is there a way to obtain F(-x) polynomial

syms  x
%if i have 
% f is the coeffents of the polynomial
f=[2 43 12];
%F(x) is the polynomial of (+x)
F(x)=poly2sym(f,x)
%F(-x) the poly nomial of(-x)

F(-x)=???

% is there a way to obtain F(-x)?

[Torsten]

Set

G(x) = F(-x);

[ali temsah]

thanks!!

it worked but i didnt understand how

[Torsten]

You define a new symbolic function G as G(x) = F(-x). That's what F(-x) means.

Answer 1

[Voss]

Here's a way to do it by operating on the coefficients f rather than the symbolic F(x).

Realize that

• , n even
• , n odd

Therefore, you can obtain the coefficients of F(-x) from the cofficients of F(x) by negating the coefficients of the odd powers of x:

syms  x
f=[2 43 12];
%F(x) is the polynomial of (+x)
F(x)=poly2sym(f,x)

F(x) = 

%F_(x) is the polynomial of (-x)
f_ = f;
f_(end-1:-2:1) = -f(end-1:-2:1);
F_(x) = poly2sym(f_,x)

F_(x) = 

[Voss]

An alternative (maybe more intuitive) way to do the same (multiplying each coefficient by (-1)^n, where n is the corresponding power of x):

syms  x
f=[2 43 12];
%F(x) is the polynomial of (+x)
F(x)=poly2sym(f,x)

F(x) = 

%F_(x) is the polynomial of (-x)
f_ = f.*(-1).^(numel(f)-1:-1:0);
F_(x) = poly2sym(f_,x)

F_(x) = 

Answer 2

[Sam Chak]

@ali temsah

Alternatively, the same you've got F(x).

H(x) = poly2sym(f, -x)

[ali temsah]

i tried it but it gives an error

syms x

f=[4 3 2 43 12];

f_x=poly2sym(f,x)

h_x= poly2sym(f,-x)

[Sam Chak]

My apologies. I quickly ran it from Octave. I was not aware that it doesn't work on MATLAB. Follow @Torsten's and @_'s methods.