Riemann surfaces ¶

In [1]:

include("Riemann.jl");

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$\bf f(z)=\sqrt{z}$¶

In [2]:

zc, w = Riemann_data(w->w^2;)
fig1 = Plot(surf(zc, w;part=z->real(z)),
           Riemann_layout(L"\Re(\sqrt{z})";ztitle="ℜ(f(z))"))

Out[2]:

4-valued function, $f(z)=\sqrt{1+\sqrt{z}}$¶

In [3]:

r = range(0, 2, 100)
θ = range(-π, π, 200)
w = r * cis.(θ)'  #w=r exp(iθ)
zc = @. (w^2 -1.0)^2
fig3 = Plot(surface(x= real(zc), y=imag(zc), z=real(w), 
                   coloraxis="coloraxis",  
                    surfacecolor=angle.(w)),
            Riemann_layout(L"\Re(\sqrt{1+\sqrt{z}})";ztitle="Re(f(z))"))

Out[3]:

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