# Black box algorithm to find standard generators of M12.2 set K 0 set L 0 set X 0 lbl ELT2BAND12 rand 1 ord 1 A incr X if X gt 1000 then timeout if A notin 1 2 3 4 5 6 8 10 11 12 then fail if K eq 0 then if A eq 8 then pwr 4 1 2 # g2 is in 2B set K 1 endif endif if L eq 0 then if A eq 12 then cp 1 3 # g3 has order 12 set L 1 endif endif if K eq 0 then jmp ELT2BAND12 if L eq 0 then jmp ELT2BAND12 set X 0 lbl ELT2C incr X if X gt 1000 then timeout rand 4 cjr 3 4 mu 2 3 5 ord 5 D if D notin 2 4 6 10 12 then fail if D notin 2 6 10 then jmp ELT2C div D 2 E pwr E 5 6 # g6 is in 2C set X 0 lbl ELT3A incr X if X gt 1000 then timeout rand 7 cjr 2 7 mu 6 2 8 ord 8 F if F notin 2 4 6 10 12 then fail if F noteq 12 then jmp ELT3A pwr 4 8 9 # g9 is in 3A set X 0 lbl CONJUGATE incr X if X gt 1000 then timeout rand 10 cjr 9 10 mu 6 9 11 ord 11 G if G notin 2 4 6 10 12 then fail if G noteq 12 then jmp CONJUGATE mu 11 9 12 mu 11 12 13 ord 13 H if H notin 5 6 11 then fail if H noteq 11 then jmp CONJUGATE oup 2 6 9