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function demo_riemann()
//demo_help demo_riemann
xbasc();
fs = get('figure_style');
set figure_style old;
xselect()
C=hotcolormap(200);C=C(1:$-40,:);
xset('wdim', 597,634);w=xget('window')
xset('colormap',C);xset('color',30);fond();
[z,s]=cplxroot(4,35) //compute
xset('pixmap',1)
cplxmap(z,s,163,69) //draw
xset('wshow')
realtimeinit(0.03)
for k=1:300,
realtime(k),
if modulo(k,10)==0 then
xset('wwpc')
cplxmap(z,s,163+k/10,69+k/20) //draw
xset('wshow')
end
end
set('figure_style',fs);
xdel(xget('window'))
endfunction
function fond()
n=size(xget('colormap'),1)
xset('background',n+1),
xset('foreground',n+2);
endfunction
function cplxmap(z,w,varargin)
//cplxmap(z,w,T,A,leg,flags,ebox)
//cplxmap Plot a function of a complex variable.
// cplxmap(z,f(z))
// Copyright INRIA
x = real(z);
y = imag(z);
u = real(w);v = imag(w);
ncols=size(xget('colormap'),1)
[X,Y,U]=nf3d(x,y,u);
[X,Y,V]=nf3d(x,y,v);
Colors = sum(V,'r');
Colors = Colors - min(Colors);
Colors = int((ncols-1)*Colors/max(Colors)+1);
plot3d(X,Y,list(U,Colors),varargin(:))
endfunction
function [z,s]=cplxroot(n,m)
//cplxroot(n,m,T,A,leg,flags,ebox)
//CPLXROOT Riemann surface for the n-th root.
// CPLXROOT(n) renders the Riemann surface for the n-th root.
// CPLXROOT, by itself, renders the Riemann surface for the cube root.
// CPLXROOT(n,m) uses an m-by-m grid. Default m = 20.
// Use polar coordinates, (r,theta).
// Cover the unit disc n times.
// Copyright INRIA
[lhs,rhs]=argn(0)
if rhs < 1, n = 3; end
if rhs < 2, m = 20; end
r = (0:m)'/m;
theta = - %pi*(-n*m:n*m)/m;
z = r * exp(%i*theta);
s = r.^(1/n) * exp(%i*theta/n);
endfunction
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