Sum polynomials function help?
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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.
采纳的回答
Dr. Seis
2011-10-7
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-');
5 个评论
Steve
2011-10-7
Dr. Seis
2011-10-7
so then x2 would yield
y = 5*x^5 + 6*x^4 + 7*x^3 + 8*x^2 + 9*x + 10
Steve
2011-10-7
Dr. Seis
2011-10-8
See edited answer above.
Bill Tubbs
2021-8-9
编辑：Bill Tubbs
2021-8-9
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
更多回答（2 个）
John D'Errico
2011-10-7
1 个投票
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.
3 个评论
Steve
2011-10-7
Walter Roberson
2011-10-8
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
2011-10-8
basilis
2022-11-7
0 个投票
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:')
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