% luaset package
% version 1.1
% Authors: Chetan Shirore and Ajit Kumar
% Licensed under LaTeX Project Public License v1.3c or later. The complete license text is available at http://www.latex-project.org/lppl.txt.


\ProvidesPackage{luaset}[1.1]
\RequirePackage{xkeyval}
\RequirePackage{amsmath}
\RequirePackage{luacode}
\RequirePackage{luamaths}
\begin{luacode*}
sets = {} -- global registry for sets.
Set = {} -- the module.
local mt = {
    __tostring = function(self)
        return "\\{" .. table.concat(table.sortedkeys(self), ", ") .. "\\}"
    end
}
-- Adding functions to the module.
function Set.new(str)
    str = str or ""
    local set = {}
    for v in utilities.parsers.iterator(str) do
        set[v] = true
    end
    return setmetatable(set, mt)
end

function Set.union (a, b)
        local union = {}
        for k in pairs(a) do union[k] = true end
        for k in pairs(b) do union[k] = true end
        return setmetatable(union, mt)
      end

function Set.intersection (a, b)
        local intersection = {}
        for k in pairs(a) do
          intersection[k] = b[k]
            end
        return setmetatable(intersection, mt)
        end

function Set.difference (a, b)
        local difference = {}
        for k in pairs(a) do
        if b[k]~= true then
          difference[k] = true
        end
        end
         setmetatable(difference, mt)
        return difference
      end

function Set.cardinal (a)
        local len = 0
        for k in pairs(a) do
          len = len + 1
          end
        return len
      end

function Set.subseteq(a, b)
        for k in pairs(a) do
          if not b[k] then return false end
        end
        return true
    end

function Set.subset (a, b)
        return Set.subseteq(a, b)  and not (Set.subseteq(b, a) )
    end

    function Set.equal (a, b)
        return Set.subseteq(a, b)  and  (Set.subseteq(b, a) )
    end


function Set.belongsto (x, s)
        if s[x] then
        return true
      else
        return false
        end
    end

\end{luacode*}

\newcommand\luaSetNew[2]{%
    \directlua{%
        sets[\luastringN{#1}] = Set.new(\luastringN{#2})
    }%
}

\newcommand\luaSetUnion[3]{%
    \directlua{%
        sets[\luastringN{#1}] = Set.union(sets[\luastringN{#2}],
                                          sets[\luastringN{#3}])
    }%
}

\newcommand\luaSetIntersection[3]{%
    \directlua{%
        sets[\luastringN{#1}] = Set.intersection(sets[\luastringN{#2}],
                                          sets[\luastringN{#3}])
    }%
}

\newcommand\luaSetDifference[3]{%
    \directlua{%
        sets[\luastringN{#1}] = Set.difference(sets[\luastringN{#2}],
                                          sets[\luastringN{#3}])
    }%
}


\newcommand\luaSetPrint[1]{%
    \directlua{tex.sprint(tostring(sets[\luastringN{#1}]))}%
}

\newcommand\luaSetCardinal[1]{%
    \directlua{tex.sprint(tostring(Set.cardinal(sets[\luastringN{#1}])))}%
}

\newcommand\luaSetSubseteq[2]{%
    \directlua{tex.sprint(tostring(Set.subseteq(sets[\luastringN{#1}],sets[\luastringN{#2}])))}%
}

\newcommand\luaSetSubset[2]{%
    \directlua{tex.sprint(tostring(Set.subset(sets[\luastringN{#1}],sets[\luastringN{#2}])))}%
}

\newcommand\luaSetEqual[2]{%
    \directlua{tex.sprint(tostring(Set.equal(sets[\luastringN{#1}],sets[\luastringN{#2}])))}%
}

\newcommand\luaSetBelongsto[2]{%
    \directlua{tex.sprint(tostring(Set.belongsto("#1",sets[\luastringN{#2}])))}%
}

\endinput