# Black box algorithm to find standard generators of J3 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 8 9 10 12 15 17 19 then fail if F eq 0 then if A in 2 4 6 8 10 12 then div A 2 B pwr B 1 2 set F 1 endif endif if G eq 0 then if A in 6 12 15 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 2 3 5 6 8 10 12 15 17 19 then fail if D noteq 19 then jmp CONJUGATE mu 5 3 6 mu 5 6 7 ord 7 E if E noteq 9 then jmp CONJUGATE oup 2 2 3