%% F1 = {["A"], [2], [0.7, 0.3]}.
%% F2 = {["B"], [3], [0.2, 0.7, 0.1]}.
%% F1 * F2 = {["A", "B"], [2, 3], [0.7 * 0.2, 0.7 * 0.7, 0.7 * 0.1,
%% 0.3 * 0.2, 0.3 * 0.7, 0.3 * 0.1]}

%% factor multiplication
mul({VarsA, CardsA, ValsA}, {VarsB, CardsB, ValsB}) ->
    ValsC =
        lists:foldl(
          fun(AElem, Acc) ->
              [lists:map(fun(BElem) -> AElem * BElem end, ValsB)|Acc]
          end, [], lists:reverse(ValsA)),
    {VarsA ++ VarsB, CardsA ++ CardsB, lists:flatten(ValsC)}.