/*Résout f(x)=0 pour x dans [a,b]
    il faut f(a) et f(b) de signes contraires
*/

function  m=dichotomie(f,a,b)
while abs(a-b)>10^(-8)
    m=(a+b)/2
    if f(a)*f(m) < 0 then
        b=m
    else
        a=m
    end
end
m=(a+b)/2
endfunction

function y=base_lagrange(x)
    for i=1:length(x)
        a=x
        a(i)=[]
        p=poly(a,'x')
        p=p/horner(p,x(i))
        y(i)=p
    end
endfunction

function P=poly_lagrange(x,y)
    P=poly(0,'x','coeff')
    L=base_lagrange(x)
    for i=1:length(x)
        P=P+y(i)*L(i)
    end
endfunction

function y=derive(x,f)
    h=10**(-8)
    y=(feval(x+h,f)-feval(x,f))/h
endfunction

function y=tangente(f,x0,x)
    y=derive(x0,f)*(x-x0)+feval(x0,f)
    printf("y=%.1f(x-%.1f)+%.1f", derive(x0,f),x0,feval(x0,f))
endfunction

function u=suite1(f,u1,n)
    u=u1
    for i=1:n-1
        u(i+1)=f(u(i))
    end
    disp(u)
    clf
    plot(u,'*-r')
    xgrid(3)
endfunction

function n0=suite2(f,u0,l,eps)
    n0=0
    u=u1
    while abs(u-l)>eps
        n0=n0+1
        u=f(u)
    end
endfunction