from sympy import *
from sympy.abc import t, n
T = 3
ti = -1
tf = 2
f = Piecewise((1, (t < 1) & (t > -1)), (0, (t < 2) & (t > 1)))
print ("n"+"Función = ")
pprint(f)
ao = integrate(2 / T * f, (t, ti, tf))
print ("n"+"a0 = ")
pprint(ao)
an = together(integrate((2 / T) * cos(2 * n * t * pi / T) * f, (t, ti, tf)))
print ("n"+"an = ")
pprint(an)
bn = together(integrate((2 / T) * sin(2 * n * t * pi / T) * f, (t, ti, tf)))
print ("n"+"bn = ")
pprint(bn)
armonicos = 5
print ("n"+"Serie de Fourier " + "(" + str(armonicos) + " armonicos) = ")
serie = (ao/2)
for i in range(1, armonicos + 1):
    serie = serie + (an*cos(2*n*t*pi/T)).subs(n, i)
for j in range(1, armonicos + 1):
    serie = serie + (bn*sin(2*n*t*pi/T)).subs(n, j)
pprint(serie)
plotting.plot(serie, ylim=(-0.5, 1.5), xlim=(-5,5))