# Black box algorithm to find standard generators of M12 # (Second listed algorithm) 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 10 11 then fail if F eq 0 then if A in 4 8 then div A 2 B pwr B 1 2 set F 1 endif endif if G eq 0 then if A eq 10 then pwr 5 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 ELTORDER3 incr X if X gt 1000 then timeout rand 4 cj 3 4 5 mu 3 5 6 ord 6 D if D notin 1 2 3 4 5 6 then fail if D notin 3 6 then jmp ELTORDER3 div D 3 E pwr E 6 7 set X 0 lbl CONJUGATE incr X if X gt 1000 then timeout rand 8 cjr 7 8 mu 2 7 9 ord 9 F if F notin 2 3 5 6 8 10 11 then fail if F noteq 11 then jmp CONJUGATE oup 2 2 7