read AllPrograms: read AllData: interface(screenwidth = 190): # A RootOf of degree n represents n complex numbers, so if f contains such a RootOf then # it represents n elements of C(x). Here we replace each such f by its n values in C(x) # (we also replace f by 1/f, see the comment at the end of Section 4.2). # RatFuncs := [seq(allvalues(1/f, 'implicit'), f = count5Belyi[infinity,2,4] )]: lprint("Up to Gal(Qbar/Q)-conjugacy we have", nops( count5Belyi[infinity,2,4] ), "elements in the (4,2,infinity)-count = 5 Belyi table, representing", nops(RatFuncs),"distinct elements of Qbar(x)"); for i to nops(RatFuncs) do Constellation[i] := g0g1( RatFuncs[i] ) od; S1 := {seq(UniqueRep_DC(Constellation[i]), i=1..nops(RatFuncs))}: nops(S1); P := PlanarDessins([4,2,infinity],5,"count"): S2 := `union`(op(P)): if S1 = S2 then lprint("Dessins match, completeness is proven") fi: