How to make a polynomial with negative power?

Hi

I want to make a polynomial with the negative power like:

 0.9 - 2.2z^(-1) + 2.2z^(-2)

The problem is i do not know how to write this in Matlab since:

p=[2.2 2.2 0.9];
p = 1/p;

won't create the polynomial

   0.9 - 2.2z^(-1) + 2.2z^(-2)

Because i want to use the roots() function on it.

Hope someone has a nice solution

Cheers

[Jay Im]

syms x y; p=poly2sym(p,y);%try intermediate poly expression maker subs(p,x^-1);%substitute y with 1/x

Hope this does the trick.

[Walter Roberson]

roots() cannot be applied to symbolic polynomials. You can solve() such a system but not roots() it

Answer 1

[KSSV]

Let x = 1/z then your polynomial will be 0.9-2.2x+2.2x^2.

[Mikkel Labori Olsen]

Thanks Siva

The problem is i do not know how to write this in Matlab since:

p=[2.2 2.2 0.9];
p = 1/p;

won't create the polynomial

 0.9 - 2.2z^(-1) + 2.2z^(-2)

Because i want to use the roots() function on it.

[KSSV]

x = roots([.9, -2.2, 2.2]) ;

reciprocal of x are your required polynomial roots.

[Walter Roberson]

No! The roots are the same, not the recipricals!

Answer 2

[Andrei Bobrov]

z = roots([.9, -2.2, 2.2]) % here your polynomial  0.9*x^2 - 2.2*x + 2.2

Answer 3

[Walter Roberson]

By definition, polynomials never have negative powers of the variable.

The roots of an expression that is like a polynomial but has negative powers, are the same as the roots of the expression divided by the variable to the most negative power -- which is the same as multiplying by the variable to the positive version of the most negative power to give a polynomial. For example the roots of 0.9 - 2.2z^(-1) + 2.2z^(-2) are the same as the roots of 0.9*(z^0*z^2) - 2.2 * (z^(-1)*z^2) + 2.2*(z^(-2)*z^2) which is 0.9*z^2 - 2.2 * z + 2.2

Exception: roots that are 0 must be discarded.