Polynomial Division

local function Divide(DividendCoefList, DivisorCoefList)
    local DividendDegree = #DividendCoefList
    local DivisorDegree = #DivisorCoefList
    local SolutionCoefList = {}
    if DivisorDegree > DividendDegree then
        print("Degree of Divisor is Greater than that of Dividend")
        os.exit()
     else
        local SolutionDegree = DividendDegree - DivisorDegree
        for clc = DividendDegree, DivisorDegree, -1 do
            frac = DividendCoefList[clc] / DivisorCoefList[DivisorDegree]
            SolutionCoefList[SolutionDegree - (DividendDegree - clc)] = frac
            temp = {}
            for i = DivisorDegree, 0, -1 do
                temp[i] = DivisorCoefList[i] * frac
            end
            for i = clc, clc - DivisorDegree, -1 do
                DividendCoefList[i] = DividendCoefList[i] - temp[DivisorDegree - (clc - i)]
            end
        end
        return SolutionCoefList, DividendCoefList, DivisorCoefList
    end
end



local function printPoly(poly)
    for i = #poly, 0, -1 do
        if(poly[i] ~= nil) then
          io.write(poly[i])
          io.write(" ")
        else
          return
        end
    end
    print()
end





io.write("enter the degree of the Dividend:")
local dividendD = io.read("*n")
io.write("enter the degree of the Divisor:")
local divisorD = io.read("*n")



if type(dividendD) ~= "number" or type(divisorD) ~= "number" then
    print()
    print()
    print("Input must be a number")
    os.exit()
    print()
end

io.write("input every coefficient of the dividend polynomial in descending order from highest power:")

local dividendCoefs = {}
for i = dividendD, 0, -1 do
    dividendCoefs[i] = io.read("*n")
    if(type(dividendCoefs[i]) ~= "number") then
        print("Input must be a number")
        os.exit()
    end
end

io.write("input every coefficient of the divisor polynomial in descending order from highest power:")



local divisorCoefs = {}
for i = divisorD, 0, -1 do
    divisorCoefs[i] = io.read("*n")
    if(type(divisorCoefs[i]) ~= "number") then
        print("Input must be a number")
        os.exit()
    end
end
io.read()
solution, remainder, divisor = Divide(dividendCoefs, divisorCoefs)

print("the coefs of the solution are: ")
print()
printPoly(solution)
print()
print("with a remainder of: ")
print()
printPoly(remainder)
io.write("divided by ")
printPoly(divisor)
print()
io.write("Press enter")
io.read()