Insert number in polynomial

So I have the polynomial p with syms x and I want the user to give me a number and calculate the polynomial at that point. The problem is that I cannot declare p as polynomial with vector because I don't know the degree. Here's my code :

clc
clear all;

syms x

x_val=[0 -pi/4 -pi/3 -pi/2 pi pi/6 pi/4 pi/3 pi/2 -pi];
y_val=[0 -sqrt(2)/2 -sqrt(3)/2 -1 0 1/2 sqrt(2)/2 sqrt(3)/2 1 0];

g=input('Give corner in raduis (from [p,-p])');
for i=1:10
  ar=1;
  par=1;
  for j=1:10
    if i==j
      continue %Αν το i==j τοτε να μην υπολογιστεί τίποτα γιατί ο παρονομαστής θα γίνει 0 και ο αριθμητής δεν περιέχει το (x-x1) στο L1
    else 
      ar=ar*(x-x_val(j));
      par=par*(x_val(i)-x_val(j));
    end
  end
  L(i)=ar/par;
end

p=0;
for i=1:10
  p=p+(y_val(i)*L(i));
end
f= @(x)p;
disp(f(g))
 

Answer 1

[Sergey Kasyanov]

Hello,

You need to replace f= @(x)p; by f = symfun(p,x);.

Answer 2

[VBBV]

You can use symsum function in place of for loop. since polynomial p is function of x, its easier to use symbolic summation for a specific range as shown to obtain the symbolic

clc
clear all;
syms x p

x_val=[0 -pi/4 -pi/3 -pi/2 pi pi/6 pi/4 pi/3 pi/2 -pi];
y_val=[0 -sqrt(2)/2 -sqrt(3)/2 -1 0 1/2 sqrt(2)/2 sqrt(3)/2 1 0];

g=4

g = 4

for i=1:10
  ar=1;
  par=1;
  for j=1:10
    if i==j
      continue %Αν το i==j τοτε να μην υπολογιστεί τίποτα γιατί ο παρονομαστής θα γίνει 0 και ο αριθμητής δεν περιέχει το (x-x1) στο L1
    else 
      ar=ar*(x-x_val(j));
      par=par*(x_val(i)-x_val(j));
    end
  end
  L(i)=ar/par;
end

% use symsum function for polynomial P
P = symsum(y_val.*L,x,1,10)

P = 

f = @(p) p + P

f = function_handle with value:
    @(p)p+P

disp(f(g))