#Importem les llibreries necessàries pel plot
import numpy as np
import matplotlib.pylab as plt

#Introduim el codi que hem fet servir anteriorment

#Les figures es presenten directament al notebook
%pylab inline
#Les figure es fan en un format adequat per impressió
%config InlineBackend.figure_format = 'svg'

#Definim les nostres variables
x = np.linspace(-np.pi, np.pi, 10)
x1 = np.linspace(-np.pi, np.pi, 100)
y = np.sin(x)
y+=np.random.normal(0, 0.3, size=x.shape)
y1=np.sin(x1)
#Creem el plot i exigim que el mostri
plt.plot(x,y, 'o')
plt.plot(x1,y1,'r')
plt.show()

#Turtle graphics is an implementation of the popular geometric 
#drawing tools introduced in Logo, developed by Wally Feurzeig, 
#Seymour Papert and Cynthia Solomon in 1967.
import turtle

def poligon(turtle, size, segments=4):
    """Draws a poligon with a turtle.
    The segments have a length of size.
    The number of segments can be also modified."""   
    angle = 360./segments   
    for i in range(segments):
        turtle.forward(size)
        turtle.left(angle)
        
wn = turtle.Screen()        # Set up the window and its attributes
wn.screensize(250, 250)
wn.setup(width=280, height=280)
wn.bgcolor("gray")
wn.title("Test turtle")

alex = turtle.Turtle()      # Create turtle named alex

size = 50 #Poligon size

alex.color('red', 'red')
poligon(alex, size) #Draw a red square

alex.color('blue', 'blue')
poligon(alex, size, 5) # Draw a blue pentagon

alex.color('orange', 'orange')
poligon(alex, size, 6) # Draw an orange hexagon

alex.color('yellow', 'yellow')
poligon(alex, 10, 40) # Draw nearly a yellow circle

wn.exitonclick()

# import for turtle
import turtle

# Starting a Working Screen
ws = turtle.Screen()

# initializing a turtle instance
geekyTurtle = turtle.Turtle()

# executing loop 5 times for a star
for i in range(5):

		# moving turtle 100 units forward
		geekyTurtle.forward(100)

		# rotating turtle 144 degree right
		geekyTurtle.right(144)

# Verifiqueu que el següent codi demana un text per pantalla 
#  el retorna imprès
nom = input("Introdueix el teu nom: ")
print("> El teu nom és", nom)

%pylab inline
#importem les seguents funcions
import matplotlib.pyplot as plt
from numpy import sqrt
#definim la nostra variable
x = range(0, 100) 
#fem el plot, éssent l'eix d'abssices el corresponent als
#valors de 'x' i el d'ordenades, sqrt(x)
plt.plot(x, sqrt(x), '-', linewidth=2)

#definim la funcio per resoldre sistemes lineals
def solve_lin_sys(mat, vec):
    """Solves linear system mat·sol = vec
    by direct inversion with numpy functions"""    
    sol = inv(mat).dot(vec)
    return sol
#variables
A = array([[1., 2., 3.],[5., 3., 7.],[9., 1., 6.]])
b = array([1., 3., 5.])
x = solve_lin_sys(A,b)
#solucions
print("A:" , A)
print("b:" , b)
print("x:", x)

from IPython.display import Latex
import sympy

x=sympy.Symbol('x')
y=sympy.Symbol('y')
f=(x+2*y**3)**2

print("Standard output:")
print(f)
print(f.diff(y))
print(f.diff(x))
print(f.diff(x).diff(x))
print(f.diff(y).diff(x))

Latex(r'Latex output: \begin{eqnarray} f(x,y) = '+ sympy.latex(f) 
      + r'\\ \frac{\partial f(x,y)}{\partial x}=' + sympy.latex(f.diff(x)) 
      + r'\\ \frac{\partial f(x,y)}{\partial y}=' + sympy.latex(f.diff(y)) 
      + r'\\ \frac{\partial^2 f(x,y)}{\partial^2 x}='+ sympy.latex(f.diff(x).diff(x)) 
      + r'\\ \frac{\partial^2 f(x,y)}{\partial x \partial y}='+ sympy.latex(f.diff(y).diff(x)) 
      + r'\end{eqnarray}')