3d plot with restricted range

edit

Jason Grout gave two solutions:

def condor(x, y):
    if -y<=x<=y:
        e = gamma(y+1)
        a = gamma(1/2*y-1/2*x+1/2)
        b = gamma(-1/2*x+1/2*y+1)
        c = gamma(1/2*x+1/2*y+1/2)
        d = gamma(1/2*x+1/2*y+1)

        alpha = cos(pi*(y-x))
        beta  = cos(pi*(y+x))

        return log(e) + log(a)*((alpha-1)/2) + log(b)*((-alpha-1)/2) \
               + log(c)*((beta-1)/2) + log(d)*((-beta-1)/2)
    else:
        return 0

g = plot3d(condor, (-8,8), (0,8))
t = threejs(g)
t.lights([sage.plot.plot3d.light.AmbientLight((0.6,0.6,0.6))])

http://sagecell.sagemath.org:8880/?q=...

Two things:

1. right now, you have to implement the region restriction in the function itself.

2. since we are now invoking python logic in the function, when calling plot3d, we should just specify the function without parameters.

That function will be called with the appropriate numbers when being plotted.

Here's another try, using the implicit_plot3d's region parameter:

def condor(x, y):
    e = gamma(y+1)
    a = gamma(1/2*y-1/2*x+1/2)
    b = gamma(-1/2*x+1/2*y+1)
    c = gamma(1/2*x+1/2*y+1/2)
    d = gamma(1/2*x+1/2*y+1)

    alpha = cos(pi*(y-x))
    beta  = cos(pi*(y+x))

    return log(e) + log(a)*((alpha-1)/2) + log(b)*((-alpha-1)/2) \
           + log(c)*((beta-1)/2) + log(d)*((-beta-1)/2)

var('x,y,z')
g = implicit_plot3d(z-condor(x,y), (x,-8,8), (y,0,8), (z,0,5), \
region=lambda x,y,z: -  y<=x<=y)
show(g)
t=threejs(g)
t.lights([sage.plot.plot3d.light.AmbientLight((0.6,0.6,0.6))])

http://sagecell.sagemath.org/?q=qelyzi

It looks like that initial show() is needed in the cell server; I'm not sure if it will be needed in cloud.

=== My comment:

The first solution has the drawback that it generates an artifact, a plane at the floor of the plot.

The second solution does not show this artifact but I get the message: "You do not have Java applets enabled in your web browser, or your browser is blocking this applet."

Indeed I would like a solution like the first one which does not use Java (which I consider unsafe).