Substitute a polynomial into another polynomial??

I want to subsitute x^2 (coefficients =[1 0 0]) into x^3+x+1 [1 0 1 1],

so I will obtain x^6+x^2+1 [1 0 0 0 1 0 1]

How can I do that?

Answer 1

[Andrei Bobrov]

p1 = [1 0 1 1];
p2 = [1 0 0];

n2 = find(fliplr(p2(1:end-1)));
n1 = find(fliplr(p1(1:end-1)));
n = n1*n2;
pout(n) = 1;
out = fliplr([p1(end) pout]);

or without fliplr

n2 = find(p2(end-1:-1:1));
n1 = find(p1(end-1:-1:1));
n = n1*n2;
pout(n) = 1;
out = [pout(end:-1:1), p1(end)];

[mintug]

Hi, I notice that it does not work for every equation such that

x^3 [1 0 0 0] ------>  x^4 +  x^2 +  x + 1 [1 0 1 1 1] 

It gives -------> x^12 +  x^6 +  x^4 +  x^3 +  x^2 + 1

Do you have a generalized method? At least could you explain the logic of your code?