%pylab inline
Populating the interactive namespace from numpy and matplotlib
def plotBL(rho, sigma, axisbox = [-2, 2, -2, 2]):
theta = linspace(0, 2*pi, 1000)
eitheta = exp(1j * theta)
z = rho(eitheta) / sigma(eitheta)
plot(z.real, z.imag, 'r', linewidth=2)
# plot axes
xa, xb, ya, yb = axisbox
plot([xa, xb], [0, 0], 'k')
plot([0, 0], [ya, yb], 'k')
axis(axisbox)
axis('scaled') # so circles are circular
rho = lambda z: (z-1.) * z**2
sigma = lambda z: ((23*z - 16)*z + 5.) / 12.
plotBL(rho,sigma)
rho = lambda z: (z-1.) * z**4
sigma = lambda z: ((((1901*z - 2774)*z +2616)*z -1274)*z + 251) / 720
plotBL(rho,sigma)
rho = lambda z: (z-1.) * z**4
sigma = lambda z: (((((475*z + 1427)*z - 798)*z + 482)*z - 173)*z + 27)/ 1440
plotBL(rho,sigma)