Short version: Is there a generic formula for a polynomial expansion of the form \prod_i{(x-p_i)}?
Long version: I need to verify finding the roots of polynomials (C++), and, while I could do it by simply evaluating at a point, or more, I'd like to have the polynomial expanded, to collect the terms. The p_i terms are complex conjugate roots (all negative real part, if that matters), and if the order N is odd, there's an additional negative real root.
Currently, I am storing each root as a vector of 2 complex values (all inside another vector of length N), with the terms of x-p_i: \left[[1, p_0], [1, p_1], ...\right]. For expansion I am convolving the 1st with the 2nd, store the result in a length 3 vector, backup this vector in order to be reused for the next convolution, which needs to resize the vector, then repeat the process. This makes me cringe, but it works, eventually. However, I'd like to know if there's a more humane way of doing this.
