# Black box algorithm to find standard generators of the Fischer-Griess # Monster group M. set F 0 set G 0 set V 0 lbl SEMISTD rand 1 ord 1 A incr V if V gt 1000 then timeout if A notin 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 & 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 & 35 36 38 39 40 41 42 44 45 46 47 48 50 51 52 & 54 55 56 57 59 60 62 66 68 69 70 71 78 84 87 & 88 92 93 94 95 104 105 110 119 then fail if F eq 0 then if A in 34 38 50 54 62 68 94 104 110 then div A 2 B pwr B 1 2 set F 1 endif endif if G eq 0 then if A in 9 18 27 36 45 54 then div A 3 C pwr C 1 3 set G 1 endif endif if F eq 0 then jmp SEMISTD if G eq 0 then jmp SEMISTD set X 0 lbl CONJUGATE incr X if X gt 1000 then timeout rand 4 cjr 3 4 mu 2 3 5 ord 5 D if D notin 3 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 & 23 24 25 26 27 28 29 30 31 32 33 34 35 36 & 38 39 40 41 42 45 46 48 50 51 55 56 60 62 & 66 68 69 70 71 78 84 88 94 104 105 then fail if D noteq 29 then jmp CONJUGATE oup 2 2 3