poly_matlab

function x = poly(arr1, arr2)
    sum = add(arr1, arr2)
    mul = multiplication(arr1, arr2)
    [q, r] = division(arr1, arr2)
    gcd = gcd_poly(arr1, arr2)
end


function ans = add(arr1, arr2)

    if (length(arr2) > length(arr1))
        c = arr1;
        arr1 = arr2;
        arr2 = c;
    end
    ans = zeros(1, length(arr1));
    n = length(arr1);
    m = length(arr2);
    for i=n:-1:1
        if (m > 0)
            ans(i) = arr1(i) + arr2(m);
            m -= 1;
        else
            ans(i) = arr1(i);
        end
    end
end


function ans = multiplication(arr1, arr2)

    n = length(arr1) + length(arr2) - 1;
    ans = zeros(1, n);

    for i=1:length(arr1)
        pw1 = length(arr1) - i;
        for j=1:length(arr2)
            pw2 = length(arr2) - j;
            ans(n - pw1 - pw2) += arr1(i) * arr2(j);
        end
    end
end


function [ans1, ans2] = division(arr1, arr2)

    ans1 = [];
    while (length(arr1) >= length(arr2) && (arr1(1) != 0))

        d = arr1(1) / arr2(1);
        ans1 = [ans1 d];
        for i=1:length(arr2)
            arr1(i) -= arr2(i) * d;
        end

        t = length(arr1);
        while (t > 1)
            arr1(1) = [];
        end
    end
    ans2 = arr1;
end


function ans = gcd_poly(arr1, arr2)

    if (length(arr2) > length(arr1))
        c = arr1;
        arr1 = arr2;
        arr2 = c;
    end
    r = 1;
    while ((length(arr1) > 1 && length(arr2) > 1) && (r != 0))

        fx = arr1;
        gx = arr2;
        [~, r]= division(fx, gx);

        i = 1;
        while ((r(i) == 0) && (length(r) > 1))
            r(i) = [];
        end
        if (r == 0)
            break;
        end

        arr1 = gx;
        arr2 = r;
    end

    ans = r;
end