maxSO3dim:=function(n) if n mod 4 eq 0 then d:=n div 2; elif n mod 2 eq 0 then d:=(n-2) div 2; else d:=(n-1) div 2; end if; return d; end function; massformula:=function(n) d:=maxSO3dim(n); e:=n-2*d; return &*[3^(d+e-i-1)+1:i in [0..d-1]]; end function; check:=function(n,CS) d:=maxSO3dim(n); return &and[IsSelfOrthogonal(x): x in CS] and &and[Dimension(x) eq d: x in CS] and &+[2^n*Factorial(n)/#AutomorphismGroup(C):C in CS] eq massformula(n) and &and{&and{not IsEquivalent(CS[i],CS[j]):j in {i+1..#CS}} :i in {1..#CS}}; end function; load "3.magma"; check(3,codes); load "4.magma"; check(4,codes); load "5.magma"; check(5,codes); load "6.magma"; check(6,codes); load "7.magma"; check(7,codes); load "8.magma"; check(8,codes); load "9.magma"; check(9,codes); load "10.magma"; check(10,codes); load "11.magma"; check(11,codes); load "12.magma"; check(12,codes); load "13.magma"; check(13,codes); load "14.magma"; check(14,codes); load "15.magma"; check(15,codes); load "16.magma"; check(16,codes); load "17.magma"; check(17,codes); load "18.magma"; check(18,codes); load "19.magma"; check(19,codes); load "20.magma"; check(20,codes); // Magma V2.15-13 Wed Sep 16 2009 15:15:31 on kiso1ws2 [Seed = 434360727] // Total time: 1.080 seconds, Total memory usage: 17.42MB