Janko group J2, Hall–Janko group HJ (Presentation 2)
The claims on this page come from https://brauer.maths.qmul.ac.uk/Atlas/v3/pres/J2G1-P2.
Claim
\[
\mathrm{J}_2 = \langle a,b \mid a^{2} = b^{3} = (ab)^{7} = [a,b]^{12} = (ababab^{-1}abab^{-1})^{6} = 1 \rangle
\]
with
\[
|\mathrm{J}_2| = 604,800.
\]
On this page, we verify that the above claimed presentation of the Janko group J2 defines a group of order \(604,800\).
The code
In libsemigroups_pybind11, the following script constructs the presentation for J2 and runs the Todd-Coxeter algorithm.
The code below took about 27 seconds to run on a 2024 MacBook Pro M4 with 48GB
Code
from libsemigroups_pybind11 import (
Presentation,
ToddCoxeter,
congruence_kind,
presentation,
)
from libsemigroups_pybind11.words import parse_relations
# Setup the presentation object with the empty word and inverses, so it can represent a group
p = Presentation("abAB")
p.contains_empty_word(True)
presentation.add_inverse_rules(p, "ABab")
# Add the defining relations
presentation.add_rule(p, parse_relations("a^2"), "")
presentation.add_rule(p, parse_relations("b^3"), "")
presentation.add_rule(p, parse_relations("(ab)^7"), "")
presentation.add_rule(p, parse_relations("(a,b)^12"), "")
presentation.add_rule(p, parse_relations("(ababaBabaB)^6"), "")
presentation.balance(p, "abAB", "ABab")
presentation.replace_subword(p, "A", "a")
presentation.replace_subword(p, "B", "bb")
p.alphabet("ab")
tc = ToddCoxeter(congruence_kind.twosided, p)
tc.lookahead_extent(ToddCoxeter.options.lookahead_extent.full)
tc.strategy(ToddCoxeter.options.strategy.felsch)
print(f"The size of the group is {tc.number_of_classes()}")
The output
The output of the enumeration is below:
Output from the Python script
++++++++++++++++++++++++++++++++
#0: ToddCoxeter: RUN 0 START (strategy() = felsch)
#0: ToddCoxeter: |A| = 2, |R| = 9, |u| + |v| ∈ [2, 75], ∑(|u| + |v|) = 169
++++++++++++++++++++++++++++++++
#0: ToddCoxeter: FELSCH 0.0 START
#0: ToddCoxeter: FELSCH 0.0.0 | active | killed |
defined
#0: ToddCoxeter: nodes | 1 | 0 |
1
#0: ToddCoxeter: | active | missing | %
complete
#0: ToddCoxeter: edges | 0 | 2 |
0.0%
#0: ToddCoxeter: time | run 0 = 29µs | all runs = 29µs | elapsed =
76µs
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.1 | active | killed |
defined
#1: ToddCoxeter: nodes | 1,054,757 | 11,665 |
1,066,442
#1: ToddCoxeter: diff 0.0.0 | +1,054,756 | +11,665 |
+1,066,441
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 1,918,733 | 190,781 |
91.0%
#1: ToddCoxeter: diff 0.0.0 | +1,918,733 | +190,779 |
+91.0%
#1: ToddCoxeter: phase 0.0 = 1.005s | run 0 = 1.005s | all runs = 1.005s |
elapsed = 1.005s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.2 | active | killed |
defined
#1: ToddCoxeter: nodes | 2,068,730 | 24,927 |
2,093,682
#1: ToddCoxeter: diff 0.0.1 | +1,013,973 | +13,262 |
+1,027,240
#1: ToddCoxeter: diff 0.0.0 | +2,068,729 | +24,927 |
+2,093,681
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 3,773,664 | 363,796 |
91.2%
#1: ToddCoxeter: diff 0.0.1 | +1,854,931 | +173,015 |
+0.3%
#1: ToddCoxeter: diff 0.0.0 | +3,773,664 | +363,794 |
+91.2%
#1: ToddCoxeter: phase 0.0 = 2.010s | run 0 = 2.010s | all runs = 2.010s |
elapsed = 2.010s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.3 | active | killed |
defined
#1: ToddCoxeter: nodes | 3,048,312 | 38,150 |
3,086,472
#1: ToddCoxeter: diff 0.0.2 | +979,582 | +13,223 |
+992,790
#1: ToddCoxeter: diff 0.0.0 | +3,048,311 | +38,150 |
+3,086,471
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 5,546,882 | 549,742 |
91.0%
#1: ToddCoxeter: diff 0.0.2 | +1,773,218 | +185,946 |
-0.2%
#1: ToddCoxeter: diff 0.0.0 | +5,546,882 | +549,740 |
+91.0%
#1: ToddCoxeter: phase 0.0 = 3.015s | run 0 = 3.015s | all runs = 3.015s |
elapsed = 3.015s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.4 | active | killed |
defined
#1: ToddCoxeter: nodes | 4,041,704 | 52,159 |
4,093,872
#1: ToddCoxeter: diff 0.0.3 | +993,392 | +14,009 |
+1,007,400
#1: ToddCoxeter: diff 0.0.0 | +4,041,703 | +52,159 |
+4,093,871
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 7,357,321 | 726,087 |
91.0%
#1: ToddCoxeter: diff 0.0.3 | +1,810,439 | +176,345 |
+0.0%
#1: ToddCoxeter: diff 0.0.0 | +7,357,321 | +726,085 |
+91.0%
#1: ToddCoxeter: phase 0.0 = 4.020s | run 0 = 4.020s | all runs = 4.020s |
elapsed = 4.020s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.5 | active | killed |
defined
#1: ToddCoxeter: nodes | 5,007,440 | 65,309 |
5,072,763
#1: ToddCoxeter: diff 0.0.4 | +965,736 | +13,150 |
+978,891
#1: ToddCoxeter: diff 0.0.0 | +5,007,439 | +65,309 |
+5,072,762
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 9,119,814 | 895,066 |
91.1%
#1: ToddCoxeter: diff 0.0.4 | +1,762,493 | +168,979 |
+0.0%
#1: ToddCoxeter: diff 0.0.0 | +9,119,814 | +895,064 |
+91.1%
#1: ToddCoxeter: phase 0.0 = 5.024s | run 0 = 5.024s | all runs = 5.024s |
elapsed = 5.024s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.6 | active | killed |
defined
#1: ToddCoxeter: nodes | 5,986,526 | 79,692 |
6,066,241
#1: ToddCoxeter: diff 0.0.5 | +979,086 | +14,383 |
+993,478
#1: ToddCoxeter: diff 0.0.0 | +5,986,525 | +79,692 |
+6,066,240
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 10,912,342 | 1,060,710 |
91.1%
#1: ToddCoxeter: diff 0.0.5 | +1,792,528 | +165,644 |
+0.1%
#1: ToddCoxeter: diff 0.0.0 | +10,912,342 | +1,060,708 |
+91.1%
#1: ToddCoxeter: phase 0.0 = 6.029s | run 0 = 6.029s | all runs = 6.029s |
elapsed = 6.029s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.7 | active | killed |
defined
#1: ToddCoxeter: nodes | 6,950,902 | 94,545 |
7,045,467
#1: ToddCoxeter: diff 0.0.6 | +964,376 | +14,853 |
+979,226
#1: ToddCoxeter: diff 0.0.0 | +6,950,901 | +94,545 |
+7,045,466
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 12,679,959 | 1,221,845 |
91.2%
#1: ToddCoxeter: diff 0.0.6 | +1,767,617 | +161,135 |
+0.1%
#1: ToddCoxeter: diff 0.0.0 | +12,679,959 | +1,221,843 |
+91.2%
#1: ToddCoxeter: phase 0.0 = 7.034s | run 0 = 7.034s | all runs = 7.034s |
elapsed = 7.034s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.8 | active | killed |
defined
#1: ToddCoxeter: nodes | 7,908,946 | 106,977 |
8,015,937
#1: ToddCoxeter: diff 0.0.7 | +958,044 | +12,432 |
+970,470
#1: ToddCoxeter: diff 0.0.0 | +7,908,945 | +106,977 |
+8,015,936
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 14,433,768 | 1,384,124 |
91.2%
#1: ToddCoxeter: diff 0.0.7 | +1,753,809 | +162,279 |
+0.0%
#1: ToddCoxeter: diff 0.0.0 | +14,433,768 | +1,384,122 |
+91.2%
#1: ToddCoxeter: phase 0.0 = 8.039s | run 0 = 8.039s | all runs = 8.039s |
elapsed = 8.039s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.9 | active | killed |
defined
#1: ToddCoxeter: nodes | 8,826,087 | 120,204 |
8,946,309
#1: ToddCoxeter: diff 0.0.8 | +917,141 | +13,227 |
+930,372
#1: ToddCoxeter: diff 0.0.0 | +8,826,086 | +120,204 |
+8,946,308
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 16,072,677 | 1,579,497 |
91.1%
#1: ToddCoxeter: diff 0.0.8 | +1,638,909 | +195,373 |
-0.2%
#1: ToddCoxeter: diff 0.0.0 | +16,072,677 | +1,579,495 |
+91.1%
#1: ToddCoxeter: phase 0.0 = 9.044s | run 0 = 9.044s | all runs = 9.044s |
elapsed = 9.044s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.10 | active | killed |
defined
#1: ToddCoxeter: nodes | 9,775,831 | 135,310 |
9,911,156
#1: ToddCoxeter: diff 0.0.9 | +949,744 | +15,106 |
+964,847
#1: ToddCoxeter: diff 0.0.0 | +9,775,830 | +135,310 |
+9,911,155
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 17,827,462 | 1,724,200 |
91.2%
#1: ToddCoxeter: diff 0.0.9 | +1,754,785 | +144,703 |
+0.1%
#1: ToddCoxeter: diff 0.0.0 | +17,827,462 | +1,724,198 |
+91.2%
#1: ToddCoxeter: phase 0.0 = 10.049s | run 0 = 10.049s | all runs = 10.049s |
elapsed = 10.049s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.11 | active | killed |
defined
#1: ToddCoxeter: nodes | 10,718,880 | 146,360 |
10,865,256
#1: ToddCoxeter: diff 0.0.10 | +943,049 | +11,050 |
+954,100
#1: ToddCoxeter: diff 0.0.0 | +10,718,879 | +146,360 |
+10,865,255
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 19,534,800 | 1,902,960 |
91.1%
#1: ToddCoxeter: diff 0.0.10 | +1,707,338 | +178,760 |
-0.1%
#1: ToddCoxeter: diff 0.0.0 | +19,534,800 | +1,902,958 |
+91.1%
#1: ToddCoxeter: phase 0.0 = 11.050s | run 0 = 11.050s | all runs = 11.050s |
elapsed = 11.050s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.12 | active | killed |
defined
#1: ToddCoxeter: nodes | 11,650,984 | 163,136 |
11,814,139
#1: ToddCoxeter: diff 0.0.11 | +932,104 | +16,776 |
+948,883
#1: ToddCoxeter: diff 0.0.0 | +11,650,983 | +163,136 |
+11,814,138
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 21,236,938 | 2,065,030 |
91.1%
#1: ToddCoxeter: diff 0.0.11 | +1,702,138 | +162,070 |
+0.0%
#1: ToddCoxeter: diff 0.0.0 | +21,236,938 | +2,065,028 |
+91.1%
#1: ToddCoxeter: phase 0.0 = 12.055s | run 0 = 12.055s | all runs = 12.055s |
elapsed = 12.055s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.13 | active | killed |
defined
#1: ToddCoxeter: nodes | 12,585,643 | 183,529 |
12,769,191
#1: ToddCoxeter: diff 0.0.12 | +934,659 | +20,393 |
+955,052
#1: ToddCoxeter: diff 0.0.0 | +12,585,642 | +183,529 |
+12,769,190
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 23,004,143 | 2,167,143 |
91.4%
#1: ToddCoxeter: diff 0.0.12 | +1,767,205 | +102,113 |
+0.3%
#1: ToddCoxeter: diff 0.0.0 | +23,004,143 | +2,167,141 |
+91.4%
#1: ToddCoxeter: phase 0.0 = 13.060s | run 0 = 13.060s | all runs = 13.060s |
elapsed = 13.060s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.14 | active | killed |
defined
#1: ToddCoxeter: nodes | 13,520,513 | 196,671 |
13,717,195
#1: ToddCoxeter: diff 0.0.13 | +934,870 | +13,142 |
+948,004
#1: ToddCoxeter: diff 0.0.0 | +13,520,512 | +196,671 |
+13,717,194
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 24,688,003 | 2,353,023 |
91.3%
#1: ToddCoxeter: diff 0.0.13 | +1,683,860 | +185,880 |
-0.1%
#1: ToddCoxeter: diff 0.0.0 | +24,688,003 | +2,353,021 |
+91.3%
#1: ToddCoxeter: phase 0.0 = 14.065s | run 0 = 14.065s | all runs = 14.065s |
elapsed = 14.065s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.15 | active | killed |
defined
#1: ToddCoxeter: nodes | 14,451,287 | 208,571 |
14,659,875
#1: ToddCoxeter: diff 0.0.14 | +930,774 | +11,900 |
+942,680
#1: ToddCoxeter: diff 0.0.0 | +14,451,286 | +208,571 |
+14,659,874
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 26,322,838 | 2,579,736 |
91.1%
#1: ToddCoxeter: diff 0.0.14 | +1,634,835 | +226,713 |
-0.2%
#1: ToddCoxeter: diff 0.0.0 | +26,322,838 | +2,579,734 |
+91.1%
#1: ToddCoxeter: phase 0.0 = 15.070s | run 0 = 15.070s | all runs = 15.070s |
elapsed = 15.070s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.16 | active | killed |
defined
#1: ToddCoxeter: nodes | 15,364,601 | 230,647 |
15,595,262
#1: ToddCoxeter: diff 0.0.15 | +913,314 | +22,076 |
+935,387
#1: ToddCoxeter: diff 0.0.0 | +15,364,600 | +230,647 |
+15,595,261
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 28,048,246 | 2,680,956 |
91.3%
#1: ToddCoxeter: diff 0.0.15 | +1,725,408 | +101,220 |
+0.2%
#1: ToddCoxeter: diff 0.0.0 | +28,048,246 | +2,680,954 |
+91.3%
#1: ToddCoxeter: phase 0.0 = 16.075s | run 0 = 16.075s | all runs = 16.075s |
elapsed = 16.075s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.17 | active | killed |
defined
#1: ToddCoxeter: nodes | 16,278,171 | 251,128 |
16,529,313
#1: ToddCoxeter: diff 0.0.16 | +913,570 | +20,481 |
+934,051
#1: ToddCoxeter: diff 0.0.0 | +16,278,170 | +251,128 |
+16,529,312
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 29,733,273 | 2,823,069 |
91.3%
#1: ToddCoxeter: diff 0.0.16 | +1,685,027 | +142,113 |
+0.1%
#1: ToddCoxeter: diff 0.0.0 | +29,733,273 | +2,823,067 |
+91.3%
#1: ToddCoxeter: phase 0.0 = 17.080s | run 0 = 17.080s | all runs = 17.080s |
elapsed = 17.080s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.18 | active | killed |
defined
#1: ToddCoxeter: nodes | 17,136,800 | 264,123 |
17,400,945
#1: ToddCoxeter: diff 0.0.17 | +858,629 | +12,995 |
+871,632
#1: ToddCoxeter: diff 0.0.0 | +17,136,799 | +264,123 |
+17,400,944
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 31,328,380 | 2,945,220 |
91.4%
#1: ToddCoxeter: diff 0.0.17 | +1,595,107 | +122,151 |
+0.1%
#1: ToddCoxeter: diff 0.0.0 | +31,328,380 | +2,945,218 |
+91.4%
#1: ToddCoxeter: phase 0.0 = 18.085s | run 0 = 18.085s | all runs = 18.085s |
elapsed = 18.085s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.19 | active | killed |
defined
#1: ToddCoxeter: nodes | 18,042,421 | 284,551 |
18,326,991
#1: ToddCoxeter: diff 0.0.18 | +905,621 | +20,428 |
+926,046
#1: ToddCoxeter: diff 0.0.0 | +18,042,420 | +284,551 |
+18,326,990
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 32,928,600 | 3,156,242 |
91.3%
#1: ToddCoxeter: diff 0.0.18 | +1,600,220 | +211,022 |
-0.2%
#1: ToddCoxeter: diff 0.0.0 | +32,928,600 | +3,156,240 |
+91.3%
#1: ToddCoxeter: phase 0.0 = 19.090s | run 0 = 19.090s | all runs = 19.090s |
elapsed = 19.090s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.20 | active | killed |
defined
#1: ToddCoxeter: nodes | 18,949,003 | 299,208 |
19,248,204
#1: ToddCoxeter: diff 0.0.19 | +906,582 | +14,657 |
+921,213
#1: ToddCoxeter: diff 0.0.0 | +18,949,002 | +299,208 |
+19,248,203
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 34,554,079 | 3,343,927 |
91.2%
#1: ToddCoxeter: diff 0.0.19 | +1,625,479 | +187,685 |
-0.1%
#1: ToddCoxeter: diff 0.0.0 | +34,554,079 | +3,343,925 |
+91.2%
#1: ToddCoxeter: phase 0.0 = 20.095s | run 0 = 20.095s | all runs = 20.095s |
elapsed = 20.095s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.21 | active | killed |
defined
#1: ToddCoxeter: nodes | 19,836,819 | 326,032 |
20,162,865
#1: ToddCoxeter: diff 0.0.20 | +887,816 | +26,824 |
+914,661
#1: ToddCoxeter: diff 0.0.0 | +19,836,818 | +326,032 |
+20,162,864
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 36,181,798 | 3,491,840 |
91.2%
#1: ToddCoxeter: diff 0.0.20 | +1,627,719 | +147,913 |
+0.0%
#1: ToddCoxeter: diff 0.0.0 | +36,181,798 | +3,491,838 |
+91.2%
#1: ToddCoxeter: phase 0.0 = 21.100s | run 0 = 21.100s | all runs = 21.100s |
elapsed = 21.100s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.22 | active | killed |
defined
#1: ToddCoxeter: nodes | 20,746,679 | 346,083 |
21,092,769
#1: ToddCoxeter: diff 0.0.21 | +909,860 | +20,051 |
+929,904
#1: ToddCoxeter: diff 0.0.0 | +20,746,678 | +346,083 |
+21,092,768
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 37,905,561 | 3,587,797 |
91.4%
#1: ToddCoxeter: diff 0.0.21 | +1,723,763 | +95,957 |
+0.2%
#1: ToddCoxeter: diff 0.0.0 | +37,905,561 | +3,587,795 |
+91.4%
#1: ToddCoxeter: phase 0.0 = 22.105s | run 0 = 22.105s | all runs = 22.105s |
elapsed = 22.105s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.23 | active | killed |
defined
#1: ToddCoxeter: nodes | 21,642,109 | 365,426 |
22,007,543
#1: ToddCoxeter: diff 0.0.22 | +895,430 | +19,343 |
+914,774
#1: ToddCoxeter: diff 0.0.0 | +21,642,108 | +365,426 |
+22,007,542
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 39,527,455 | 3,756,763 |
91.3%
#1: ToddCoxeter: diff 0.0.22 | +1,621,894 | +168,966 |
-0.0%
#1: ToddCoxeter: diff 0.0.0 | +39,527,455 | +3,756,761 |
+91.3%
#1: ToddCoxeter: phase 0.0 = 23.110s | run 0 = 23.110s | all runs = 23.110s |
elapsed = 23.110s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.24 | active | killed |
defined
#1: ToddCoxeter: nodes | 22,545,900 | 383,811 |
22,929,721
#1: ToddCoxeter: diff 0.0.23 | +903,791 | +18,385 |
+922,178
#1: ToddCoxeter: diff 0.0.0 | +22,545,899 | +383,811 |
+22,929,720
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 41,219,413 | 3,872,387 |
91.4%
#1: ToddCoxeter: diff 0.0.23 | +1,691,958 | +115,624 |
+0.1%
#1: ToddCoxeter: diff 0.0.0 | +41,219,413 | +3,872,385 |
+91.4%
#1: ToddCoxeter: phase 0.0 = 24.115s | run 0 = 24.115s | all runs = 24.115s |
elapsed = 24.115s
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.25 | active | killed |
defined
#1: ToddCoxeter: nodes | 21,779,189 | 1,989,573 |
23,768,083
#1: ToddCoxeter: diff 0.0.24 | -766,711 | +1,605,762 |
+838,362
#1: ToddCoxeter: diff 0.0.0 | +21,779,188 | +1,989,573 |
+23,768,082
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 39,817,438 | 3,740,940 |
91.4%
#1: ToddCoxeter: diff 0.0.24 | -1,401,975 | -131,447 |
-0.0%
#1: ToddCoxeter: diff 0.0.0 | +39,817,438 | +3,740,938 |
+91.4%
#1: ToddCoxeter: phase 0.0 = 25.120s | run 0 = 25.120s | all runs = 25.120s |
elapsed = 25.120s
#0: ToddCoxeter: large collapse, number of coincidences 100,000 >= 100,000 =
large_collapse()!
++++++++++++++++++++++++++++++++
#1: ToddCoxeter: FELSCH 0.0.26 | active | killed |
defined
#1: ToddCoxeter: nodes | 2,806,820 | 20,961,781 |
23,768,083
#1: ToddCoxeter: diff 0.0.25 | -18,972,369 | +18,972,208 |
+0
#1: ToddCoxeter: diff 0.0.0 | +2,806,819 | +20,961,781 |
+23,768,082
#1: ToddCoxeter: | active | missing |
% complete
#1: ToddCoxeter: edges | 0 | 5,613,640 |
0.0%
#1: ToddCoxeter: diff 0.0.25 | -39,817,438 | +1,872,700 |
-91.4%
#1: ToddCoxeter: diff 0.0.0 | +0 | +5,613,638 |
+0.0%
#1: ToddCoxeter: phase 0.0 = 26.121s | run 0 = 26.121s | all runs = 26.121s |
elapsed = 26.121s
++++++++++++++++++++++++++++++++
#0: ToddCoxeter: FELSCH 0.0 STOP
#0: ToddCoxeter: FELSCH 0.0.27 | active | killed |
defined
#0: ToddCoxeter: nodes | 604,800 | 23,163,283 |
23,768,083
#0: ToddCoxeter: diff 0.0.26 | -2,202,020 | +2,201,502 |
+0
#0: ToddCoxeter: diff 0.0.0 | +604,799 | +23,163,283 |
+23,768,082
#0: ToddCoxeter: | active | missing |
% complete
#0: ToddCoxeter: edges | 1,209,600 | 0 |
100.0%
#0: ToddCoxeter: diff 0.0.26 | +1,209,600 | -5,613,640 |
+100.0%
#0: ToddCoxeter: diff 0.0.0 | +1,209,600 | -2 |
+100.0%
#0: ToddCoxeter: phase 0.0 = 26.308s | run 0 = 26.308s | all runs = 26.308s |
elapsed = 26.308s
++++++++++++++++++++++++++++++++
#0: ToddCoxeter: LOOKAHEAD 0.1 START (lookahead_extent() = full,
lookahead_style() = hlt)
#0: ToddCoxeter: LOOKAHEAD 0.1.0 | active | killed |
defined
#0: ToddCoxeter: nodes | 604,800 | 23,163,283 |
23,768,083
#0: ToddCoxeter: | active | missing |
% complete
#0: ToddCoxeter: edges | 1,209,600 | 0 |
100.0%
#0: ToddCoxeter: time | run 0 = 26.308s | all runs = 26.308s |
elapsed = 26.308s
#0: ToddCoxeter: triggered because there are skipped definitions (604,800
active nodes)!
++++++++++++++++++++++++++++++++
#0: ToddCoxeter: LOOKAHEAD 0.1 STOP
#0: ToddCoxeter: LOOKAHEAD 0.1.1 | active | killed |
defined
#0: ToddCoxeter: nodes | 604,800 | 23,163,283 |
23,768,083
#0: ToddCoxeter: diff 0.1.0 | +0 | +0 |
+0
#0: ToddCoxeter: | active | missing |
% complete
#0: ToddCoxeter: edges | 1,209,600 | 0 |
100.0%
#0: ToddCoxeter: diff 0.1.0 | +0 | +0 |
+0.0%
#0: ToddCoxeter: phase 0.1 = 254ms | run 0 = 26.563s | all runs = 26.563s |
elapsed = 26.563s
#0: ToddCoxeter: lookahead_next() is now max(f x a = 1,209,600, m = 10,000)
(-3,790,400)
#0: ToddCoxeter: because f x a < n
#0: ToddCoxeter: where: a = number_of_nodes_active() = 604,800
#0: ToddCoxeter: f = lookahead_growth_factor() = 2
#0: ToddCoxeter: m = lookahead_min() = 10,000
#0: ToddCoxeter: n = lookahead_next() = 5,000,000
++++++++++++++++++++++++++++++++
#0: ToddCoxeter: FELSCH 0.2.2 | active | killed |
defined
#0: ToddCoxeter: nodes | 604,800 | 23,163,283 |
23,768,083
#0: ToddCoxeter: diff 0.2.1 | +0 | +0 |
+0
#0: ToddCoxeter: diff 0.2.0 | +0 | +0 |
+0
#0: ToddCoxeter: | active | missing |
% complete
#0: ToddCoxeter: edges | 1,209,600 | 0 |
100.0%
#0: ToddCoxeter: diff 0.2.1 | +0 | +0 |
+0.0%
#0: ToddCoxeter: diff 0.2.0 | +0 | +0 |
+0.0%
#0: ToddCoxeter: phase 0.2 = 254ms | run 0 = 26.563s | all runs = 26.563s |
elapsed = 26.563s
++++++++++++++++++++++++++++++++
#0: ToddCoxeter: RUN 0 STOP (finished)
#0: ToddCoxeter: run 0 | lookahead | lookbehind |
hlt | felsch
#0: ToddCoxeter: num. phases | 1 | 0 |
0 | 1
#0: ToddCoxeter: time spent in phases | 254ms (1%) | - (0%) |
- (0%) | 26.308s (99%)
#0: ToddCoxeter: phase 0.2 = 256ms | run 0 = 26.565s | all runs = 26.565s |
elapsed = 26.565s
The size of the group is 604800
The computed size of the group matches the size of the group provided on the ATLAS: \(604,800\).