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 __future__ import division
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()

# coding: utf-8
from __future__ import division
from scipy.integrate import odeint
from pylab import *

#Simulação dinâmica: Enchimento de um tanque cilíndrico
#Parâmetros
A=1			#m2
Qe=1 	        	#m3s-1
#Variáveis
ho=0 	        	#m
t=arange(0,100,10)
#Equações
dh=lambda h,t:Qe/A
#Resolução
h=odeint(dh,ho,t)
#Representação
figure()
xlabel('tempo (s)')
ylabel(u'Altura de líquido (m)')
z=lambda x: ho+Qe/A*x
plot(t,h,'wo',label=u"$Solução\ Numérica$")
plot(t,z(t),'b--',label=u'$Solução\ Analítica$')
legend(loc=2)
show()

from __future__ import division
from matplotlib.pyplot import *
from scipy.integrate import odeint
from pylab import *
import numpy as np
close('all')
##################################################################
#Simulação dinâmica: ordem num reactor descontínuo
#Influência da ordem da reacção na variação da concentração com o tempo
#
#	Parâmetros
k=0.01		        #s^-1 /(mol/L)^(n-1)
Co=1 	        	#mol L^-1
n=[-1,0,1/2,1,2]
col=['k','b','r','g','y']
mark=['d--','s-','o:','+--','2-.']
#
#	Variáveis
ti=0
tf=101
npt=5
t=np.arange(ti,tf,npt)
#
#Equações
C=lambda C,t:-k*Co**(i-1)*C**i
#
#Resolução
figure()
xlabel('tempo (s)')
ylabel(u'Concentração $(mol/L)$')
ylim([0,Co])
for i in n:
    CS=odeint(C,Co,t)
#
#          Representação
    plot(t,CS,col[n.index(i)]+mark[n.index(i)],label="n= %s" % i)
legend()

show()