chembal.lua

local isSolid = {
    ["Ba"]={},
    ["Cl"]={},
    ["Cu"]={},
    ["SO_4"]={
        ["Ca"]=true,
        ["Ba"]=true
    },
    ["Ca"]={},
    ["Na"]={},
    ["CO_3"]={
        ["Ba"]=true,
        ["Cl"]=true,
        ["Cu"]=true,
        ["SO_4"]=true,
        ["Ca"]=true,
        ["CO_3"]=true,
        ["OH"]=true,
        ["S"]=true,
    },
    ["OH"]={
        ["Cl"]=true,
        ["Cu"]=true,
        ["SO_4"]=true,
        ["CO_3"]=true,
        ["OH"]=true,
        ["S"]=true,
    },
    ["S"]={
        ["Ba"]=true,
        ["Cl"]=true,
        ["Cu"]=true,
        ["SO_4"]=true,
        ["Ca"]=true,
        ["CO_3"]=true,
        ["OH"]=true,
        ["S"]=true,
    },
    ["NH_4"]={}
}

for i,v in pairs(isSolid) do
    for ii,vv in pairs(v) do
        isSolid[ii][i] = vv
    end
end

local charges = {["Ba"]=2, ["Cl"]=-1, ["Cu"]=2, ["SO_4"]=-2, ["Ca"]=2, ["Na"]=1, ["CO_3"]=-2, ["OH"]=-1, ["S"]=-2, ["NH_4"]=1}

local complex = {["SO_4"]=true, ["CO_3"]=true, ["OH"]=true, ["NH_4"]=true}

local function gcd(a, b)
    if b == 0 then
        return a
    else
        return gcd(b, a % b)
    end
end

function lcm(...)
    local function lcm2(a, b)
        return (a * b / gcd(a, b))
    end

    local args = {...}

    if #args == 2 then
        return lcm2(args[1], args[2])
    else
        local arg0 = table.remove(args,1)
        return lcm2(arg0, lcm(unpack(args)))
    end
end

local function chemamt(c1, c2)
    local n = gcd(math.abs(charges[c1]), math.abs(charges[c2]))
    return math.abs(charges[c2]/n), math.abs(charges[c1]/n)
end

local function isaq(c1, c2)
    return not isSolid[c1][c2]
end

local function chemname(c1, c2, m)
    local n1, n2 = chemamt(c1, c2)

    return  ((complex[c1] and n1 ~= 1) and "(" or "") .. c1 .. ((complex[c1] and n1 ~= 1) and ")" or "") .. (n1 == 1 and "" or ("_" .. n1))
            ..
            ((complex[c2] and n2 ~= 1) and "(" or "") .. c2 .. ((complex[c2] and n2 ~= 1) and ")" or "") .. (n2 == 1 and "" or ("_" .. n2))
            ..
            (isaq(c1, c2) and " (aq)" or " (s)")
end

local function ionsname(c1, c2, m)
    local n1, n2 = chemamt(c1, c2)
    m = m or 1
    n1 = n1 * m; n2 = n2 * m

    return  "" ..
            (n1 ~= 1 and n1 or "") .. c1 .. "^{" .. (math.abs(charges[c1]) == 1 and "" or math.abs(charges[c1])) .. (charges[c1] < 0 and "-" or "+") .. "} (aq)"
            .. " + " ..
            (n2 ~= 1 and n2 or "") .. c2 .. "^{" .. (math.abs(charges[c2]) == 1 and "" or math.abs(charges[c2])) .. (charges[c2] < 0 and "-" or "+") .. "} (aq)"
end

local function chembal(c1, c2, c3, c4)
    local a, b = chemamt(c1, c2)
    local c1s = {a, b, chemamt(c3, c4)}
    c, b = chemamt(c3, c2)
    local a, d = chemamt(c1, c4)
    local c2s = {a, b, c, d}

    local mults = {1, 1, 1, 1}

    while true do
        local done = true

        for i,lhs in ipairs({unpack(c1s)}) do
            local rhs = c2s[i]
            if lhs ~= rhs then
                done = false

                local fact = lcm(lhs, rhs)
                local f1, f2 = fact/lhs, fact/rhs

                if i == 1 then
                    mults[1] = mults[1] * f1
                    c1s[1] = c1s[1] * f1
                    c1s[2] = c1s[2] * f1

                    mults[4] = mults[4] * f2
                    c2s[1] = c2s[1] * f2
                    c2s[4] = c2s[4] * f2
                elseif i == 2 then
                    mults[1] = mults[1] * f1
                    c1s[1] = c1s[1] * f1
                    c1s[2] = c1s[2] * f1

                    mults[3] = mults[3] * f2
                    c2s[2] = c2s[2] * f2
                    c2s[3] = c2s[3] * f2
                elseif i == 3 then
                    mults[2] = mults[2] * f1
                    c1s[3] = c1s[3] * f1
                    c1s[4] = c1s[4] * f1

                    mults[3] = mults[3] * f2
                    c2s[2] = c2s[2] * f2
                    c2s[3] = c2s[3] * f2
                elseif i == 4 then
                    mults[2] = mults[2] * f1
                    c1s[3] = c1s[3] * f1
                    c1s[4] = c1s[4] * f1

                    mults[4] = mults[4] * f2
                    c2s[1] = c2s[1] * f2
                    c2s[4] = c2s[4] * f2
                end

                break
            end
        end

        if done then
            --[[mults = {
                mults[1]/gcd(mults[1],gcd(mults[2],mults[3]))/gcd(mults[1],gcd(mults[3],mults[4]))/gcd(mults[1],gcd(mults[2],mults[4])),
                mults[2]/gcd(mults[2],gcd(mults[3],mults[4]))/gcd(mults[2],gcd(mults[1],mults[4]))/gcd(mults[2],gcd(mults[1],mults[3])),
                mults[3]/gcd(mults[3],gcd(mults[2],mults[1]))/gcd(mults[3],gcd(mults[1],mults[4]))/gcd(mults[3],gcd(mults[2],mults[4])),
                mults[4]/gcd(mults[4],gcd(mults[1],mults[2]))/gcd(mults[4],gcd(mults[1],mults[3]))/gcd(mults[4],gcd(mults[2],mults[3]))
            }]]
            return unpack(mults)
        end
    end
end

local function equation1(c1, c2, c3, c4)
    local m1, m2, m3, m4 = chembal(c1, c2, c3, c4)
    return  (m1 == 1 and "" or (m1 .. " ")) .. chemname(c1, c2)
            .. " + " ..
            (m2 == 1 and "" or (m2 .. " ")) .. chemname(c3, c4)
            .. " \\rightarrow " ..
            (m3 == 1 and "" or (m3 .. " ")) .. chemname(c3, c2)
            .. " + " ..
            (m4 == 1 and "" or (m4 .. " ")) .. chemname(c1, c4)
end

local function equation2(c1, c2, c3, c4)
    local m1, m2, m3, m4 = chembal(c1, c2, c3, c4)
    return  (isaq(c1, c2) and ionsname(c1, c2, m1) or ((m1 == 1 and "" or (m1 .. " ")) .. chemname(c1, c2)))
            .. " + " ..
            (isaq(c3, c4) and ionsname(c3, c4, m2) or ((m2 == 1 and "" or (m2 .. " ")) .. chemname(c3, c4)))
            .. " \\rightarrow " ..
            (isaq(c3, c2) and ionsname(c3, c2, m3) or ((m3 == 1 and "" or (m3 .. " ")) .. chemname(c3, c2)))
            .. " + " ..
            (isaq(c1, c4) and ionsname(c1, c4, m4) or ((m4 == 1 and "" or (m4 .. " ")) .. chemname(c1, c4)))
end

local function equation3(c1, c2, c3, c4)
    local m1, m2, m3, m4 = chembal(c1, c2, c3, c4)
    if not isaq(c3, c2) then
        return ionsname(c3, c2, m3) .. " \\rightarrow " .. (m3 == 1 and "" or (m3 .. " ")) .. chemname(c3, c2)
    elseif not isaq(c1, c4) then
        return ionsname(c1, c4, m4) .. " \\rightarrow " .. (m4 == 1 and "" or (m4 .. " ")) .. chemname(c1, c4)
    else
        return "ERROR"
    end
end

local chems = {{"Ba", "Cl"}, {"Cu", "SO_4"}, {"Ca", "Cl"}, {"Na", "CO_3"}, {"Na", "OH"}, {"Na", "S"}, {"NH_4", "OH"}}

for i,v in ipairs(chems) do
    for ii,vv in ipairs(chems) do
        if i<ii then
            local c1, c2, c3, c4 = v[1], v[2], vv[1], vv[2]
            io.write(i.."+"..ii..":\t")
            --if not isaq(c3, c2) or not isaq(c1, c4) then
                print(equation1(c1,c2,c3,c4))
                print("\t"..equation2(c1,c2,c3,c4))
                print("\t"..equation3(c1,c2,c3,c4))
            --else
            --  print("NR")
            --end
        end
    end
end