# Black box algorithm to find standard generators of J2 set F 0 set G 0 set H 0 set V 0 set X 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 10 12 15 then fail if F eq 0 then if A in 2 6 10 then div A 2 B pwr B 1 2 set F 1 endif endif if G eq 0 then if A in 3 6 then div A 3 C pwr C 1 3 set G 1 endif endif # As well as finding elements of order 2 and 3 (for the # generators), we find a 2A-element. This allows us # to prove that the elements we have are in the right classes # before starting the random conjugating. if H eq 0 then if A in 4 8 12 then div A 2 D pwr D 1 4 set H 1 endif endif if F eq 0 then jmp SEMISTD if G eq 0 then jmp SEMISTD if H eq 0 then jmp SEMISTD mu 2 4 5 ord 5 D if D in 1 2 3 4 5 then # Probably a 2A element set F 0 jmp SEMISTD endif mu 3 4 6 ord 6 E if E in 6 12 then # Probably a 3A element set G 0 jmp SEMISTD endif # The elements are definitely in classes 2B and 3B now. lbl CONJUGATE incr X if X gt 1000 then timeout rand 7 cjr 3 7 mu 2 3 8 ord 8 D if D notin 2 3 5 6 7 8 10 12 15 then fail if D noteq 7 then jmp CONJUGATE mu 8 3 9 mu 8 9 10 ord 10 E if E notin 10 12 15 then fail if E noteq 12 then jmp CONJUGATE oup 2 2 3