require "poly"

local function ldiv(p1, p2)
    local num = p1:toarray():reverse()
    local den = p2:toarray():reverse()
    local result = {}
    local base = #num - #den
    while base >= 0 do
        local res = num:back() / den:back()
        result:insert(res)
        num = num:slice(1, #num - 1)
        for i = 1, #den - 1 do
            num[base + i] -= res * den[i]
        end
        base -= 1
    end
    local quot = poly.of(result)
    local rem = poly.of(num)
    return {quot, rem}
end

local num = poly.of({1, -12, 0, -42})
local den = poly.of({1, -3})
local res = ldiv(num, den)
print("Dividing polynomials:")
print($"N = {num}")
print($"D = {den}")
print("---------------------")
print($"Q = {res[1]}")
print($"R = {res[2]}")