Métodos Práctica 2

//Ejercicio 1
function r = misraices2(poli)
    a = coeff(poli, 2);
    b = coeff(poli, 1);
    c = coeff(poli, 0);
    if b < 0 then
        r(1) = (2*c) / (-b + sqrt(b^2-4*a*c));
        r(2) = (-b + sqrt(b^2-4*a*c)) / (2*a);
    else
        r(1) = (-b - sqrt(b^2-4*a*c)) / (2*a);
        r(2) = (2*c) / (-b - sqrt(b^2-4*a*c));
    end;
endfunction

//Ejercicio 2
//Justificación en carpeta
-->0.9222 * 10^4
 ans  =
    9222.
-->0.9222 * 10^4 + 0
 ans  =
    9222.
-->0.9222 * 10^4 + 0.9123 * 10^3
 ans  =
    10134.3
-->0.1013 * 10^4
 ans  =
    1013.
-->0.1013 * 10^5
 ans  =
    10130.
-->0.1013 * 10^5 + 0.3244 * 10^3
 ans  =
    10454.4
-->0.1045 * 10^5
 ans  =
    10450.
-->0.1045 * 10^5 + 0.2849 * 10^3
 ans  =
    10734.9
-->resultado1 = 0.1073 * 10^5
 resultado1  =
    10730.
-->0.2849 * 10^3 + 0.3244 * 10 ^ 3
 ans  =
    609.3
-->0.6093 * 10^3
 ans  =
    609.3
-->0.6093 * 10^3 + 0.9123 * 10^3
 ans  =
    1521.6
-->0.1522 * 10 ^ 4
 ans  =
    1522.
-->0.1522 * 10 ^ 4 + 0.9222 * 10 ^ 4
 ans  =
    10744.
-->resultado2 = 0.1074 * 10^5
 resultado2  =
    10740
-->resultadoPosta = 9222 + 912.3 + 324.4 + 284.9
 resultadoPosta  =
    10743.6



//Ejercicio 3
//Apartado b
function r = horny(polinomio, valor)
    grado = length(coeff(polinomio))
    r = coeff(polinomio, grado)
    for i = grado-1:-1:0
        r = r * valor + coeff(polinomio, i)
    end
endfunction

//Apartado d
function r = horny2(polinomio, valor)
    grado = length(coeff(polinomio))
    r(1) = coeff(polinomio, grado)
    r(2) = coeff(polinomio, grado)
    for i = grado-1:-1:1
        r(1) = r(1) * valor + coeff(polinomio, i)
        r(2) = r(2) * valor + r(1)
    end
    r(1) = r(1) * valor + coeff(polinomio, 0)
endfunction


//Ejercicio 4
//La introducción de error viene de un método malo, y se va propagando en cada iteración.
function y = aplicar(f,var,x)
    deff("z=F("+var+")","z="+f)
    y = F(x)
endfunction

function y = derivame(fun, var, orden, step, valor)
    if orden == 0 then
        y = aplicar(fun, var, valor)
    else
        deff("z = Pepe0("+var+")", "z =" + fun)
        for i=1:orden-1
            deff("z = Pepe"+string(i)+"("+var+")", "z = numderivative(Pepe"+string(i-1)+","+var+","+string(step)+",4)")
        end;
        deff("z = Fin("+var+")", "z = numderivative(Pepe"+string(orden-1)+","+var+","+string(step)+",4)")
        y = Fin(valor)
    end;
endfunction


function y = MInumderivative(fun, step, valor)
    y = (fun(valor + step) - fun(valor)) / step
endfunction


function y = MIderivame(fun, var, orden, step, valor)
    if orden == 0 then
        y = aplicar(fun, var, valor)
    else
        deff("z = Pepe0("+var+")", "z =" + fun)
        for i=1:orden-1
            deff("z = Pepe"+string(i)+"("+var+")", "z = MInumderivative(Pepe"+string(i-1)+","+string(step)+","+var+")")
        end;
        deff("z = Fin("+var+")", "z = MInumderivative(Pepe"+string(orden-1)+","+string(step)+","+var+")")
        y = Fin(valor)
    end;
endfunction



//Ejercicio 5
function y = aplicar(f,var,x)
    deff("z=F("+var+")","z="+f)
    y = F(x)
endfunction

function y = derivame(fun, var, orden, step, valor)
    if orden == 0 then
        y = aplicar(fun, var, valor)
    else
        deff("z = Pepe0("+var+")", "z =" + fun)
        for i=1:orden-1
            deff("z = Pepe"+string(i)+"("+var+")", "z = numderivative(Pepe"+string(i-1)+","+var+","+string(step)+",4)")
        end;
        deff("z = Fin("+var+")", "z = numderivative(Pepe"+string(orden-1)+","+var+","+string(step)+",4)")
        y = Fin(valor)
    end;
endfunction

function y = factorial (n)
    if n == 0 then
        y = 1
    else
        y = n * factorial (n-1)
    end
endfunction

function y = taylor(fun, var, inicio, grado, valor)
    deff("z = Funcion("+var+")", "z =" + fun)
    y = Funcion(inicio)
    for i=1:grado
        y = y + (derivame(fun, var, i, 0.01, inicio) * (valor - inicio)**i / factorial(i))
    end
endfunction




// Ejercicio 6
function y = ejercicio6(valor, grado)
    y = 1
    for i = 1:grado
        y = y + valor**i / factorial(i)
    end
endfunction

--> ejercicio6(-2,10)
 ans  =
   0.1353792
--> %e**-2
 ans  =
   0.1353353