Question

Problem Six: Given two polynomials: g(x) = anx" + an-iz"-1 +--+ aix + ao Write a MATLAB function (name it polyadd) to add the two polynomials and returns a polynomial t(x) = g(x) + h(x), whether m = n, m < n or m > n. Polynomials are added by adding the coefficients of the terms with same power. Represent the polynomials as vectors of coefficients. Hence, the input to the function are the vectors: g=[an an-1 ao] and h=[am o] al am-1 a1 Test the function using the following polynomials: a) g [12 3 4] and h -[10 20 30 41]. b) g [11 12 13 14] andh [101 102]. c) g 143 54 55] and h [77 66 88 44 33]. erm

Answer 1

MATLAB CODE :

function x = polyadd(g,h)
length_g = length(g) ; % length of vector g
length_h = length(h) ; % length of vector h
if length_g > length_h % if length of g is grater than h
x = g; % initialize x with g
i = length_g ; % i is last index of g
j = length_h ; % j is last index of h
for k = 1 : length_h % loop from 1 to length_h
x(i) = x(i)+ h(j) ;% add h to x starting from last index
i = i - 1 ; % decrease i
j = j - 1 ; % decrease j
end

else % if length of h is greater than equal to length of g
x = h ; % initialize x with h
i = length_h ; % i is last index of h
j = length_g ; % j is last index of g
for k = 1 : length_g % loop from 1 to length_g
x(i) = x(i) + g(j);% add g to x starting from last index
i = i - 1 ; % decrease i
j = j - 1 ; % decrease j
end
end
end

OUTPUT :

(a)

g[l 2 3 4] h[o 20 30 41 >>h-[10 20 30 41] >>polyadd (g, h) ans - 11 22 33 45

(b)

>>g [11 12 13 14] h[101 102] >>polyadd (g,h) ans - 11 12 114 116

(c)

>>g [43 54 55] h(77 66 88 44 331 >>polyadd (g,h) ans - 77 66 131 98 88