# Black box algorithm to find standard generators of Co2 set F 0 set G 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 9 10 11 12 14 15 16 18 20 & 23 24 28 30 then fail if F eq 0 then if A in 16 18 28 then div A 2 B pwr B 1 2 set F 1 endif endif if G eq 0 then if A in 15 30 then div A 5 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 Y 0 set Z 0 set U 0 lbl CONJUGATE incr X if X gt 1000 then timeout incr Y rand 4 cjr 3 4 mu 2 3 5 ord 5 D if D notin 4 5 6 7 8 9 10 11 12 14 15 16 18 20 23 24 28 30 then fail if D eq 7 then set Z 1 # We are in the correct conjugacy class! endif if Z eq 0 then if Y gt 35 then set G 0 jmp SEMISTD endif # Certain product orders are much more likely to # occur with 5B elements (and vice versa) if D in 6 12 14 24 30 then incr U if D in 9 11 15 23 then decr U if U eq 3 then # Probably a 5B element. set G 0 jmp SEMISTD endif endif if D noteq 28 then jmp CONJUGATE # Once we've got y s.t. o(xy) = 28, we need to check # o(xyy) = 9 if we don't yet know that y is in the right # class. if Z eq 0 then mu 5 3 6 # abb ord 6 E if E notin 9 15 then fail if E eq 15 then set G 0 jmp SEMISTD endif endif oup 2 2 3