Julien's profile - activity

Hi,

How did Sage come up with a nice answer when being asked to compute the following elliptic integral of the second kind? $$\int \sqrt{1-(1/2)\sin^2(x)}dx$$

Using integral(f(x),x), SageMathCell returns: $$-\frac{\sqrt{2}}{48}(\sin(3x)-\sin(x))$$

Here is the link.

Is it my maths, or is it bug?

Thanks, Julien

This code works for my 3d graph.

But when I turn it into a function for an @interact, it does not work anymore.

How can I fix this? Thanks.

Edit: here is the code:

x, y, z = var('x, y, z')
@interact
def graphe(f = input_box(default=cos(y), label="$f(x,y)$"), r = input_box(default=10, label="$r$")):
    G = implicit_plot3d(z==f(x,y), (x, -r, r), (y, -r, r), (z, -r, r), plot_points=30, color='orange', mesh=1, opacity=.7)
    show(G, spin=1)

thanks a lot.

thanks @kcrisman: if possible, I was hoping for a ready-made command because I have not been able to adapt the documentation I found (including the one you refer to) about input_grid to this context. I really tried before asking.

It works, thanks. Do you know how to use input_grid in this context?

I found the following example here.

@interact
def _(m=('matrix', identity_matrix(2))):
    print m.eigenvalues()

Unlike the other examples I've tried, this one does not work when evaluated in SageMathCell. But it works well in a SageMathCloud Worksheet.

What am I supposed to do to produce such a matrix interact that works when I embed it in html pages?

I've tried to compute the following integral wth integral() in a SageMathCloud worksheet: $\displaystyle \int_{-\pi/6}^{\pi/6}\frac{\cos x}{1+\sin x}dx$.

The output was an error message (saying the integral is divergent), just like the one I got in SageMathCell (see link): https://sagecell.sagemath.org/?z=eJzz...

So I tried with integrate() and with numerical_integral() as well. I was never able to obtain the value of this integral, which turns out to be $\ln(3)$ after an obvious substitution.

Is this a bug?

Note that replacing 1 by 1.1 yields this: https://sagecell.sagemath.org/?z=eJzz...

while we get that when replacing 1 by 2: https://sagecell.sagemath.org/?z=eJzz...