(x, y, z)==G23.N_ijk(y, z, x) for x in b for y in b for z in b) ## line 787 ##
2025-02-16T18:17:16.3889164Z True
2025-02-16T18:17:16.3889705Z sage: all(G23.N_ijk(x, y, z)==G23.N_ijk(y, x, z) for x in b for y in b for z in b) ## line 789 ##
2025-02-16T18:17:16.3890334Z True
2025-02-16T18:17:16.3890831Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 791 ##
2025-02-16T18:17:16.3891451Z 0
2025-02-16T18:17:16.3891790Z sage: A22 = FusionRing("A2", 2) ## line 807 ##
2025-02-16T18:17:16.3892253Z sage: b = A22.basis().list() ## line 808 ##
2025-02-16T18:17:16.3892832Z sage: all(x*y == sum(A22.Nk_ij(x, y, k)*k for k in b) for x in b for y in b) ## line 809 ##
2025-02-16T18:17:16.3893392Z True
2025-02-16T18:17:16.3893852Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 811 ##
2025-02-16T18:17:16.3894442Z 0
2025-02-16T18:17:16.3894757Z sage: G21 = FusionRing("G2", 1) ## line 841 ##
2025-02-16T18:17:16.3895196Z sage: b = G21.basis() ## line 842 ##
2025-02-16T18:17:16.3895666Z sage: [G21.s_ij(x, y) for x in b for y in b] ## line 843 ##
2025-02-16T18:17:16.3896270Z [1, -zeta60^14 + zeta60^6 + zeta60^4, -zeta60^14 + zeta60^6 + zeta60^4, -1]
2025-02-16T18:17:16.3897020Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 845 ##
2025-02-16T18:17:16.3897592Z 0
2025-02-16T18:17:16.3898110Z sage: G21 = FusionRing("G2", 1) ## line 863 ##
2025-02-16T18:17:16.3898544Z sage: b = G21.basis() ## line 864 ##
2025-02-16T18:17:16.3899039Z sage: [G21.s_ijconj(x, y) for x in b for y in b] ## line 865 ##
2025-02-16T18:17:16.3899658Z [1, -zeta60^14 + zeta60^6 + zeta60^4, -zeta60^14 + zeta60^6 + zeta60^4, -1]
2025-02-16T18:17:16.3900238Z sage: E62 = FusionRing("E6", 2) ## line 873 ##
2025-02-16T18:17:16.3900804Z sage: E62.fusion_labels("e", inject_variables=True) ## line 874 ##
2025-02-16T18:17:16.3901703Z sage: E62.s_ij(e8, e1).conjugate() == E62.s_ijconj(e8, e1) ## line 875 ##
2025-02-16T18:17:16.3902231Z True
2025-02-16T18:17:16.3902552Z sage: F41 = FusionRing("F4", 1) ## line 877 ##
2025-02-16T18:17:16.3903024Z sage: fmats = F41.get_fmatrix() ## line 878 ##
2025-02-16T18:17:16.3903818Z sage: fmats.find_orthogonal_solution(verbose=False) ## line 879 ##
2025-02-16T18:17:16.3904394Z sage: b = F41.basis() ## line 880 ##
2025-02-16T18:17:16.3905181Z sage: all(F41.s_ijconj(x, y) == F41._basecoer(F41.s_ij(x, y, base_coercion=False).conjugate()) for x in b for y in b) ## line 881 ##
2025-02-16T18:17:16.3905953Z True
2025-02-16T18:17:16.3906266Z sage: G22 = FusionRing("G2", 2) ## line 883 ##
2025-02-16T18:17:16.3906735Z sage: fmats = G22.get_fmatrix() ## line 884 ##
2025-02-16T18:17:16.3907347Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 889 ##
2025-02-16T18:17:16.3908123Z 0
2025-02-16T18:17:16.3908582Z sage: D91 = FusionRing("D9", 1) ## line 909 ##
2025-02-16T18:17:16.3909035Z sage: D91.s_matrix() ## line 910 ##
2025-02-16T18:17:16.3909437Z [          1           1           1           1]
2025-02-16T18:17:16.3909859Z [          1           1          -1          -1]
2025-02-16T18:17:16.3910288Z [          1          -1 -zeta136^34  zeta136^34]
2025-02-16T18:17:16.3910724Z [          1          -1  zeta136^34 -zeta136^34]
2025-02-16T18:17:16.3911215Z sage: S = D91.s_matrix(unitary=True); S ## line 915 ##
2025-02-16T18:17:16.3911705Z [            1/2             1/2             1/2             1/2]
2025-02-16T18:17:16.3912172Z [            1/2             1/2            -1/2            -1/2]
2025-02-16T18:17:16.3912630Z [            1/2            -1/2 -1/2*zeta136^34  1/2*zeta136^34]
2025-02-16T18:17:16.3913088Z [            1/2            -1/2  1/2*zeta136^34 -1/2*zeta136^34]
2025-02-16T18:17:16.3913550Z sage: S*S.conjugate() ## line 920 ##
2025-02-16T18:17:16.3913938Z [1 0 0 0]
2025-02-16T18:17:16.3914210Z [0 1 0 0]
2025-02-16T18:17:16.3914475Z [0 0 1 0]
2025-02-16T18:17:16.3914736Z [0 0 0 1]
2025-02-16T18:17:16.3915200Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 925 ##
2025-02-16T18:17:16.3915785Z 0
2025-02-16T18:17:16.3916215Z sage: I = FusionRing("E8", 2, conjugate=True)  # Ising MTC ## line 966 ##
2025-02-16T18:17:16.3916929Z sage: I.fusion_labels(["i0", "p", "s"], inject_variables=True) ## line 967 ##
2025-02-16T18:17:16.3917605Z sage: I.r_matrix(s, s, i0) == I.root_of_unity(-1/8) ## line 968 ##
2025-02-16T18:17:16.3918463Z True
2025-02-16T18:17:16.3918778Z sage: I.r_matrix(p, p, i0) ## line 970 ##
2025-02-16T18:17:16.3919159Z -1
2025-02-16T18:17:16.3919526Z sage: I.r_matrix(p, s, s) == I.root_of_unity(-1/2) ## line 972 ##
2025-02-16T18:17:16.3919998Z True
2025-02-16T18:17:16.3920369Z sage: I.r_matrix(s, p, s) == I.root_of_unity(-1/2) ## line 974 ##
2025-02-16T18:17:16.3920858Z True
2025-02-16T18:17:16.3921223Z sage: I.r_matrix(s, s, p) == I.root_of_unity(3/8) ## line 976 ##
2025-02-16T18:17:16.3921709Z True
2025-02-16T18:17:16.3922167Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 978 ##
2025-02-16T18:17:16.3922746Z 0
2025-02-16T18:17:16.3923134Z sage: FusionRing("E6", 1).global_q_dimension() ## line 1003 ##
2025-02-16T18:17:16.3923632Z 3
2025-02-16T18:17:16.3924090Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1005 ##
2025-02-16T18:17:16.3924674Z 0
2025-02-16T18:17:16.3924984Z sage: F = FusionRing("G2", 1) ## line 1021 ##
2025-02-16T18:17:16.3925459Z sage: tqo=F.total_q_order(); tqo ## line 1022 ##
2025-02-16T18:17:16.3925964Z zeta60^15 - zeta60^11 - zeta60^9 + 2*zeta60^3 + zeta60
2025-02-16T18:17:16.3926457Z sage: tqo.is_real_positive() ## line 1024 ##
2025-02-16T18:17:16.3926861Z True
2025-02-16T18:17:16.3927200Z sage: tqo^2 == F.global_q_dimension() ## line 1026 ##
2025-02-16T18:17:16.3927642Z True
2025-02-16T18:17:16.3928269Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1028 ##
2025-02-16T18:17:16.3928995Z 0
2025-02-16T18:17:16.3929303Z sage: B31 = FusionRing("B3", 1) ## line 1044 ##
2025-02-16T18:17:16.3929762Z sage: Dp = B31.D_plus(); Dp ## line 1045 ##
2025-02-16T18:17:16.3930188Z 2*zeta48^13 - 2*zeta48^5
2025-02-16T18:17:16.3930561Z sage: Dm = B31.D_minus(); Dm ## line 1047 ##
2025-02-16T18:17:16.3930954Z -2*zeta48^3
2025-02-16T18:17:16.3931308Z sage: Dp*Dm == B31.global_q_dimension() ## line 1049 ##
2025-02-16T18:17:16.3931942Z True
2025-02-16T18:17:16.3932315Z sage: c = B31.virasoro_central_charge(); c ## line 1051 ##
2025-02-16T18:17:16.3932775Z 7/2
2025-02-16T18:17:16.3933099Z sage: Dp/Dm == B31.root_of_unity(c/2) ## line 1053 ##
2025-02-16T18:17:16.3933529Z True
2025-02-16T18:17:16.3933982Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1055 ##
2025-02-16T18:17:16.3934554Z 0
2025-02-16T18:17:16.3934930Z sage: E83 = FusionRing("E8", 3, conjugate=True) ## line 1070 ##
2025-02-16T18:17:16.3935507Z sage: [Dp, Dm] = [E83.D_plus(), E83.D_minus()] ## line 1071 ##
2025-02-16T18:17:16.3936183Z sage: Dp*Dm == E83.global_q_dimension() ## line 1072 ##
2025-02-16T18:17:16.3936622Z True
2025-02-16T18:17:16.3936967Z sage: c = E83.virasoro_central_charge(); c ## line 1074 ##
2025-02-16T18:17:16.3937428Z -248/11
2025-02-16T18:17:16.3937761Z sage: Dp*Dm == E83.global_q_dimension() ## line 1076 ##
2025-02-16T18:17:16.3938357Z True
2025-02-16T18:17:16.3938820Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1078 ##
2025-02-16T18:17:16.3939384Z 0
2025-02-16T18:17:16.3939950Z sage: [FusionRing(ct, k).is_multiplicity_free() for ct in ("A1", "A2", "B2", "C3") for k in (1, 2, 3)] ## line 1094 ##
2025-02-16T18:17:16.3940804Z [True, True, True, True, True, False, True, True, False, True, False, False]
2025-02-16T18:17:16.3941592Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1096 ##
2025-02-16T18:17:16.3942158Z 0
2025-02-16T18:17:16.3942468Z sage: A14 = FusionRing("A1", 4) ## line 1162 ##
2025-02-16T18:17:16.3942917Z sage: A14.get_order() ## line 1163 ##
2025-02-16T18:17:16.3943329Z [(0, 0), (1/2, -1/2), (1, -1), (3/2, -3/2), (2, -2)]
2025-02-16T18:17:16.3943998Z sage: A14.fusion_labels(["zero", "one", "two", "three", "four"], inject_variables=True) ## line 1165 ##
2025-02-16T18:17:16.3944705Z sage: [A14(x) for x in A14.get_order()] ## line 1166 ##
2025-02-16T18:17:16.3945171Z [zero, one, two, three, four]
2025-02-16T18:17:16.3945654Z sage: A14.get_computational_basis(one, two, 4) ## line 1168 ##
2025-02-16T18:17:16.3946178Z [(two, two), (two, zero), (zero, two)]
2025-02-16T18:17:16.3946746Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1170 ##
2025-02-16T18:17:16.3947308Z 0
2025-02-16T18:17:16.3947617Z sage: A15 = FusionRing("A1", 5) ## line 1193 ##
2025-02-16T18:17:16.3948210Z sage: A15.get_fmatrix() ## line 1194 ##
2025-02-16T18:17:16.3948885Z F-Matrix factory for The Fusion Ring of Type A1 and level 5 with Integer Ring coefficients
2025-02-16T18:17:16.3949695Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1196 ##
2025-02-16T18:17:16.3950264Z 0
2025-02-16T18:17:16.3950579Z sage: FR = FusionRing("A1", 4) ## line 1232 ##
2025-02-16T18:17:16.3951248Z sage: FR.fusion_labels(['idd', 'one', 'two', 'three', 'four'], inject_variables=True) ## line 1233 ##
2025-02-16T18:17:16.3951930Z sage: fmats = FR.get_fmatrix() ## line 1234 ##
2025-02-16T18:17:16.3952382Z sage: FR = FusionRing("A1", 2) ## line 1238 ##
2025-02-16T18:17:16.3952936Z sage: FR.fusion_labels("a", inject_variables=True) ## line 1239 ##
2025-02-16T18:17:16.3953501Z sage: fmats = FR.get_fmatrix() ## line 1240 ##
2025-02-16T18:17:16.3954080Z sage: fmats.find_orthogonal_solution(verbose=False) ## line 1241 ##
2025-02-16T18:17:16.3954709Z sage: len(FR._emap('odd_one_out', (a1, a1, 7))) ## line 1242 ##
2025-02-16T18:17:16.3955177Z 16
2025-02-16T18:17:16.3955617Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1244 ##
2025-02-16T18:17:16.3956174Z 0
2025-02-16T18:17:16.3956478Z sage: A14 = FusionRing("A1", 4) ## line 1327 ##
2025-02-16T18:17:16.3957049Z sage: A14.get_order() ## line 1328 ##
2025-02-16T18:17:16.3957464Z [(0, 0), (1/2, -1/2), (1, -1), (3/2, -3/2), (2, -2)]
2025-02-16T18:17:16.3958266Z sage: A14.fusion_labels(["one", "two", "three", "four", "five"], inject_variables=True) ## line 1330 ##
2025-02-16T18:17:16.3958974Z sage: [A14(x) for x in A14.get_order()] ## line 1331 ##
2025-02-16T18:17:16.3959618Z [one, two, three, four, five]
2025-02-16T18:17:16.3959999Z sage: two ** 5 ## line 1333 ##
2025-02-16T18:17:16.3960352Z 5*two + 4*four
2025-02-16T18:17:16.3960819Z sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 1340 ##
2025-02-16T18:17:16.3961386Z 0
2025-02-16T18:17:16.3961854Z sage: F41 = FusionRing("F4", 1, fusion_labels='f', inject_variables=True) ## line 1400 ##
2025-02-16T18:17:16.3962461Z sage: f1*f1 ## line 1401 ##
2025-02-16T18:17:16.3962798Z f0 + f1
2025-02-16T18:17:16.3963258Z sage: comp, sig = F41.get_braid_generators(f1, f0, 4, verbose=False) ## line 1403 ##
2025-02-16T18:17:16.3964038Z ------------------------------------------------------------------------
2025-02-16T18:17:16.3965146Z /home/runner/miniconda3/envs/sage-dev/lib/python3.11/site-packages/cysignals/signals.cpython-311-x86_64-linux-gnu.so(+0x795d)[0x7f736474595d]
2025-02-16T18:17:16.3966769Z /home/runner/miniconda3/envs/sage-dev/lib/python3.11/site-packages/cysignals/signals.cpython-311-x86_64-linux-gnu.so(+0x7a1b)[0x7f7364745a1b]
2025-02-16T18:17:16.3968510Z /home/runner/miniconda3/envs/sage-dev/lib/python3.11/site-packages/cysignals/signals.cpython-311-x86_64-linux-gnu.so(+0x9f62)[0x7f7364747f62]
2025-02-16T18:17:16.3969588Z /lib/x86_64-linux-gnu/libc.so.6(+0x45330)[0x7f7365645330]
2025-02-16T18:17:16.3970408Z /home/runner/miniconda3/envs/sage-dev/lib/libgmp.so.10(__gmpn_mul_basecase_zen+0x32e)[0x7f7364e4b28e]
2025-02-16T18:17:16.3971241Z ------------------------------------------------------------------------
2025-02-16T18:17:16.3971742Z Attaching gdb to process id 47801.
2025-02-16T18:17:16.3972621Z /home/runner/miniconda3/envs/sage-dev/bin/cysignals-CSI:86: DeprecationWarning: Use shutil.which instead of find_executable
2025-02-16T18:17:16.3973545Z   whichgdb = find_executable('gdb')
2025-02-16T18:17:16.3973952Z Cannot find gdb installed
2025-02-16T18:17:16.3974295Z GDB is not installed.
2025-02-16T18:17:16.3974649Z Install gdb for enhanced tracebacks.
2025-02-16T18:17:16.3975137Z ------------------------------------------------------------------------
2025-02-16T18:17:16.3975500Z 
2025-02-16T18:17:16.3975655Z **********************************************************************