output = '##p: 7\n##id: yw\n';
% Q1
x = zeros(1, 6);
x(1) = -7;
for t = 2:6
    x(t) = x(t - 1) - polyval([3, -5, 3, -9, 7, -9], x(t - 1)) / polyval([15, -20, 9, -18, 7], x(t - 1));
end
x(1:6)
output = [output '##1: ' mat2str(ans) '\n'];
% Q2
x = zeros(1, 111);
x(1) = 2;
for t = 2:111
    if polyval([15, -20, 9, -18, 7], x(t - 1)) == 0
        x(t) = x(t - 1);
    else
        x(t) = x(t - 1) - polyval([3, -5, 3, -9, 7, -9], x(t - 1)) / polyval([15, -20, 9, -18, 7], x(t - 1));
    end
end
x(1:111)
output = [output '##2: ' mat2str(ans) '\n'];
% Q3
x = zeros(1, 1000);
x(1) = -8;
f = polyval([3, -5, 3, -9, 7, -9], x(1));
df = polyval([15, -20, 9, -18, 7], x(1));
t = 2;
while abs(f) >= 0.005 && abs(f) <= 10^7 && df ~= 0
    x(t) = x(t - 1) - f / df;
    f = polyval([3, -5, 3, -9, 7, -9], x(t));
    df = polyval([15, -20, 9, -18, 7], x(t));
    t = t + 1;
end
x(1:t-1)
output = [output '##3: ' mat2str(ans) '\n'];
% Q4
x = zeros(1, 7);
x(1:2) = [-7 -6];
f = polyval([3, -5, 3, -9, 7, -9], x(2:-1:1));
for t = 3:7
    x(t) = (x(t - 2) * f(1) - x(t - 1) * f(2)) / (f(1) - f(2));
    f(2) = f(1);
    f(1) = polyval([3, -5, 3, -9, 7, -9], x(t));
end
x(1:7)
output = [output '##4: ' mat2str(ans) '\n'];
% Q5
x = zeros(1, 112);
x(1:2) = [2 3];
f = polyval([3, -5, 3, -9, 7, -9], x(2:-1:1));
for t = 3:112
    if f(1) == f(2)
        x(t) = x(t - 1);
    else
        x(t) = (x(t - 2) * f(1) - x(t - 1) * f(2)) / (f(1) - f(2));
    end
    f(2) = f(1);
    f(1) = polyval([3, -5, 3, -9, 7, -9], x(t));
end
x(1:112)
output = [output '##5: ' mat2str(ans) '\n'];
% Q6
x = zeros(1, 1000);
x(1:2) = [-8 -7];
f = polyval([3, -5, 3, -9, 7, -9], x(2:-1:1));
t = 3;
while abs(f(1)) >= 0.005 && abs(f(1)) <= 10^7 && f(1) ~= f(2)
    x(t) = (x(t - 2) * f(1) - x(t - 1) * f(2)) / (f(1) - f(2));
    f(2) = f(1);
    f(1) = polyval([3, -5, 3, -9, 7, -9], x(t));
    t = t + 1;
end
x(1:t-1)
output = [output '##6: ' mat2str(ans) '\n'];
% Q7
[-6 11; 0 17 * phi(2.5)]
output = [output '##7: ' mat2str(ans) '\n'];
% Q8
x = -6:17/9:11;
m = x + 17/18;
[x; 0 17/9 * phi(m(1:9))];
output = [output '##8: ' mat2str(ans) '\n'];
% Q9 either same as Q8 or actually random
x = sort(rand(1, 10)) .* 17 - 6;
m = ([0 x] + [x 0]) .* 0.5;
[x; 0 diff(x) .* phi(m(2:10))]
output = [output '##9: ' mat2str(ans) '\n'];
% Q10 and write to file
output = [output '##10: None'];
file = fopen('P7.txt', 'wt');
fprintf(file, output);
fclose(file);
function p = phi(x)
    z = (x - 3) ./ 5;
    p = 1 / (5 * sqrt(2 * pi)) .* exp(-0.5 .* z .* z);
end