Sum polynomials function help?

Hello Experts,

I have 2 or more polynomials of different degrees. Let x1 = [1,2,3,4] and x2=[5,6,7,8,9,10]

I need to sum x1 and x2 polynomials, please tell me what function does it.

Will appreciate any help.

Answer 1

[Dr. Seis]

If you mean you have polynomials with coefficients defined in x1 and x2 - for example the values in x1 would yield:

y = 1*x^3 + 2*x^2 + 3*x + 4;

Then you would sum the coefficients by pre-padding the array(s) of polynomial coefficients that are of smaller order. Example:

Create array of polynomial coefficients:

x1 = 1:4;
x2 = 5:10;

Create and save a new Matlab function:

function coeff_sum = sum_poly_coeff(x1, x2)

x1_order = length(x1);
x2_order = length(x2);

if x1_order > x2_order
     max_order = size(x1);
else
     max_order = size(x2);
end

new_x1 = padarray(x1,max_order-size(x1),0,'pre');
new_x2 = padarray(x2,max_order-size(x2),0,'pre');

coeff_sum = new_x1 + new_x2;

return

You can run this from the command line and view results by:

x3 = sum_poly_coeff(x1, x2);
x = 0:0.1:10;
plot(x,polyval(x1,x),'b-',x,polyval(x2,x),'r-',x,polyval(x3,x),'g-');

Or if you just want to see the result, you don't even have to create a function. Just do this at the command line:

x = 0:0.1:10;
plot(x,polyval(x1,x),'b-',x,polyval(x2,x),'r-',x,polyval(x1,x)+polyval(x2,x),'g-');

[Steve]

second option sum polynomials of different degrees.

maybe you have a code of this.

[Dr. Seis]

so then x2 would yield

y = 5*x^5 + 6*x^4 + 7*x^3 + 8*x^2 + 9*x + 10

[Steve]

and I need to sum them :

y = 1*x^3 + 2*x^2 + 3*x + 4

+

y = 5*x^5 + 6*x^4 + 7*x^3 + 8*x^2 + 9*x + 10

using a matlab function or a code...

[Dr. Seis]

See edited answer above.

[Bill Tubbs]

The only exception to this rule, is when the terms are decreasing negative powers. It seems that in this case, the first coefficient in the shorter vector corresponds to order zero (z^0) which is the highest order, and therefore the vector needs to be padded at the end, not the beginning.

Well, I assume that is the convention based on the following test.

1. polynomial in z is pre-padded:

>> tf1 = tf(1, [2 1], Ts)
>> tf1.Numerator{1}

ans =

     0     1

2. polynomial in z^-1 is 'post-padded':

>> tf2 = tf(1, [2 1], Ts, 'Variable', 'z^-1')
>> tf2.Numerator{1}

ans =

     1     0

Answer 2

[John D'Errico]

These are not truly polynomials. They are vectors of coefficients, that you choose to interpret as polynomials. How do you add them? Trivial. Pad the shorter one with zeros on the left, so they two vectors are the same length. Then adding the two vectors is truly trivial.

[Steve]

I know but say I have k polynomials. I need to add them in a function I am building. Is there a function that will get those polynomials and the result will be the sum of polynomials?

[Walter Roberson]

Find the max() of the length() of the coefficient vectors, and pad everything on the left to match that size, and then just add the padded vectors.

[Steve]

Thanks!

Walter and others who helped me, thank you very much!

You know I have a blog dedicated to learning and sharing information.

If it is acceptable and you are interested here is the address:

shareinfoblog.blogspot.com

Answer 3

[basilis]

hello experts,i have 2 polynomials to sum with different degree in line 16 (error)

clc

clear

%%Data Input

k=5*(10^6);

m=1000;

a=k/(4*m*(pi^2));

p1=[-1 0 a];

p2=[-1 0 2*a];

p3=[a^2 0 -2*(a^3)];

%%Calculations

p4=p2.^2-a^2;

p5=conv(p1,p4);

P=p3+p5;

roots(P)

%%Results Output

disp('the frequences are:')