[Math] math.bhaskara

--Creator: Bolodefchoco
--Made in: 18/09/2016
--Last update: 18/09/2016
--[[ Notes:
    Does:
        Retorna o bhaskara da equação
    Args:
        e --> A equação (xy²+xy+x)
]]--

local cfact = function(x)
    local num,den = x:match("(%d+)/(%d+)")
    num,den = tonumber(num),tonumber(den)
    while den ~= 0 do
        local t = den
        den = num%den
        num = t
    end
    return num
end

local isInteger = function(x)
    return math.floor(x) - x == 0
end

local simplify = function(x)
    local num,den = x:match("(%d+)/(%d+)")
    local f = cfact(x)
    local n,d = num/f,den/f
    if isInteger(n/d) then
        return n/d
    else
        return n.."/"..d
    end
end

math.reduceDec = function(x,n)
    local d = n and "1"..("0"):rep(n) or 100
    return math.floor(x*d)/d
end

math.toFraction = function(x,reduce)
    if reduce then
        x = math.reduceDec(x,1)
    end
    local int,dec = math.modf(x)
    if dec == 0 then
        return x
    else
        local numb,frac = tostring(x):match("(%d+)%.(%d+)")
        local fracDen = "1" .. ("0"):rep(#frac)
        local result = numb..frac.."/"..fracDen
        return simplify(result)
    end
end

local getDiv = function(d)
    if type(d) == "string" then
        local f,d = d:match("(%d+)/(%d+)")
        return f/d
    else
        return d
    end
end

math.bhaskara = function(e)
    e = e:gsub(" ","")
    local a,x,b,c = e:match("(%p*%d+)(%a*)²*.*(%p%d+).*(%p%d+)")
    a,b,c,x = tonumber(a),tonumber(b),tonumber(c),x or "x"
    local delta = (b^2) - 4*a*c
    delta = delta^.5
    if delta < 0 or delta ~= delta then
        return "Delta is negative"
    else
        local x1 = (-b + delta) / (2*a)
        local x2 = (-b - delta) / (2*a)
        x1,x2 = x1~=x1 and 0 or math.toFraction(x1,true),x2~=x2 and 0 or math.toFraction(x2,true)
        local max = getDiv(x1) > getDiv(x2) and {x1,x2} or {x2,x1}
        return x:upper() .. " = {"..max[1]..", "..max[2].."}"
    end
end