n=4 R=150: {'points': 10743, 'states': 694830, 'Nodd': 3577, 'Neven': 7166, 'rule_ok': 10743, 'both_multiples': 3, 'plain_unique': 10742, 'plain_two': 1, 'dict_ok': 10743, 'def11_ok': 10743, 'central_ok': 10743, 'A0': 7168, 'A0_evenN': 7166, 'maxN': 211} types {0: 7168, 1: 3575}  [4.5s]
n=4: the 10743 reachable points and their types agree with the description of the source (p,q coprime; A_1 iff both odd)
n=5 R=150: {'points': 11637, 'states': 546551, 'Nodd': 3376, 'Neven': 8261, 'rule_ok': 11637, 'both_multiples': 4, 'plain_unique': 11635, 'plain_two': 2, 'dict_ok': 11637, 'def11_ok': 11637, 'central_ok': 11637, 'A0': 6601, 'A0_evenN': 6599, 'maxN': 184} types {0: 6601, 1: 2518, 2: 2518}  [4.1s]
n=6 R=150: {'points': 11887, 'states': 446108, 'Nodd': 3659, 'Neven': 8228, 'rule_ok': 11887, 'both_multiples': 5, 'plain_unique': 11884, 'plain_two': 3, 'dict_ok': 11887, 'def11_ok': 11887, 'central_ok': 11887, 'A0': 6210, 'A0_evenN': 6208, 'maxN': 172} types {0: 6210, 1: 2065, 2: 1547, 3: 2065}  [3.6s]
n=6: the 11887 reachable points and their types agree with the description of the source (Sect. 2.3)
n=7 R=150: {'points': 12029, 'states': 376681, 'Nodd': 3526, 'Neven': 8503, 'rule_ok': 12029, 'both_multiples': 6, 'plain_unique': 12025, 'plain_two': 4, 'dict_ok': 12029, 'def11_ok': 12029, 'central_ok': 12029, 'A0': 5981, 'A0_evenN': 5979, 'maxN': 164} types {0: 5981, 1: 1844, 2: 1180, 3: 1180, 4: 1844}  [3.7s]
n=8 R=150: {'points': 11949, 'states': 327066, 'Nodd': 3535, 'Neven': 8414, 'rule_ok': 11949, 'both_multiples': 7, 'plain_unique': 11944, 'plain_two': 5, 'dict_ok': 11949, 'def11_ok': 11949, 'central_ok': 11949, 'A0': 5768, 'A0_evenN': 5766, 'maxN': 160} types {0: 5768, 1: 1687, 2: 987, 3: 833, 4: 987, 5: 1687}  [3.5s]
n=9 R=150: {'points': 11967, 'states': 291155, 'Nodd': 3496, 'Neven': 8471, 'rule_ok': 11967, 'both_multiples': 8, 'plain_unique': 11961, 'plain_two': 6, 'dict_ok': 11967, 'def11_ok': 11967, 'central_ok': 11967, 'A0': 5639, 'A0_evenN': 5637, 'maxN': 158} types {0: 5639, 1: 1596, 2: 886, 3: 682, 4: 682, 5: 886, 6: 1596}  [3.3s]
n=10 R=150: {'points': 11839, 'states': 264698, 'Nodd': 3487, 'Neven': 8352, 'rule_ok': 11839, 'both_multiples': 9, 'plain_unique': 11832, 'plain_two': 7, 'dict_ok': 11839, 'def11_ok': 11839, 'central_ok': 11839, 'A0': 5530, 'A0_evenN': 5528, 'maxN': 156} types {0: 5530, 1: 1525, 2: 795, 3: 575, 4: 519, 5: 575, 6: 795, 7: 1525}  [3.2s]
n=11 R=150: {'points': 11757, 'states': 244165, 'Nodd': 3462, 'Neven': 8295, 'rule_ok': 11757, 'both_multiples': 10, 'plain_unique': 11749, 'plain_two': 8, 'dict_ok': 11757, 'def11_ok': 11757, 'central_ok': 11757, 'A0': 5417, 'A0_evenN': 5415, 'maxN': 154} types {0: 5417, 1: 1462, 2: 742, 3: 522, 4: 444, 5: 444, 6: 522, 7: 742, 8: 1462}  [3.5s]
n=12 R=150: {'points': 11753, 'states': 228454, 'Nodd': 3495, 'Neven': 8258, 'rule_ok': 11753, 'both_multiples': 11, 'plain_unique': 11744, 'plain_two': 9, 'dict_ok': 11753, 'def11_ok': 11753, 'central_ok': 11753, 'A0': 5348, 'A0_evenN': 5346, 'maxN': 154} types {0: 5348, 1: 1429, 2: 713, 3: 489, 4: 391, 5: 361, 6: 391, 7: 489, 8: 713, 9: 1429}  [3.1s]
n=4 R=120: {'points': 6875, 'states': 357216, 'Nodd': 2293, 'Neven': 4582, 'rule_ok': 6875, 'both_multiples': 3, 'plain_unique': 6874, 'plain_two': 1, 'dict_ok': 6875, 'def11_ok': 6875, 'central_ok': 6875, 'A0': 4584, 'A0_evenN': 4582, 'maxN': 168} types {0: 4584, 1: 2291}  [2.4s]
n=4: the 6875 reachable points and their types agree with the description of the source (p,q coprime; A_1 iff both odd)
n=6 R=120: {'points': 7605, 'states': 229538, 'Nodd': 2373, 'Neven': 5232, 'rule_ok': 7605, 'both_multiples': 5, 'plain_unique': 7602, 'plain_two': 3, 'dict_ok': 7605, 'def11_ok': 7605, 'central_ok': 7605, 'A0': 3970, 'A0_evenN': 3968, 'maxN': 136} types {0: 3970, 1: 1321, 2: 993, 3: 1321}  [1.9s]
n=6: the 7605 reachable points and their types agree with the description of the source (Sect. 2.3)
n=4 R=30: {'points': 427, 'states': 5942, 'Nodd': 147, 'Neven': 280, 'rule_ok': 427, 'both_multiples': 3, 'plain_unique': 426, 'plain_two': 1, 'dict_ok': 427, 'def11_ok': 427, 'central_ok': 427, 'A0': 282, 'A0_evenN': 280, 'maxN': 41} types {0: 282, 1: 145}  [0.1s]
n=4: the 427 reachable points and their types agree with the description of the source (p,q coprime; A_1 iff both odd)
n=6 R=40: {'points': 841, 'states': 8992, 'Nodd': 267, 'Neven': 574, 'rule_ok': 841, 'both_multiples': 5, 'plain_unique': 838, 'plain_two': 3, 'dict_ok': 841, 'def11_ok': 841, 'central_ok': 841, 'A0': 444, 'A0_evenN': 442, 'maxN': 44} types {0: 444, 1: 145, 2: 107, 3: 145}  [0.1s]
n=6: the 841 reachable points and their types agree with the description of the source (Sect. 2.3)
n=13 R=60: {'points': 1843, 'states': 15193, 'Nodd': 620, 'Neven': 1223, 'rule_ok': 1843, 'both_multiples': 12, 'plain_unique': 1833, 'plain_two': 10, 'dict_ok': 1843, 'def11_ok': 1843, 'central_ok': 1843, 'A0': 843, 'A0_evenN': 841, 'maxN': 60} types {0: 843, 1: 222, 2: 106, 3: 74, 4: 52, 5: 46, 6: 46, 7: 52, 8: 74, 9: 106, 10: 222}  [0.4s]
n=14 R=60: {'points': 1853, 'states': 14674, 'Nodd': 631, 'Neven': 1222, 'rule_ok': 1853, 'both_multiples': 13, 'plain_unique': 1842, 'plain_two': 11, 'dict_ok': 1853, 'def11_ok': 1853, 'central_ok': 1853, 'A0': 840, 'A0_evenN': 838, 'maxN': 60} types {0: 840, 1: 217, 2: 107, 3: 69, 4: 49, 5: 43, 6: 43, 7: 43, 8: 49, 9: 69, 10: 107, 11: 217}  [0.3s]
n=15 R=60: {'points': 1849, 'states': 14141, 'Nodd': 634, 'Neven': 1215, 'rule_ok': 1849, 'both_multiples': 14, 'plain_unique': 1837, 'plain_two': 12, 'dict_ok': 1849, 'def11_ok': 1849, 'central_ok': 1849, 'A0': 821, 'A0_evenN': 819, 'maxN': 60} types {0: 821, 1: 222, 2: 100, 3: 64, 4: 46, 5: 42, 6: 40, 7: 40, 8: 42, 9: 46, 10: 64, 11: 100, 12: 222}  [0.3s]
n=16 R=60: {'points': 1885, 'states': 13814, 'Nodd': 639, 'Neven': 1246, 'rule_ok': 1885, 'both_multiples': 15, 'plain_unique': 1872, 'plain_two': 13, 'dict_ok': 1885, 'def11_ok': 1885, 'central_ok': 1885, 'A0': 832, 'A0_evenN': 830, 'maxN': 60} types {0: 832, 1: 225, 2: 103, 3: 63, 4: 45, 5: 41, 6: 33, 7: 33, 8: 33, 9: 41, 10: 45, 11: 63, 12: 103, 13: 225}  [0.4s]
n=17 R=60: {'points': 1877, 'states': 13481, 'Nodd': 652, 'Neven': 1225, 'rule_ok': 1877, 'both_multiples': 16, 'plain_unique': 1863, 'plain_two': 14, 'dict_ok': 1877, 'def11_ok': 1877, 'central_ok': 1877, 'A0': 821, 'A0_evenN': 819, 'maxN': 60} types {0: 821, 1: 218, 2: 102, 3: 58, 4: 46, 5: 36, 6: 34, 7: 34, 8: 34, 9: 34, 10: 36, 11: 46, 12: 58, 13: 102, 14: 218}  [0.4s]
n=18 R=60: {'points': 1843, 'states': 13120, 'Nodd': 643, 'Neven': 1200, 'rule_ok': 1843, 'both_multiples': 17, 'plain_unique': 1828, 'plain_two': 15, 'dict_ok': 1843, 'def11_ok': 1843, 'central_ok': 1843, 'A0': 818, 'A0_evenN': 816, 'maxN': 58} types {0: 818, 1: 211, 2: 95, 3: 57, 4: 45, 5: 35, 6: 33, 7: 25, 8: 23, 9: 25, 10: 33, 11: 35, 12: 45, 13: 57, 14: 95, 15: 211}  [0.4s]
n=20 R=60: {'points': 1817, 'states': 12602, 'Nodd': 637, 'Neven': 1180, 'rule_ok': 1817, 'both_multiples': 19, 'plain_unique': 1800, 'plain_two': 17, 'dict_ok': 1817, 'def11_ok': 1817, 'central_ok': 1817, 'A0': 802, 'A0_evenN': 800, 'maxN': 58} types {0: 802, 1: 211, 2: 93, 3: 55, 4: 47, 5: 31, 6: 21, 7: 21, 8: 19, 9: 19, 10: 19, 11: 21, 12: 21, 13: 31, 14: 47, 15: 55, 16: 93, 17: 211}  [0.4s]
n=24 R=40: {'points': 787, 'states': 3868, 'Nodd': 301, 'Neven': 486, 'rule_ok': 787, 'both_multiples': 23, 'plain_unique': 766, 'plain_two': 21, 'dict_ok': 787, 'def11_ok': 787, 'central_ok': 787, 'A0': 348, 'A0_evenN': 346, 'maxN': 38} types {0: 348, 1: 89, 2: 43, 3: 21, 4: 15, 5: 13, 6: 7, 7: 7, 8: 7, 9: 7, 10: 7, 11: 7, 12: 7, 13: 7, 14: 7, 15: 7, 16: 7, 17: 13, 18: 15, 19: 21, 20: 43, 21: 89}  [0.2s]
n=25 R=40: {'points': 791, 'states': 3843, 'Nodd': 308, 'Neven': 483, 'rule_ok': 791, 'both_multiples': 24, 'plain_unique': 769, 'plain_two': 22, 'dict_ok': 791, 'def11_ok': 791, 'central_ok': 791, 'A0': 343, 'A0_evenN': 341, 'maxN': 38} types {0: 343, 1: 90, 2: 43, 3: 21, 4: 15, 5: 13, 6: 7, 7: 7, 8: 7, 9: 7, 10: 7, 11: 7, 12: 7, 13: 7, 14: 7, 15: 7, 16: 7, 17: 7, 18: 13, 19: 15, 20: 21, 21: 43, 22: 90}  [0.2s]
n=30 R=40: {'points': 787, 'states': 3720, 'Nodd': 295, 'Neven': 492, 'rule_ok': 787, 'both_multiples': 29, 'plain_unique': 760, 'plain_two': 27, 'dict_ok': 787, 'def11_ok': 787, 'central_ok': 787, 'A0': 346, 'A0_evenN': 344, 'maxN': 38} types {0: 346, 1: 95, 2: 43, 3: 19, 4: 13, 5: 13, 6: 7, 7: 7, 8: 7, 9: 3, 10: 3, 11: 3, 12: 3, 13: 3, 14: 3, 15: 3, 16: 3, 17: 3, 18: 3, 19: 3, 20: 7, 21: 7, 22: 7, 23: 13, 24: 13, 25: 19, 26: 43, 27: 95}  [0.2s]
n=4, length <= 30: 427 reachable points; Definition 2.1 with the rule reproduces the type of the source's description for all 427; points with even N: 280; with the other convention 280 of them receive another type than in the source (280 of these: no line of the definition applies)
n=6, length <= 40: 841 reachable points; Definition 2.1 with the rule reproduces the type of the source's description for all 841; points with even N: 574; with the other convention 574 of them receive another type than in the source (287 of these: no line of the definition applies)
n=4, length <= 120: 6875 reachable points; Definition 2.1 with the rule reproduces the type of the source's description for all 6875; points with even N: 4582; with the other convention 4582 of them receive another type than in the source (4582 of these: no line of the definition applies)
n=6, length <= 120: 7605 reachable points; Definition 2.1 with the rule reproduces the type of the source's description for all 7605; points with even N: 5232; with the other convention 5232 of them receive another type than in the source (2616 of these: no line of the definition applies)
ALL CHECKS PASSED
n=4 R=60: 1721 reachable points, 3446 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 59.94 (N=83)  [1.1s]
n=5 R=60: 1855 reachable points, 11138 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 97.04 (N=91)  [2.8s]
n=6 R=60: 1905 reachable points, 7626 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 119.82 (N=101)  [1.7s]
n=7 R=60: 1931 reachable points, 19322 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 134.79 (N=89)  [4.4s]
n=8 R=60: 1925 reachable points, 11558 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 144.60 (N=78)  [2.6s]
n=9 R=60: 1903 reachable points, 26658 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 172.68 (N=88)  [5.9s]
n=10 R=60: 1907 reachable points, 15266 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 194.08 (N=89)  [3.4s]
n=11 R=60: 1865 reachable points, 33590 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 210.51 (N=85)  [8.5s]
n=12 R=60: 1883 reachable points, 18842 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 223.83 (N=80)  [4.2s]
n=13 R=30: 471 reachable points, 10386 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 123.85 (N=37)  [1.8s]
n=16 R=30: 465 reachable points, 6526 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 150.44 (N=42)  [1.3s]
n=15 R=16: 125 reachable points, 3278 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 75.68 (N=19)  [0.4s]
n=21 R=20: 197 reachable points, 7526 instances (point, l, eps): parallel trajectory exists, type A_(eps k - l), length ratio sin((k+1)pi/n):sin((k'+1)pi/n) exact; longest traced 125.76 (N=21)  [1.3s]
n=5: 133 reachable points of length <= 15.812 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 53 ; pairs of types: {(0, 0): 19, (0, 2): 17, (1, 0): 17}
unitary pairs: 19 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 38 lines (u+tv and v+tu for the unitary pairs); 188 reachable points on them inside the disc; predicted 188; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 201, not reachable or wrong type 0; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', -2): 1, ('a', -1): 2, ('a', 0): 15, ('a', 1): 19, ('a', 2): 19, ('a', 3): 19, ('a', 4): 19, ('b', -3): 1, ('b', -2): 2, ('b', -1): 9, ('b', 0): 19, ('b', 1): 19, ('b', 2): 19, ('b', 3): 19, ('b', 4): 19}
Theorem F(b): reachable points of type != A_0 and length <= 9: 16 ; vertex of no reachable n-gon: 6 (37.5%), of exactly one: 10, of more: 0
  shortest points which are vertices of none: |w|=4.0406 type A_1 N=3; |w|=4.0406 type A_2 N=3; |w|=6.6138 type A_1 N=5; |w|=6.6138 type A_2 N=5
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 4.0406, N = 3, type A_2 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 5 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 15.81: min 4, max 7
ALL CHECKS PASSED  [0.1s]
n=6: 183 reachable points of length <= 18.500 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 47 ; pairs of types: {(0, 0): 17, (0, 3): 15, (1, 0): 15}
unitary pairs: 17 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 34 lines (u+tv and v+tu for the unitary pairs); 176 reachable points on them inside the disc; predicted 176; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 184, not reachable or wrong type 163; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 13, ('b', -1): 8}
Theorem F(b): reachable points of type != A_0 and length <= 9: 21 ; vertex of no reachable n-gon: 10 (47.6%), of exactly one: 11, of more: 0
  shortest points which are vertices of none: |w|=4.5826 type A_3 N=3; |w|=4.5826 type A_1 N=3; |w|=5.2915 type A_2 N=3; |w|=5.2915 type A_2 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 4.5826, N = 3, type A_3 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 6 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 18.50: min 2, max 7
n=6: X_2 = (1,2), w_6 = (5,4), mirror image (4,5): as in Example 6.2
ALL CHECKS PASSED  [0.1s]
n=7: 241 reachable points of length <= 21.243 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 41 ; pairs of types: {(0, 0): 13, (0, 4): 14, (1, 0): 14}
unitary pairs: 13 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 26 lines (u+tv and v+tu for the unitary pairs); 142 reachable points on them inside the disc; predicted 142; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 137, not reachable or wrong type 121; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 10, ('b', -1): 6}
Theorem F(b): reachable points of type != A_0 and length <= 9: 26 ; vertex of no reachable n-gon: 14 (53.8%), of exactly one: 12, of more: 0
  shortest points which are vertices of none: |w|=4.9328 type A_1 N=3; |w|=4.9328 type A_4 N=3; |w|=6.1511 type A_2 N=3; |w|=6.1511 type A_3 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 4.9328, N = 3, type A_4 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 6 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 21.24: min 2, max 7
ALL CHECKS PASSED  [0.1s]
n=8: 307 reachable points of length <= 24.018 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 35 ; pairs of types: {(0, 0): 11, (0, 5): 12, (1, 0): 12}
unitary pairs: 11 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 22 lines (u+tv and v+tu for the unitary pairs); 144 reachable points on them inside the disc; predicted 144; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 117, not reachable or wrong type 104; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 8, ('b', -1): 5}
Theorem F(b): reachable points of type != A_0 and length <= 9: 23 ; vertex of no reachable n-gon: 12 (52.2%), of exactly one: 11, of more: 0
  shortest points which are vertices of none: |w|=5.1699 type A_5 N=3; |w|=5.1699 type A_1 N=3; |w|=6.7548 type A_4 N=3; |w|=6.7548 type A_2 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.1699, N = 3, type A_5 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 24.02: min 6, max 8
ALL CHECKS PASSED  [0.1s]
n=9: 379 reachable points of length <= 26.814 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 35 ; pairs of types: {(0, 0): 11, (0, 6): 12, (1, 0): 12}
unitary pairs: 11 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 22 lines (u+tv and v+tu for the unitary pairs); 150 reachable points on them inside the disc; predicted 150; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 117, not reachable or wrong type 104; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 8, ('b', -1): 5}
Theorem F(b): reachable points of type != A_0 and length <= 9: 26 ; vertex of no reachable n-gon: 14 (53.8%), of exactly one: 12, of more: 0
  shortest points which are vertices of none: |w|=5.3370 type A_6 N=3; |w|=5.3370 type A_1 N=3; |w|=7.1905 type A_2 N=3; |w|=7.1905 type A_5 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.3370, N = 3, type A_6 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 26.81: min 6, max 8
ALL CHECKS PASSED  [0.2s]
n=10: 463 reachable points of length <= 29.625 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 31 ; pairs of types: {(0, 0): 11, (0, 7): 10, (1, 0): 10}
unitary pairs: 11 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 22 lines (u+tv and v+tu for the unitary pairs); 162 reachable points on them inside the disc; predicted 162; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 117, not reachable or wrong type 104; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 8, ('b', -1): 5}
Theorem F(b): reachable points of type != A_0 and length <= 9: 23 ; vertex of no reachable n-gon: 12 (52.2%), of exactly one: 11, of more: 0
  shortest points which are vertices of none: |w|=5.4588 type A_7 N=3; |w|=5.4588 type A_1 N=3; |w|=7.5134 type A_6 N=3; |w|=7.5134 type A_6 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.4588, N = 3, type A_7 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 29.62: min 6, max 9
ALL CHECKS PASSED  [0.2s]
n=11: 547 reachable points of length <= 32.445 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 31 ; pairs of types: {(0, 0): 11, (0, 8): 10, (1, 0): 10}
unitary pairs: 11 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 22 lines (u+tv and v+tu for the unitary pairs); 174 reachable points on them inside the disc; predicted 174; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 117, not reachable or wrong type 104; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 8, ('b', -1): 5}
Theorem F(b): reachable points of type != A_0 and length <= 9: 20 ; vertex of no reachable n-gon: 8 (40.0%), of exactly one: 12, of more: 0
  shortest points which are vertices of none: |w|=5.5502 type A_8 N=3; |w|=5.5502 type A_1 N=3; |w|=7.7584 type A_7 N=3; |w|=7.7584 type A_2 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.5502, N = 3, type A_8 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 32.45: min 6, max 10
ALL CHECKS PASSED  [0.3s]
n=12: 651 reachable points of length <= 35.273 (R1=9, Rpair=9)
pairs (u,v) of reachable points of length <= 9 with det(u,v) = S: 31 ; pairs of types: {(0, 0): 11, (0, 9): 10, (1, 0): 10}
unitary pairs: 11 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 22 lines (u+tv and v+tu for the unitary pairs); 182 reachable points on them inside the disc; predicted 182; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 117, not reachable or wrong type 104; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 8, ('b', -1): 5}
Theorem F(b): reachable points of type != A_0 and length <= 9: 21 ; vertex of no reachable n-gon: 8 (38.1%), of exactly one: 13, of more: 0
  shortest points which are vertices of none: |w|=5.6204 type A_9 N=3; |w|=5.6204 type A_1 N=3; |w|=7.9484 type A_2 N=3; |w|=7.9484 type A_8 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.6204, N = 3, type A_9 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 35.27: min 7, max 10
ALL CHECKS PASSED  [0.4s]
n=5: 1371 reachable points of length <= 51.539 (R1=9, Rpair=30)
pairs (u,v) of reachable points of length <= 30 with det(u,v) = S: 601 ; pairs of types: {(0, 0): 205, (0, 2): 198, (1, 0): 198}
unitary pairs: 205 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 410 lines (u+tv and v+tu for the unitary pairs); 2458 reachable points on them inside the disc; predicted 2458; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 2260, not reachable or wrong type 0; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', -4): 7, ('a', -3): 10, ('a', -2): 16, ('a', -1): 34, ('a', 0): 193, ('a', 1): 205, ('a', 2): 205, ('a', 3): 205, ('a', 4): 205, ('b', -4): 10, ('b', -3): 15, ('b', -2): 28, ('b', -1): 102, ('b', 0): 205, ('b', 1): 205, ('b', 2): 205, ('b', 3): 205, ('b', 4): 205}
Theorem F(b): reachable points of type != A_0 and length <= 9: 16 ; vertex of no reachable n-gon: 6 (37.5%), of exactly one: 10, of more: 0
  shortest points which are vertices of none: |w|=4.0406 type A_1 N=3; |w|=4.0406 type A_2 N=3; |w|=6.6138 type A_1 N=5; |w|=6.6138 type A_2 N=5
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 4.0406, N = 3, type A_2 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 5 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 51.54: min 12, max 20
ALL CHECKS PASSED  [1.4s]
n=6: 1929 reachable points of length <= 60.500 (R1=9, Rpair=30)
pairs (u,v) of reachable points of length <= 30 with det(u,v) = S: 499 ; pairs of types: {(0, 0): 169, (0, 3): 165, (1, 0): 165}
unitary pairs: 169 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 338 lines (u+tv and v+tu for the unitary pairs); 2172 reachable points on them inside the disc; predicted 2172; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 1872, not reachable or wrong type 1630; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 158, ('b', -1): 84}
Theorem F(b): reachable points of type != A_0 and length <= 9: 21 ; vertex of no reachable n-gon: 10 (47.6%), of exactly one: 11, of more: 0
  shortest points which are vertices of none: |w|=4.5826 type A_3 N=3; |w|=4.5826 type A_1 N=3; |w|=5.2915 type A_2 N=3; |w|=5.2915 type A_2 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 4.5826, N = 3, type A_3 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 6 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 60.50: min 10, max 21
n=6: X_2 = (1,2), w_6 = (5,4), mirror image (4,5): as in Example 6.2
ALL CHECKS PASSED  [1.5s]
n=7: 2577 reachable points of length <= 69.643 (R1=9, Rpair=30)
pairs (u,v) of reachable points of length <= 30 with det(u,v) = S: 421 ; pairs of types: {(0, 0): 141, (0, 4): 140, (1, 0): 140}
unitary pairs: 141 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 282 lines (u+tv and v+tu for the unitary pairs); 1986 reachable points on them inside the disc; predicted 1986; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 1557, not reachable or wrong type 1356; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 131, ('b', -1): 70}
Theorem F(b): reachable points of type != A_0 and length <= 9: 26 ; vertex of no reachable n-gon: 14 (53.8%), of exactly one: 12, of more: 0
  shortest points which are vertices of none: |w|=4.9328 type A_1 N=3; |w|=4.9328 type A_4 N=3; |w|=6.1511 type A_2 N=3; |w|=6.1511 type A_3 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 4.9328, N = 3, type A_4 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 6 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 69.64: min 10, max 22
ALL CHECKS PASSED  [1.8s]
n=8: 3303 reachable points of length <= 78.894 (R1=9, Rpair=30)
pairs (u,v) of reachable points of length <= 30 with det(u,v) = S: 399 ; pairs of types: {(0, 0): 133, (0, 5): 133, (1, 0): 133}
unitary pairs: 133 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 266 lines (u+tv and v+tu for the unitary pairs); 1996 reachable points on them inside the disc; predicted 1996; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 1469, not reachable or wrong type 1279; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 124, ('b', -1): 66}
Theorem F(b): reachable points of type != A_0 and length <= 9: 23 ; vertex of no reachable n-gon: 12 (52.2%), of exactly one: 11, of more: 0
  shortest points which are vertices of none: |w|=5.1699 type A_5 N=3; |w|=5.1699 type A_1 N=3; |w|=6.7548 type A_4 N=3; |w|=6.7548 type A_2 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.1699, N = 3, type A_5 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 78.89: min 17, max 24
ALL CHECKS PASSED  [2.1s]
n=9: 2661 reachable points of length <= 70.671 (R1=9, Rpair=24)
pairs (u,v) of reachable points of length <= 24 with det(u,v) = S: 241 ; pairs of types: {(0, 0): 81, (0, 6): 80, (1, 0): 80}
unitary pairs: 81 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 162 lines (u+tv and v+tu for the unitary pairs); 1328 reachable points on them inside the disc; predicted 1328; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 895, not reachable or wrong type 782; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 73, ('b', -1): 40}
Theorem F(b): reachable points of type != A_0 and length <= 9: 26 ; vertex of no reachable n-gon: 14 (53.8%), of exactly one: 12, of more: 0
  shortest points which are vertices of none: |w|=5.3370 type A_6 N=3; |w|=5.3370 type A_1 N=3; |w|=7.1905 type A_2 N=3; |w|=7.1905 type A_5 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.3370, N = 3, type A_6 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 70.67: min 14, max 21
ALL CHECKS PASSED  [1.7s]
n=10: 3249 reachable points of length <= 78.166 (R1=9, Rpair=24)
pairs (u,v) of reachable points of length <= 24 with det(u,v) = S: 239 ; pairs of types: {(0, 0): 77, (0, 7): 81, (1, 0): 81}
unitary pairs: 77 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 154 lines (u+tv and v+tu for the unitary pairs); 1326 reachable points on them inside the disc; predicted 1326; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 846, not reachable or wrong type 738; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 70, ('b', -1): 38}
Theorem F(b): reachable points of type != A_0 and length <= 9: 23 ; vertex of no reachable n-gon: 12 (52.2%), of exactly one: 11, of more: 0
  shortest points which are vertices of none: |w|=5.4588 type A_7 N=3; |w|=5.4588 type A_1 N=3; |w|=7.5134 type A_6 N=3; |w|=7.5134 type A_6 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.4588, N = 3, type A_7 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 78.17: min 16, max 22
ALL CHECKS PASSED  [2.1s]
n=11: 2665 reachable points of length <= 71.489 (R1=9, Rpair=20)
pairs (u,v) of reachable points of length <= 20 with det(u,v) = S: 157 ; pairs of types: {(0, 0): 53, (0, 8): 52, (1, 0): 52}
unitary pairs: 53 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 106 lines (u+tv and v+tu for the unitary pairs); 932 reachable points on them inside the disc; predicted 932; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 580, not reachable or wrong type 507; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 47, ('b', -1): 26}
Theorem F(b): reachable points of type != A_0 and length <= 9: 20 ; vertex of no reachable n-gon: 8 (40.0%), of exactly one: 12, of more: 0
  shortest points which are vertices of none: |w|=5.5502 type A_8 N=3; |w|=5.5502 type A_1 N=3; |w|=7.7584 type A_7 N=3; |w|=7.7584 type A_2 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.5502, N = 3, type A_8 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 71.49: min 14, max 20
ALL CHECKS PASSED  [1.8s]
n=12: 3151 reachable points of length <= 77.774 (R1=9, Rpair=20)
pairs (u,v) of reachable points of length <= 20 with det(u,v) = S: 155 ; pairs of types: {(0, 0): 51, (0, 9): 52, (1, 0): 52}
unitary pairs: 51 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 102 lines (u+tv and v+tu for the unitary pairs); 996 reachable points on them inside the disc; predicted 996; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 559, not reachable or wrong type 489; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 45, ('b', -1): 25}
Theorem F(b): reachable points of type != A_0 and length <= 9: 21 ; vertex of no reachable n-gon: 8 (38.1%), of exactly one: 13, of more: 0
  shortest points which are vertices of none: |w|=5.6204 type A_9 N=3; |w|=5.6204 type A_1 N=3; |w|=7.9484 type A_2 N=3; |w|=7.9484 type A_8 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.6204, N = 3, type A_9 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 77.77: min 15, max 22
ALL CHECKS PASSED  [2.1s]
n=13: 1335 reachable points of length <= 50.643 (R1=7, Rpair=12)
pairs (u,v) of reachable points of length <= 12 with det(u,v) = S: 51 ; pairs of types: {(0, 0): 17, (0, 10): 17, (1, 0): 17}
unitary pairs: 17 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 34 lines (u+tv and v+tu for the unitary pairs); 344 reachable points on them inside the disc; predicted 344; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 185, not reachable or wrong type 164; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 13, ('b', -1): 8}
Theorem F(b): reachable points of type != A_0 and length <= 7: 14 ; vertex of no reachable n-gon: 2 (14.3%), of exactly one: 12, of more: 0
  shortest points which are vertices of none: |w|=5.6754 type A_10 N=3; |w|=5.6754 type A_1 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.6754, N = 3, type A_10 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 50.64: min 10, max 14
ALL CHECKS PASSED  [0.9s]
n=15: 1213 reachable points of length <= 48.597 (R1=7, Rpair=10)
pairs (u,v) of reachable points of length <= 10 with det(u,v) = S: 35 ; pairs of types: {(0, 0): 11, (0, 12): 12, (1, 0): 12}
unitary pairs: 11 ; each spans a reachable n-gon with vertex types A_0,A_1,...,A_(n-3),A_0 ; no other pair with det = S does; 'four vertices reachable => all reachable' holds on all pairs
Theorem E: 22 lines (u+tv and v+tu for the unitary pairs); 242 reachable points on them inside the disc; predicted 242; sets and types identical
printed constants (lambda+1, lambda) on u+tv, |m| <= 4, points in the upper half-plane: tested 117, not reachable or wrong type 104; (item, m) -> number of pairs for which the printed point is reachable with the printed type: {('a', 0): 8, ('b', -1): 5}
Theorem F(b): reachable points of type != A_0 and length <= 7: 16 ; vertex of no reachable n-gon: 2 (12.5%), of exactly one: 14, of more: 0
  shortest points which are vertices of none: |w|=5.7550 type A_12 N=3; |w|=5.7550 type A_1 N=3
w_n = 2+3zeta+zeta^2: reachable, |w_n| = 5.7550, N = 3, type A_12 ; reachable n-gons through it: 0 ; mirror image: type A_1, n-gons: 0
  the two shortest reachable points which are vertices of no reachable n-gon are w_n and its mirror image
X_2 (type A_1): vertex of exactly one reachable n-gon (P_0)
Theorem F(a): for the 4 points of type A_0 and length <= 4, the numbers of reachable n-gons through them whose two sides at O have length <= 48.60: min 9, max 13
ALL CHECKS PASSED  [0.9s]
n = 5 (m = 2): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_10)
j= 1  simple preclosed piece: 2 segments, length 2.6180 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 1.6180 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [5, 5] ; gcd = 5 ; a quotient equals n: False
DONE [0.0s]
n = 7 (m = 3): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_14)
j= 1  simple preclosed piece: 2 segments, length 3.2470 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 4.0489 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 1.8019 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [7, 7, 7] ; gcd = 7 ; a quotient equals n: False
DONE [0.0s]
n = 9 (m = 4): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_18)
j= 1  simple preclosed piece: 2 segments, length 3.5321 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 5.4115 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 4.7588 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 1.8794 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [9, 9, 3, 9] ; gcd = 3 ; a quotient equals n: False
DONE [0.0s]
n = 11 (m = 5): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_22)
j= 1  simple preclosed piece: 2 segments, length 3.6825 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 6.1958 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 6.7420 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 5.1477 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 1.9190 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [11, 11, 11, 11, 11] ; gcd = 11 ; a quotient equals n: False
DONE [0.1s]
n = 13 (m = 6): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_26)
j= 1  simple preclosed piece: 2 segments, length 3.7709 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 6.6780 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 8.0552 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 7.5870 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 5.3808 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 1.9419 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [13, 13, 13, 13, 13, 13] ; gcd = 13 ; a quotient equals n: False
DONE [0.1s]
n = 15 (m = 7): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_30)
j= 1  simple preclosed piece: 2 segments, length 3.8271 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 6.9924 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 8.9487 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 9.3577 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 8.1487 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 5.5306 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 1.9563 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [15, 15, 5, 15, 3, 5, 15] ; gcd = 1 ; a quotient equals n: True
DONE [0.1s]
n = 21 (m = 10): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_42)
j= 1  simple preclosed piece: 2 segments, length 3.9111 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 17 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.4748 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 13 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 10.3742 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 12.3519 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 13.2320 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 12.9364 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 11.4914 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 9.0253 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 5.7573 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 1.9777 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [21, 21, 7, 21, 21, 7, 3, 21, 7, 21] ; gcd = 1 ; a quotient equals n: True
DONE [0.4s]
n = 25 (m = 12): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_50)
j= 1  simple preclosed piece: 2 segments, length 3.9372 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 21 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.6269 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 17 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 10.8375 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 13 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 13.3671 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 15.0568 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 15.8004 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 15.5512 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 14.3249 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 12.1985 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 9.3056 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 5.8280 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 1.9842 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 25 = n/gcd(n,j); closed trajectory: 50 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [25, 25, 25, 25, 5, 25, 25, 25, 25, 5, 25, 25] ; gcd = 5 ; a quotient equals n: False
DONE [0.7s]
n = 27 (m = 13): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_54)
j= 1  simple preclosed piece: 2 segments, length 3.9461 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.6794 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 10.9988 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 13.7252 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 15.7117 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 16.8511 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 17.0821 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 16.3922 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 14.8186 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 12.4462 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 9.4027 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 5.8523 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 1.9865 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [27, 27, 9, 27, 27, 9, 27, 27, 3, 27, 27, 9, 27] ; gcd = 3 ; a quotient equals n: False
DONE [0.6s]
n = 33 (m = 16): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_66)
j= 1  simple preclosed piece: 2 segments, length 3.9639 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 29 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.7845 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 25 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.3237 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 21 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 14.4537 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 17 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 17.0613 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 13 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 19.0522 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 20.3545 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 20.9212 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 20.7318 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 19.7930 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 18.1389 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 15.8291 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 12.9473 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 9.5975 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 5.9009 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 1.9909 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 33 = n/gcd(n,j); closed trajectory: 66 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [33, 33, 11, 33, 33, 11, 33, 33, 11, 33, 3, 11, 33, 33, 11, 33] ; gcd = 1 ; a quotient equals n: True
DONE [1.6s]
n = 35 (m = 17): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_70)
j= 1  simple preclosed piece: 2 segments, length 3.9679 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 31 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.8082 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 27 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.3976 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 14.6206 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 17.3737 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 19.5684 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 21.1342 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 22.0207 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 22.1994 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 21.6647 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 20.4336 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 18.5457 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 16.0618 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 13.0617 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 9.6417 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 5.9118 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 1.9919 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 35 = n/gcd(n,j); closed trajectory: 70 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [35, 35, 35, 35, 7, 35, 5, 35, 35, 7, 35, 35, 35, 5, 7, 35, 35] ; gcd = 1 ; a quotient equals n: True
DONE [3.0s]
n = 39 (m = 19): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_78)
j= 1  simple preclosed piece: 2 segments, length 3.9741 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 35 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.8453 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 31 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.5133 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 27 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 14.8831 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 17.8674 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 20.3890 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 22.3825 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 23.7963 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 24.5938 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 24.7544 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 24.2738 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 23.1645 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 21.4553 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 19.1904 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 16.4285 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 13.2411 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 9.7108 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=18  simple preclosed piece: 2 segments, length 5.9289 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=19  simple preclosed piece: 2 segments, length 1.9935 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [39, 39, 13, 39, 39, 13, 39, 39, 13, 39, 39, 13, 3, 39, 13, 39, 39, 13, 39] ; gcd = 1 ; a quotient equals n: True
DONE [2.7s]
n = 45 (m = 22): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_90)
j= 1  simple preclosed piece: 2 segments, length 3.9805 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 41 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.8836 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 37 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.6332 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 33 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 15.1564 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 29 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 18.3846 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 25 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 21.2549 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 21 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 23.7116 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 17 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 25.7067 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 13 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 27.2015 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 28.1668 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 28.5839 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 28.4447 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 42 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 27.7518 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 26.5187 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 24.7695 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 22.5382 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 19.8682 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=18  simple preclosed piece: 2 segments, length 16.8114 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=19  simple preclosed piece: 2 segments, length 13.4275 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=20  simple preclosed piece: 2 segments, length 9.7822 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=21  simple preclosed piece: 2 segments, length 5.9466 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=22  simple preclosed piece: 2 segments, length 1.9951 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [45, 45, 15, 45, 9, 15, 45, 45, 5, 9, 45, 15, 45, 45, 3, 45, 45, 5, 45, 9, 15, 45] ; gcd = 1 ; a quotient equals n: True
DONE [2.7s]
n = 49 (m = 24): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_98)
j= 1  simple preclosed piece: 2 segments, length 3.9836 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 45 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.9017 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 41 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.6902 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 37 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 15.2866 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 33 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 18.6321 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 29 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 21.6716 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 25 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 24.3553 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 21 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 26.6391 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 17 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 28.4854 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 13 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 29.8641 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 30.7523 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 31.1356 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 31.0077 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 46 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 30.3706 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 42 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 29.2348 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 27.6190 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 25.5497 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=18  simple preclosed piece: 2 segments, length 23.0609 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=19  simple preclosed piece: 2 segments, length 20.1934 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=20  simple preclosed piece: 2 segments, length 16.9943 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=21  simple preclosed piece: 2 segments, length 13.5162 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=22  simple preclosed piece: 2 segments, length 9.8161 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=23  simple preclosed piece: 2 segments, length 5.9549 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=24  simple preclosed piece: 2 segments, length 1.9959 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 49 = n/gcd(n,j); closed trajectory: 98 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [49, 49, 49, 49, 49, 49, 7, 49, 49, 49, 49, 49, 49, 7, 49, 49, 49, 49, 49, 49, 7, 49, 49, 49] ; gcd = 7 ; a quotient equals n: False
DONE [6.7s]
n = 51 (m = 25): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_102)
j= 1  simple preclosed piece: 2 segments, length 3.9848 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 47 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.9093 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 43 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.7138 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 39 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 15.3408 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 35 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 18.7352 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 31 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 21.8456 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 27 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 24.6249 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 27.0308 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 29.0270 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 30.5832 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 31.6758 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 32.2882 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 32.4112 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 50 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 32.0428 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 46 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 31.1887 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 42 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 29.8618 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 28.0822 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=18  simple preclosed piece: 2 segments, length 25.8769 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=19  simple preclosed piece: 2 segments, length 23.2794 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=20  simple preclosed piece: 2 segments, length 20.3290 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=21  simple preclosed piece: 2 segments, length 17.0704 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=22  simple preclosed piece: 2 segments, length 13.5530 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=23  simple preclosed piece: 2 segments, length 9.8302 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=24  simple preclosed piece: 2 segments, length 5.9584 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 17 = n/gcd(n,j); closed trajectory: 34 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=25  simple preclosed piece: 2 segments, length 1.9962 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 51 = n/gcd(n,j); closed trajectory: 102 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [51, 51, 17, 51, 51, 17, 51, 51, 17, 51, 51, 17, 51, 51, 17, 51, 3, 17, 51, 51, 17, 51, 51, 17, 51] ; gcd = 1 ; a quotient equals n: True
DONE [6.1s]
n = 55 (m = 27): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_110)
j= 1  simple preclosed piece: 2 segments, length 3.9870 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 51 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.9220 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 47 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.7537 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 43 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 15.4321 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 39 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 18.9095 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 35 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 22.1402 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 31 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 25.0824 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 27 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 27.6976 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 29.9517 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 31.8153 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 33.2642 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 34.2794 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 34.8477 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 34.9617 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 54 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 34.6200 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 50 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 33.8269 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 46 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 32.5929 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 42 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=18  simple preclosed piece: 2 segments, length 30.9339 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=19  simple preclosed piece: 2 segments, length 28.8717 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=20  simple preclosed piece: 2 segments, length 26.4331 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=21  simple preclosed piece: 2 segments, length 23.6499 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=22  simple preclosed piece: 2 segments, length 20.5584 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=23  simple preclosed piece: 2 segments, length 17.1989 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=24  simple preclosed piece: 2 segments, length 13.6151 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=25  simple preclosed piece: 2 segments, length 9.8539 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 11 = n/gcd(n,j); closed trajectory: 22 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=26  simple preclosed piece: 2 segments, length 5.9642 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=27  simple preclosed piece: 2 segments, length 1.9967 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 55 = n/gcd(n,j); closed trajectory: 110 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [55, 55, 55, 55, 11, 55, 55, 55, 55, 11, 5, 55, 55, 55, 11, 55, 55, 55, 55, 11, 55, 5, 55, 55, 11, 55, 55] ; gcd = 1 ; a quotient equals n: True
DONE [13.0s]
n = 63 (m = 31): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_126)
j= 1  simple preclosed piece: 2 segments, length 3.9901 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 59 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.9405 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 55 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 11.8120 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 51 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 15.5661 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 47 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 19.1655 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 43 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 22.5744 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 39 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 25.7589 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 35 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 28.6875 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 31 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 31.3310 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 27 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 33.6630 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 35.6605 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 37.3036 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 38.5760 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 39.4650 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 39.9617 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=16  simple preclosed piece: 2 segments, length 40.0613 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 62 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 39.7628 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 58 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=18  simple preclosed piece: 2 segments, length 39.0691 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 54 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=19  simple preclosed piece: 2 segments, length 37.9870 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 50 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=20  simple preclosed piece: 2 segments, length 36.5275 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 46 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=21  simple preclosed piece: 2 segments, length 34.7049 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 42 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=22  simple preclosed piece: 2 segments, length 32.5374 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=23  simple preclosed piece: 2 segments, length 30.0466 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=24  simple preclosed piece: 2 segments, length 27.2571 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=25  simple preclosed piece: 2 segments, length 24.1967 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=26  simple preclosed piece: 2 segments, length 20.8959 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=27  simple preclosed piece: 2 segments, length 17.3874 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=28  simple preclosed piece: 2 segments, length 13.7060 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=29  simple preclosed piece: 2 segments, length 9.8885 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=30  simple preclosed piece: 2 segments, length 5.9727 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=31  simple preclosed piece: 2 segments, length 1.9975 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 63 = n/gcd(n,j); closed trajectory: 126 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [63, 63, 21, 63, 63, 21, 9, 63, 7, 63, 63, 21, 63, 9, 21, 63, 63, 7, 63, 63, 3, 63, 63, 21, 63, 63, 7, 9, 63, 21, 63] ; gcd = 1 ; a quotient equals n: True
DONE [9.2s]
n=9: 1903 reachable points of length <= 60, 454 classes of parallel directions
  class of alpha=2.079097: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
  class of alpha=0.720967: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
  class of alpha=1.073071: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
  class of alpha=2.144570: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
  class of alpha=0.462025: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
  class of alpha=0.546399: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
  class of alpha=0.539383: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
  class of alpha=0.531648: floating billiard finds 4 of the 4 (length, factor) pairs of the unfolding, none else
bands computed: 12684 (rays from O, both sides); largest number of segments of a simple preclosed piece: 156
odd n: in every class exactly m = 4 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {9: 338, 3: 75, 1: 41}
  n'=9: factors 9,9,3,9  gcd 3  a quotient is n: no  classes: 338
  n'=3: factors 3,3,1,3  gcd 1  a quotient is n: no  classes: 75
  n'=1: factors 1,1,1,1  gcd 1  a quotient is n: no  classes: 41
DONE n=9 [8.2s]
n=15: 825 reachable points of length <= 40, 181 classes of parallel directions
  class of alpha=0.196937: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
  class of alpha=0.398595: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
  class of alpha=2.491381: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
  class of alpha=0.664469: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
  class of alpha=2.578964: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
  class of alpha=0.068360: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
  class of alpha=0.344936: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
  class of alpha=2.595295: floating billiard finds 7 of the 7 (length, factor) pairs of the unfolding, none else
bands computed: 9360 (rays from O, both sides); largest number of segments of a simple preclosed piece: 106
odd n: in every class exactly m = 7 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {15: 116, 5: 38, 3: 22, 1: 5}
  n'=15: factors 15,15,5,15,3,5,15  gcd 1  a quotient is n: yes  classes: 116
  n'=5: factors 5,5,5,5,1,5,5  gcd 1  a quotient is n: no  classes: 38
  n'=3: factors 3,3,1,3,3,1,3  gcd 1  a quotient is n: no  classes: 22
  n'=1: factors 1,1,1,1,1,1,1  gcd 1  a quotient is n: no  classes: 5
DONE n=15 [6.4s]
n=21: 439 reachable points of length <= 30, 102 classes of parallel directions
  class of alpha=0.139552: floating billiard finds 10 of the 10 (length, factor) pairs of the unfolding, none else
  class of alpha=0.284830: floating billiard finds 10 of the 10 (length, factor) pairs of the unfolding, none else
  class of alpha=0.165158: floating billiard finds 10 of the 10 (length, factor) pairs of the unfolding, none else
  class of alpha=0.474613: floating billiard finds 10 of the 10 (length, factor) pairs of the unfolding, none else
  class of alpha=0.246769: floating billiard finds 10 of the 10 (length, factor) pairs of the unfolding, none else
  class of alpha=0.826627: floating billiard finds 10 of the 10 (length, factor) pairs of the unfolding, none else
bands computed: 7676 (rays from O, both sides); largest number of segments of a simple preclosed piece: 78
odd n: in every class exactly m = 10 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {21: 74, 7: 18, 3: 4, 1: 6}
  n'=21: factors 21,21,7,21,21,7,3,21,7,21  gcd 1  a quotient is n: yes  classes: 74
  n'=7: factors 7,7,7,7,7,7,1,7,7,7  gcd 1  a quotient is n: no  classes: 18
  n'=3: factors 3,3,1,3,3,1,3,3,1,3  gcd 1  a quotient is n: no  classes: 4
  n'=1: factors 1,1,1,1,1,1,1,1,1,1  gcd 1  a quotient is n: no  classes: 6
DONE n=21 [6.0s]
n=25: 285 reachable points of length <= 24, 64 classes of parallel directions
  class of alpha=0.118233: floating billiard finds 12 of the 12 (length, factor) pairs of the unfolding, none else
  class of alpha=0.357002: floating billiard finds 12 of the 12 (length, factor) pairs of the unfolding, none else
  class of alpha=0.035996: floating billiard finds 12 of the 12 (length, factor) pairs of the unfolding, none else
  class of alpha=2.814116: floating billiard finds 12 of the 12 (length, factor) pairs of the unfolding, none else
  class of alpha=2.692348: floating billiard finds 12 of the 12 (length, factor) pairs of the unfolding, none else
  class of alpha=0.321018: floating billiard finds 12 of the 12 (length, factor) pairs of the unfolding, none else
bands computed: 5796 (rays from O, both sides); largest number of segments of a simple preclosed piece: 54
odd n: in every class exactly m = 12 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {25: 54, 5: 6, 1: 4}
  n'=25: factors 25,25,25,25,5,25,25,25,25,5,25,25  gcd 5  a quotient is n: no  classes: 54
  n'=5: factors 5,5,5,5,1,5,5,5,5,1,5,5  gcd 1  a quotient is n: no  classes: 6
  n'=1: factors 1,1,1,1,1,1,1,1,1,1,1,1  gcd 1  a quotient is n: no  classes: 4
DONE n=25 [6.6s]
n=27: 279 reachable points of length <= 24, 64 classes of parallel directions
  class of alpha=2.799402: floating billiard finds 13 of the 13 (length, factor) pairs of the unfolding, none else
  class of alpha=0.330577: floating billiard finds 12 of the 13 (length, factor) pairs of the unfolding, none else
  class of alpha=2.826847: floating billiard finds 13 of the 13 (length, factor) pairs of the unfolding, none else
  class of alpha=2.723019: floating billiard finds 13 of the 13 (length, factor) pairs of the unfolding, none else
  class of alpha=0.298752: floating billiard finds 12 of the 13 (length, factor) pairs of the unfolding, none else
  class of alpha=0.413119: floating billiard finds 12 of the 13 (length, factor) pairs of the unfolding, none else
bands computed: 6300 (rays from O, both sides); largest number of segments of a simple preclosed piece: 52
odd n: in every class exactly m = 13 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {27: 49, 9: 11, 3: 3, 1: 1}
  n'=27: factors 27,27,9,27,27,9,27,27,3,27,27,9,27  gcd 3  a quotient is n: no  classes: 49
  n'=9: factors 9,9,3,9,9,3,9,9,1,9,9,3,9  gcd 1  a quotient is n: no  classes: 11
  n'=3: factors 3,3,1,3,3,1,3,3,1,3,3,1,3  gcd 1  a quotient is n: no  classes: 3
  n'=1: factors 1,1,1,1,1,1,1,1,1,1,1,1,1  gcd 1  a quotient is n: no  classes: 1
DONE n=27 [5.9s]
n=45: 136 reachable points of length <= 16, 25 classes of parallel directions
  class of alpha=0.064434: floating billiard finds 22 of the 22 (length, factor) pairs of the unfolding, none else
  class of alpha=0.062044: floating billiard finds 22 of the 22 (length, factor) pairs of the unfolding, none else
  class of alpha=0.042909: floating billiard finds 22 of the 22 (length, factor) pairs of the unfolding, none else
  class of alpha=2.546069: floating billiard finds 19 of the 22 (length, factor) pairs of the unfolding, none else
bands computed: 4214 (rays from O, both sides); largest number of segments of a simple preclosed piece: 30
odd n: in every class exactly m = 22 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {45: 15, 15: 1, 9: 2, 5: 3, 3: 4}
  n'=45: factors 45,45,15,45,9,15,45,45,5,9,45,15,45,45,3,45,45,5,45,9,15,45  gcd 1  a quotient is n: yes  classes: 15
  n'=15: factors 15,15,5,15,3,5,15,15,5,3,15,5,15,15,1,15,15,5,15,3,5,15  gcd 1  a quotient is n: no  classes: 1
  n'=9: factors 9,9,3,9,9,3,9,9,1,9,9,3,9,9,3,9,9,1,9,9,3,9  gcd 1  a quotient is n: no  classes: 2
  n'=5: factors 5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5  gcd 1  a quotient is n: no  classes: 3
  n'=3: factors 3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3  gcd 1  a quotient is n: no  classes: 4
DONE n=45 [6.1s]
n=5: 1855 reachable points of length <= 60, 528 classes of parallel directions
  class of alpha=0.668138: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=1.326662: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.547766: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.154719: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.229561: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.354626: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.339721: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.326056: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
bands computed: 6324 (rays from O, both sides); largest number of segments of a simple preclosed piece: 148
odd n: in every class exactly m = 2 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {5: 437, 1: 91}
  n'=5: factors 5,5  gcd 5  a quotient is n: no  classes: 437
  n'=1: factors 1,1  gcd 1  a quotient is n: no  classes: 91
DONE n=5 [3.6s]
n=7: 1931 reachable points of length <= 60, 476 classes of parallel directions
  class of alpha=0.430965: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.868213: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.415666: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.511033: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.309674: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.262922: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.194297: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.206432: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
bands computed: 9500 (rays from O, both sides); largest number of segments of a simple preclosed piece: 150
odd n: in every class exactly m = 3 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {7: 419, 1: 57}
  n'=7: factors 7,7,7  gcd 7  a quotient is n: no  classes: 419
  n'=1: factors 1,1,1  gcd 1  a quotient is n: no  classes: 57
DONE n=7 [6.5s]
n=11: 851 reachable points of length <= 40, 196 classes of parallel directions
  class of alpha=2.015103: floating billiard finds 5 of the 5 (length, factor) pairs of the unfolding, none else
  class of alpha=1.974455: floating billiard finds 5 of the 5 (length, factor) pairs of the unfolding, none else
  class of alpha=0.543837: floating billiard finds 5 of the 5 (length, factor) pairs of the unfolding, none else
  class of alpha=1.094566: floating billiard finds 5 of the 5 (length, factor) pairs of the unfolding, none else
  class of alpha=0.105566: floating billiard finds 5 of the 5 (length, factor) pairs of the unfolding, none else
  class of alpha=1.285197: floating billiard finds 5 of the 5 (length, factor) pairs of the unfolding, none else
bands computed: 7020 (rays from O, both sides); largest number of segments of a simple preclosed piece: 106
odd n: in every class exactly m = 5 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {11: 180, 1: 16}
  n'=11: factors 11,11,11,11,11  gcd 11  a quotient is n: no  classes: 180
  n'=1: factors 1,1,1,1,1  gcd 1  a quotient is n: no  classes: 16
DONE n=11 [4.9s]
n=13: 823 reachable points of length <= 40, 192 classes of parallel directions
  class of alpha=2.644212: floating billiard finds 6 of the 6 (length, factor) pairs of the unfolding, none else
  class of alpha=2.636898: floating billiard finds 6 of the 6 (length, factor) pairs of the unfolding, none else
  class of alpha=0.942413: floating billiard finds 6 of the 6 (length, factor) pairs of the unfolding, none else
  class of alpha=1.007906: floating billiard finds 6 of the 6 (length, factor) pairs of the unfolding, none else
  class of alpha=0.079188: floating billiard finds 6 of the 6 (length, factor) pairs of the unfolding, none else
  class of alpha=1.300802: floating billiard finds 5 of the 6 (length, factor) pairs of the unfolding, none else
bands computed: 8404 (rays from O, both sides); largest number of segments of a simple preclosed piece: 110
odd n: in every class exactly m = 6 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {13: 176, 1: 16}
  n'=13: factors 13,13,13,13,13,13  gcd 13  a quotient is n: no  classes: 176
  n'=1: factors 1,1,1,1,1,1  gcd 1  a quotient is n: no  classes: 16
DONE n=13 [6.9s]
n=33: 192 reachable points of length <= 20, 45 classes of parallel directions
  class of alpha=0.087855: floating billiard finds 16 of the 16 (length, factor) pairs of the unfolding, none else
  class of alpha=0.179160: floating billiard finds 16 of the 16 (length, factor) pairs of the unfolding, none else
  class of alpha=0.170290: floating billiard finds 16 of the 16 (length, factor) pairs of the unfolding, none else
  class of alpha=0.338168: floating billiard finds 16 of the 16 (length, factor) pairs of the unfolding, none else
bands computed: 5518 (rays from O, both sides); largest number of segments of a simple preclosed piece: 50
odd n: in every class exactly m = 16 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {33: 31, 11: 9, 3: 5}
  n'=33: factors 33,33,11,33,33,11,33,33,11,33,3,11,33,33,11,33  gcd 1  a quotient is n: yes  classes: 31
  n'=11: factors 11,11,11,11,11,11,11,11,11,11,1,11,11,11,11,11  gcd 1  a quotient is n: no  classes: 9
  n'=3: factors 3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3  gcd 1  a quotient is n: no  classes: 5
DONE n=33 [7.3s]
n=35: 192 reachable points of length <= 20, 44 classes of parallel directions
  class of alpha=2.879236: floating billiard finds 17 of the 17 (length, factor) pairs of the unfolding, none else
  class of alpha=0.168927: floating billiard finds 17 of the 17 (length, factor) pairs of the unfolding, none else
  class of alpha=0.160566: floating billiard finds 17 of the 17 (length, factor) pairs of the unfolding, none else
  class of alpha=0.318878: floating billiard finds 17 of the 17 (length, factor) pairs of the unfolding, none else
bands computed: 5742 (rays from O, both sides); largest number of segments of a simple preclosed piece: 46
odd n: in every class exactly m = 17 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {35: 34, 7: 6, 5: 4}
  n'=35: factors 35,35,35,35,7,35,5,35,35,7,35,35,35,5,7,35,35  gcd 1  a quotient is n: yes  classes: 34
  n'=7: factors 7,7,7,7,7,7,1,7,7,7,7,7,7,1,7,7,7  gcd 1  a quotient is n: no  classes: 6
  n'=5: factors 5,5,5,5,1,5,5,5,5,1,5,5,5,5,1,5,5  gcd 1  a quotient is n: no  classes: 4
DONE n=35 [9.2s]
n=39: 110 reachable points of length <= 14, 21 classes of parallel directions
  class of alpha=0.073215: floating billiard finds 19 of the 19 (length, factor) pairs of the unfolding, none else
  class of alpha=0.069022: floating billiard finds 19 of the 19 (length, factor) pairs of the unfolding, none else
  class of alpha=0.143157: floating billiard finds 19 of the 19 (length, factor) pairs of the unfolding, none else
  class of alpha=0.286220: floating billiard finds 19 of the 19 (length, factor) pairs of the unfolding, none else
bands computed: 3034 (rays from O, both sides); largest number of segments of a simple preclosed piece: 26
odd n: in every class exactly m = 19 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {39: 11, 13: 4, 3: 6}
  n'=39: factors 39,39,13,39,39,13,39,39,13,39,39,13,3,39,13,39,39,13,39  gcd 1  a quotient is n: yes  classes: 11
  n'=13: factors 13,13,13,13,13,13,13,13,13,13,13,13,1,13,13,13,13,13,13  gcd 1  a quotient is n: no  classes: 4
  n'=3: factors 3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3  gcd 1  a quotient is n: no  classes: 6
DONE n=39 [4.3s]
n=49: 74 reachable points of length <= 12, 15 classes of parallel directions
  class of alpha=2.955087: floating billiard finds 24 of the 24 (length, factor) pairs of the unfolding, none else
  class of alpha=2.956384: floating billiard finds 24 of the 24 (length, factor) pairs of the unfolding, none else
  class of alpha=0.042717: floating billiard finds 24 of the 24 (length, factor) pairs of the unfolding, none else
  class of alpha=2.848574: floating billiard finds 24 of the 24 (length, factor) pairs of the unfolding, none else
bands computed: 2726 (rays from O, both sides); largest number of segments of a simple preclosed piece: 22
odd n: in every class exactly m = 24 preclosed lengths c*lambda*sin(2j pi/n)/sin(pi/n), factors d_j = n'/gcd(n',j); classes by n': {49: 12, 7: 3}
  n'=49: factors 49,49,49,49,49,49,7,49,49,49,49,49,49,7,49,49,49,49,49,49,7,49,49,49  gcd 7  a quotient is n: no  classes: 12
  n'=7: factors 7,7,7,7,7,7,1,7,7,7,7,7,7,1,7,7,7,7,7,7,1,7,7,7  gcd 1  a quotient is n: no  classes: 3
DONE n=49 [7.0s]
n=6: 1905 reachable points of length <= 60, 663 classes of parallel directions
  class of alpha=0.052438: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.095930: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.938010: floating billiard finds 1 of the 1 (length, factor) pairs of the unfolding, none else
  class of alpha=1.254138: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.363327: floating billiard finds 1 of the 1 (length, factor) pairs of the unfolding, none else
  class of alpha=1.429767: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.400506: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.461819: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
bands computed: 5296 (rays from O, both sides); largest number of segments of a simple preclosed piece: 138
even n: every factor divides n/2; classes by (class name of Sect. 1 of the source, factors in the order of increasing preclosed length, ratios of the preclosed lengths):
  even  factors (1, 1)       ratios (1.0, 2.0)                   classes: 44
  even  factors (3, 1)       ratios (1.0, 2.0)                   classes: 122
  odd   factors (1,)         ratios (1.0,)                       classes: 123
  odd   factors (3,)         ratios (1.0,)                       classes: 374
DONE n=6 [2.8s]
n=8: 1925 reachable points of length <= 60, 596 classes of parallel directions
  class of alpha=0.042426: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=2.276634: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.090847: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.610990: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.482320: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=2.038209: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=2.020523: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.382079: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
bands computed: 7140 (rays from O, both sides); largest number of segments of a simple preclosed piece: 158
even n: every factor divides n/2; classes by (class name of Sect. 1 of the source, factors in the order of increasing preclosed length, ratios of the preclosed lengths):
  even  factors (4, 4)       ratios (1.0, 2.41421)               classes: 136
  odd   factors (2, 1)       ratios (1.0, 1.41421)               classes: 460
DONE n=8 [4.1s]
n=10: 1907 reachable points of length <= 60, 568 classes of parallel directions
  class of alpha=0.591478: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=1.188892: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.552370: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.484967: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.411695: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=2.258276: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.266111: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
  class of alpha=0.347425: floating billiard finds 2 of the 2 (length, factor) pairs of the unfolding, none else
bands computed: 9072 (rays from O, both sides); largest number of segments of a simple preclosed piece: 148
even n: every factor divides n/2; classes by (class name of Sect. 1 of the source, factors in the order of increasing preclosed length, ratios of the preclosed lengths):
  even  factors (1, 1, 1)    ratios (1.0, 2.61803, 3.23607)      classes: 17
  even  factors (5, 5, 1)    ratios (1.0, 2.61803, 3.23607)      classes: 106
  odd   factors (1, 1)       ratios (1.0, 1.61803)               classes: 72
  odd   factors (5, 5)       ratios (1.0, 1.61803)               classes: 373
DONE n=10 [6.3s]
n=12: 1883 reachable points of length <= 60, 542 classes of parallel directions
  class of alpha=2.126042: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=1.104744: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=1.113315: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=2.220897: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.335708: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.222204: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=2.328669: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
  class of alpha=0.278830: floating billiard finds 3 of the 3 (length, factor) pairs of the unfolding, none else
bands computed: 10820 (rays from O, both sides); largest number of segments of a simple preclosed piece: 162
even n: every factor divides n/2; classes by (class name of Sect. 1 of the source, factors in the order of increasing preclosed length, ratios of the preclosed lengths):
  even  factors (2, 2, 2)    ratios (1.0, 2.73205, 3.73205)      classes: 29
  even  factors (6, 2, 6)    ratios (1.0, 2.73205, 3.73205)      classes: 86
  odd   factors (1, 1, 1)    ratios (1.0, 1.73205, 2.0)          classes: 108
  odd   factors (3, 3, 1)    ratios (1.0, 1.73205, 2.0)          classes: 319
DONE n=12 [6.7s]
vertices 20, edges 30 faces 12 ; distinct half-turns: 15
for every vertex v, the numbers of half-turns h with d(v,h(v)) = 0,1,2,3,4,5 are [0, 3, 0, 6, 3, 3]
N_1, N_2, -N_2, -N_1, -v are the vertices at distance 1, 2, 3, 4, 5 from v = (1,1,1): ok
the table in the proof of Lemma 7.2 (four sign patterns, a.a = 4, v.a, h_a(v)) and h_(1,0,0)(v) = (1,-1,-1): ok
15 axes through the midpoints of the 30 edges: ok
distance matrix rows (vertex order: 8 cube vertices, then (0,+-1/phi,+-phi) and cyclic permutations):
02232335111333222444
20323253321143412234
23023523213431124342
32205332423241314132
23350223132314241423
32532032342124431213
35232302234412143321
53323220444222333111
13241324022423132533
12123434202342213353
11332244220234321335
31423142432033522123
34341212243303252312
33114422324330225231
24132413123522033432
21214343312252303243
22441133231225330324
42314231533132423022
43432121353213342202
44223311335321234220
ALL CHECKS PASSED
start vertex 0 face [0, 10, 16, 4, 8] edge (0, 10) ; states 178410 ; points with alpha < 3pi/10 + 1e-6 and length <= 130: 4357 [1.6s]
points exactly on the bisector direction: 1 [(3.0777, 0, 2)]
census, length < 120, alpha in [0, 3pi/10):
  type A_0        by distance 0..5: [0, 662, 0, 766, 336, 332] total 2096
  types A_1, A_2  by distance 0..5: [126, 206, 523, 304, 323, 124] total 1606
  total 3702
  source: A_0 [0, 672, 0, 778, 342, 330] 2122 ; A_1&A_2 [128, 211, 529, 313, 322, 125] 1628 ; total 3750
variants: bisector included: total 3703 ; edge e excluded: total 3701
lengths within 0.01 of 120: [120.00474527096553, 120.00633672252717, 119.9909743933448, 120.00633672252717, 119.99294175833563]
N(L) for L = 60, 80, 100, 110, 120, 125, 130: [927, 1644, 2573, 3129, 3702, 4013, 4356]  N(L)/L^2: ['0.2575', '0.2569', '0.2573', '0.2586', '0.2571', '0.2568', '0.2578']  3750/120^2 = 0.2604
entry (A_0, distance 5) exceeds 330 for every bound above 119.2177; just below this bound the entry (A_0, distance 1) is 655
smallest sum of absolute differences of the twelve entries over all bounds up to 130: 18, for a bound just above 120.8566, with 3752 geodesics; A_0 [0, 672, 0, 779, 339, 336], others [126, 210, 529, 312, 325, 124]
type A_0 geodesics (alpha <= 3pi/10, length <= 130): 2485; with an even number of segments: 2484; for all of them the end vertex is h(v), h = half-turn about the midpoint of the middle crossed edge; distances which occur: [1, 3, 4, 5]
  of these, with length < 120 and alpha < 3pi/10: 2095
other convention for beta (even N: 2 pi s/n in place of 2 pi (s+1)/n): column 'A_0' by distance: [46, 77, 162, 108, 117, 20] total 530
other convention, e = the other edge of f at v (by the mirror symmetry: even N and s = 4 in this half sector, and the edge): column 'A_0': [0, 1, 0, 0, 0, 0]
DONE [1.6s]
the face cycles of the record: 20 vertices, 30 edges, 12 faces, every directed edge in exactly one face, distance profile 1,3,6,6,3,1 from every vertex: ok
graph distance of the vertices 0 and 2: 2
reachable points of length <= 18 in the full sector: 167 ; with the face word of the record: 1
crossed edges: identical with the list of the record
end vertex: 2 ; N = 16 segments; length 17.512014631639 ; slope angle alpha = 0.028007 pi
2|B|^2 = 307 + 137 sqrt 5 exactly; |B|^2 = 306.670656458736, |B| = 17.512014631639
angles of Fig. 8 for the billiard trajectory: alpha = 0.028007 pi, beta = 0.828007 pi, beta - alpha = 0.800000 pi = 2 * (2pi/5)
type by Definition 2.1 as printed (all triples): [1] ; with the rule on the parity of N: 1
last polygon = c - P_0, end point = c - X_s with s = 1 ; c == B: False (central symmetry would require s = 0)
fractions of the length at which the 15 edges are crossed: 0.059017 0.145898 0.213525 0.291796 0.368034 0.437694 0.522542 0.583592 0.669153 0.683282 0.751865 0.788854 0.834576 0.894427 0.917288
they agree with the 15 values of t printed in the record (to 1e-9)
t_8 = 0.583592 (in place of 1/2); t_i + t_(16-i) ranges from 0.9763 to 1.1917 (in place of 1)
in the unfolding: -S0 = eta^2 * S1 for S0 = 0->16, S1 = 2->10 (the relation of the record): confirmed exactly
the image in the last face of the boundary edge which leaves the last vertex of the billiard trajectory counterclockwise: 2 -> 16
the edge which leaves the vertex 2 counterclockwise in the face F1: 2 -> 10
angle between the reversed last segment and 2->10: 0.428007 pi; and 2->16: 0.171993 pi (= pi - beta)
with the angle at 2->10 taken as the terminal angle: (angle) - alpha = 0.400000 pi = 2pi/5;  pi - (angle) - alpha = 0.543986 pi, pi - (angle) + alpha = 0.600000 pi
all short geodesics from the vertex 0 in F1 with this length: (N, type, end vertex): [(16, 1, 2), (16, 1, 2), (16, 2, 10), (16, 2, 10)]
ALL CHECKS PASSED
(A) Lemma 2.8: circumference |c_1|+|c_2| = lambda*lambda_(j-2), height sin((j-1)pi/n), modulus 2cot(pi/n): 70151 strips, 3 <= n <= 60: ok
(D),(E) Theorem D: sin(pi/n)sin(2pi/n) >= sin((k+1)pi/n)sin((k+2)pi/n) only for k = 0, n-3 (equality); (lambda^2-2)sin(pi/n) = sin(3pi/n)-sin(pi/n) in (0, sin(3pi/n)): 5 <= n <= 200: ok
(F) Lemma 6.1: a*c_1 = b*c_2 = kappa > 1 for 1 <= k <= n-3; c_1 = lambda^2-1, c_2 = 1 for k = n-3: 5 <= n <= 200: ok
    (6.1): X_(k+1) = a*eta + b*xi with the stated a, b: exact in the ring, 5 <= n <= 16: ok
(G) proof of Theorem F(c): T_1(eta-xi) = w_n = eta-xi+lambda^2 X_(n-2); g_0 xi, g_0 eta; g_0 X_(n-2) = w_n; f_eta values; no admissible i; and T_1 T = -R_(2pi/n) (Lemma 8.11): exact, 5 <= n <= 16: ok
    trace(T R^-1) = 0 and T_1 T = -R_(2pi/n) in floating point, 3 <= n <= 61: ok
(I) Lemma 8.9 from the formulas of Lemma 8.8: <c_i,c_j> = <c'_i,c'_j> = 0, <c'_j,c_i> = -eps_0 [i+j in {m,m+1}], the two sums (8.2): odd n, 5 <= n <= 61: ok
(H) Lemma 8.5(a) and Lemma 8.6: after 2t crossings g_2t(X_a) = c_2t + X_(a+rot) with rot = 2 sum(s_2i - s_2i-1) from the labels of the crossed sides of D_n, and a_* = -rot, tau = c_2t: 2557 unfolded bands (n = 5,6,7,8,9,10,12,15,21): ok
(J) Lemma 8.10(a): the horizontal line in the strip S_j meets the sides e_(j-1) and e_(n-1-j) of P_0; rot(c_j) = 2((j-1)-(n-1-j)) = 4j mod n: ok
(L) Lemma 8.1: trajectories through the midpoint of a side against a neighbour in the same band (floating billiard): 867 cases, 119 with an odd number j_1 of segments: there j_* = 2 j_1, a_* = 2 a_1, double length; for odd n the same factor: ok
(M) Remark 8.4(a), n=6: the regular n-gon through the midpoints of the sides: 1 segment, x_1 = r^(+-1) x_0, factor 6; its neighbours: 2 segments, factor 3; factors of the bands of this class (direction of a shortest diagonal): (3, 1)
(M) Remark 8.4(a), n=8: the regular n-gon through the midpoints of the sides: 1 segment, x_1 = r^(+-1) x_0, factor 8; its neighbours: 2 segments, factor 4; factors of the bands of this class (direction of a shortest diagonal): (4, 4)
(M) Remark 8.4(a), n=10: the regular n-gon through the midpoints of the sides: 1 segment, x_1 = r^(+-1) x_0, factor 10; its neighbours: 2 segments, factor 5; factors of the bands of this class (direction of a shortest diagonal): (5, 5, 1)
(M) Remark 8.4(a), n=12: the regular n-gon through the midpoints of the sides: 1 segment, x_1 = r^(+-1) x_0, factor 12; its neighbours: 2 segments, factor 6; factors of the bands of this class (direction of a shortest diagonal): (6, 2, 6)
ALL CHECKS PASSED
n=5: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 24 words; (T, R^-1): 30 words
n=7: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 25 words; (T, R^-1): 30 words
n=9: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 20 words; (T, R^-1): 30 words
n=15: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 20 words; (T, R^-1): 30 words
n=21: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 20 words; (T, R^-1): 30 words
n=25: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 17 words; (T, R^-1): 30 words
n=27: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 19 words; (T, R^-1): 30 words
n=33: 12 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 7 words; (T, R^-1): 12 words
n=35: 12 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 9 words; (T, R^-1): 12 words
n=45: 12 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 7 words; (T, R^-1): 12 words
total 246 words: agreement for (T, R): 168, for (T, R^-1): 246
patterns from Veech's formulas over all first rows (a,b):
  n=5 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [5, 1]
  n=7 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [7, 1]
  n=9 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [9, 3, 1]
  n=15 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [15, 5, 3, 1]
  n=21 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [21, 7, 3, 1]
  n=25 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [25, 5, 1]
  n=27 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [27, 9, 3, 1]
  n=45 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [45, 15, 9, 5, 3, 1]
  n=6 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(1, 1), (3, 1)] ; class of the direction of a side ('odd'): [(1,), (3,)]
  n=8 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(4, 4)] ; class of the direction of a side ('odd'): [(2, 1)]
  n=10 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(1, 1, 1), (5, 5, 1)] ; class of the direction of a side ('odd'): [(1, 1), (5, 5)]
  n=12 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(2, 2, 2), (6, 2, 6)] ; class of the direction of a side ('odd'): [(1, 1, 1), (3, 3, 1)]
  these are the factor patterns of Table 4 of the note
ALL CHECKS PASSED
Figure 1: B = 2.3090+0.9511i, N = 2, alpha = 22.3862 deg, beta = 94.3862 deg, beta - alpha = 72 deg, type A_0; the comment line of the figure agrees
Figure 3: the 31 reachable points of length <= 7.3 for n = 6 and their types (16 of type A_0, 5 each of A_1, A_2, A_3) agree with the enumeration
Figure 4, j = 5: the 6 vertices of the drawn trajectory agree with a literal billiard (max deviation 0.00002, side 1); it closes after 6 segments
Figure 4, j = 2: the 30 vertices of the drawn trajectory agree with a literal billiard (max deviation 0.00008, side 1); it closes after 30 segments
Figure 4: the labels d_1..d_7 = 15,15,5,15,3,5,15 agree
ALL CHECKS PASSED
run_all.sh: all programs ended without a failed assertion
