from matplotlib.pyplot import *
x=[1,2,3]
y=[2.3,3.5,10.0]
plot(x,y)
show()

plot(x,y,'o--')

xlabel('x')
ylabel('y')
xlim(0,4)
ylim(0,15)
title('$F(x)=\\frac{x^2}{y_i}$')
show()

close('all')
x=arange(0,10,0.2)
plot(x,sin(x),'gd:',label='$sin(x)$')
plot(x,cos(x),'rq:',label='cos(x)')
legend(loc=0)
show()

grid('on')

from sympy import *
x=Symbol('x') #  (.. , real=true, positive=true )

integrate(1/x,x)

integrate(1/(1-x),(x,0,x))

integrate(1/(1-x),(x,0,0.9))

solve(x**2-2*x-1,x)

diff(x**2+2*x+4)

from matplotlib.pyplot import *
from sympy import *
from pylab import *
from sympy.solvers import solve
close('all')
##################################################################
# Embelezamento
from fractions import Fraction
C=Symbol('C')
k=Symbol('k')
Co=Symbol('Co')
t=Symbol('t')
n=[-1,0,1/2,1,1.5,2]
figure(facecolor='white')
ax1=axes(frameon=False)
ax1.get_xaxis().tick_bottom()
ax1.axes.get_yaxis().set_visible(False)
ax1.axes.get_xaxis().set_visible(False)
annotate('$n \qquad  \qquad t=%s \qquad \qquad \qquad C(t)=f(t)$'
% '\int_{Co}^C \frac{dC}{kC^n}',xy=(0.1,1))
ax1.add_artist(Line2D((0, 0.9), (0.95, 0.95), color='black', linewidth=2))
ax1.add_artist(Line2D((0, 0.9), (0.05, 0.05), color='black', linewidth=2))
##################################################################
# Integração analítica de Equações Diferenciais
for i in n:

    s=integrate(1/(-k*C**i),(C,Co,C))
    annotate('$%.1f\qquad  \qquad   t=%s$'%(i,latex(s)),xy=(0.1,(i+1)/4+0.1))
    s=s-t
    s=solve(s,C)
    if i==-1:
        annotate('$C(t)=%s$'%latex(s[1]),xy=(0.6,(i+1)/4+0.1))
    else:
        annotate'$C(t)=%s$'%latex(s[0]),xy=(0.6,(i+1)/4+0.1))
show()