[yangmp]

function f=language(x,y,x0)
syms t;
if length(x)==length(y)
n=length(x);
else
disp('x和y的维数不相等');
return;
end

f=0.0;
for i=1:n
l=y(i);
for j=1:i-1
l=l*(t-x(j))/(x(i)-x(j));
end
for j=i+1:n
l=l*(t-x(j))/(x(i)-x(j));
end

f=f+l;
simplify(f);

if i==n
if nargin==3
f=subs(f,'t',x0);
else
f=collect(f);
f=vpa(f,6);
end
end
end


function f=newton(x,y,x0)
syms t;
if length(x)==length(y)
n=length(x);
c(1:n)=0.0;
else
disp('x和y的维数不相等！');
return;
end

f=y(1);
y1=0;
l=1;

for i=1:n-1
for j=i+1:n
y1(j)=(y(j)-y(i))/(x(j)-x(i));
end
c(i)=y1(i+1);
l=l*(t-x(i));
f=f+c(i)*l;
simplify(f);
y=y1;

if i==n-1
if nargin==3
f=subs(f,'t',x0);
else
f=collect(f);
f=vpa(f,6);
end
end
end