# Let's initialize pylab so we can plot later
%pylab inline

x = linspace(0, 2*pi)
plot(x, sin(x), label=r'$\sin(x)$')
plot(x, cos(x), 'ro', label=r'$\cos(x)$')
title(r'Two familiar functions')
legend();

%load_ext sympyprinting
import sympy as sym
from sympy import *
x, y, z = sym.symbols("x y z")

Rational(3,2)*pi + exp(I*x) / (x**2 + y)

eq = ((x+y)**2 * (x+1))
eq

expand(eq)

diff(cos(x**2)**2 / (1+x), x)

from IPython.display import Image
Image(filename='fig/img_4926.jpg')

from IPython.display import YouTubeVideo
YouTubeVideo('iwVvqwLDsJo')

%%ruby
puts "Hello from Ruby #{RUBY_VERSION}"

%%bash
echo "hello from $BASH"

%load_ext octavemagic

%%octave -s 500,500

# butterworth filter, order 2, cutoff pi/2 radians
b = [0.292893218813452  0.585786437626905  0.292893218813452];
a = [1  0  0.171572875253810];
freqz(b, a, 32);

%load_ext rmagic 

X = np.array([0,1,2,3,4])
Y = np.array([3,5,4,6,7])

%%R -i X,Y -o XYcoef
XYlm = lm(Y~X)
XYcoef = coef(XYlm)
print(summary(XYlm))
par(mfrow=c(2,2))
plot(XYlm)

XYcoef

%load_ext cythonmagic

%%cython -lm
from libc.math cimport sin
print 'sin(1)=', sin(1)