How do I generate a polynomial from roots that are repeated?

So I've got the roots of a polynomial from which I want to design the polynomial.

The thing is that I've got 8 roots, 4 of which are repeated. These are the roots I have:

-0.7437 - 1.4178i

-0.7437 - 1.4178i

-1.1031 + 0.1267i

-1.1031 + 0.1267i

-0.4571 + 0.9526i

-0.4571 + 0.9526i

-0.0977 + 1.0976i

-0.0977 + 1.0976i

When I do the polynomial by using the function poly, I get the polynomial that corresponds to the 8 roots but I'd like the polynomial for only the 4, non-repeated roots.

How could I do this? (I know I could probably eliminate the repeated, but I'd like a function that considers repeated roots or something).

Thanks in advance

Answer 1

[Star Strider]

Iinteresting. I would expect no repeats, and complex conjugate values instead.

Try this:

rts = [ -0.7437 - 1.4178i
        -0.7437 - 1.4178i
        -1.1031 + 0.1267i
        -1.1031 + 0.1267i
        -0.4571 + 0.9526i
        -0.4571 + 0.9526i
        -0.0977 + 1.0976i
        -0.0977 + 1.0976i];

Urts = unique(rts);
p1 = poly(Urts);

Ucrts = [Urts; conj(Urts)];
p2 = poly(Ucrts);

.

[Guillem Campins]

Ahhh yes, I just found that. But apparently my values are very slightly different, so it doesn't work hahaha

Thanks anyway :)

I tried uniquetol but it seems to only work with matrices :(

[Star Strider]

The uniquetol function works with any real argument you give it.

It does not work with complex values, however there is a work-around for that, as well:

rts = [ -0.7437 - 1.4178i
        -0.7437 - 1.4178i
        -1.1031 + 0.1267i
        -1.1031 + 0.1267i
        -0.4571 + 0.9526i
        -0.4571 + 0.9526i
        -0.0977 + 1.0976i
        -0.0977 + 1.0976i];
    
Urts = uniquetol([real(rts), imag(rts)], 0.01, 'ByRows',1);
Urts = Urts(:,1) + 1i*Urts(:,2)

Use whatever value you want for the tolerance argument. I used 0.01 here simply to demonstrate that it works.

[Guillem Campins]

Alright, that works! Thanks very much :)

[Star Strider]

As always, my pleasure!

Answer 2

[Image Analyst]

Did you try just multiplying them all together?

x = linspace(-8, 5, 1000);
r1 =  -0.7437 - 1.4178i
r2 =  -0.7437 - 1.4178i
r3 =  -1.1031 + 0.1267i
r4 =  -1.1031 + 0.1267i
r5 =  -0.4571 + 0.9526i
r6 =  -0.4571 + 0.9526i
r7 =  -0.0977 + 1.0976i
r8 =  -0.0977 + 1.0976i
y = (x-r1).*(x-r2).*(x-r3).*(x-r4).*(x-r5).*(x-r6).*(x-r7).*(x-r8)
plot(x, real(y), 'r-', 'LineWidth', 2);
hold on;
plot(x, imag(y), 'b-', 'LineWidth', 2);
grid on;
legend('Real', 'Imaginary');

[Guillem Campins]

Hmm the problem with that is that I need the value of the polynomial in a straight form (as in x^3+2x^2+1) more than I need the plot, and the polynomial is expressed in a very non-straight form by doing that.

Thanks for the effort, though :)

[Image Analyst]

Maybe might have to use the symbolic toolbox, which I don't have, to do the multiplication.