/* black box recognition procedure for O'N.2 */ StandardGeneratorsONAutm := function (G : Projective := false, Limit := 40) Fct := Projective select ProjectiveOrder else Order; P := RandomProcessWithWords (G); g, w := ElementOfOrder (P, {22,30,38}, Limit: Fct := Fct); if Type (g) eq BoolElt then return false, _; end if; h, v := ElementOfOrder (P, {20,28,56}, Limit: Fct := Fct); if Type (h) eq BoolElt then return false, _; end if; o1 := Fct (g); o2 := Fct (h); x := g^(o1 div 2); xw := w^(o1 div 2); b := h^(o2 div 4); bw := v^(o2 div 4); nmr := Limit; repeat nmr -:= 1; c, cw := Random (P); a := x^c; until Fct (a * b) eq 22 or nmr eq 0; if nmr eq 0 then return false, _; end if; aw := xw^cw; if not PresentationONAutm (G: UserGenerators := [a, b], Projective := Projective) then return false, _; end if; return [a, b], [aw, bw]; end function;