Contents Previous Next Subchapters

Converting A Set Of Roots To A Descending Polynomial
Syntax poly(z)
See Also zero2pol

Vector Argument
If z is a vector, poly returns a row vector p that corresponds to a descending polynomial p[x] which is zero at each of the elements of z where z is an integer real, double-precision, or complex column vector; that is
     p[z ] = 0 for i = 1, . . . , n
        i
where n is the length of the vector z. The return has length n+1 and the first element of the return value is 1. If the imaginary part of z is zero, the return value has type double-precision, otherwise the return value is complex.

Matrix Argument
If z is a square matrix , poly returns the polynomial that has zeros at the eigen values of z; i.e.,
     poly(eigen(z))

Example
We can compute the product
     x^2 - 1 = (x + 1) * (x - 1)
which has the descending polynomial representation
     [ 1 , 0 , -1 ]
by
     z = [-1, +1]
     poly(z)
which returns
     [ 1 , 0 , -1 ]