# How to compute and display a conformal map in Sage

I am trying to create conformal maps of complex functions, ie something like this:

I have looked over the manuel, but the only thing I can find that is remotely related is the entry on Riemann mappings, which is not what I want. There is an interact that is capable of generating some of the functions I want to display, but it requires entering the functions for x and y manually and would become unmanageable for more complicated functions. Is there a better way to go about this?

Edit: I am using the latest version at time of writing, which is v. 10.0.

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Cosider the two options:

f(z)=z^2
complex_plot(f, (-3, 3), (-3, 3), plot_points=300,
contoured=True, tiled=True, cmap='plasma',aspect_ratio=1)


or

M = Manifold(2, 'M')
X.<x,y> = M.chart()
N = Manifold(2,'N')
U.<u,v> = N.chart()
z=(x+I*y)
def f(z):
return z^2
F = M.diff_map(N,[f(z).real(),f(z).imag()], name='F')
p1=X.plot(U,mapping=F,number_values={x:20,y:20},
ranges={x:(-3,3),y:(-3,3)},
color='grey',thickness=1,label_axes=False)
p1.show(aspect_ratio=0.6)

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