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2019-04-10 00:56:34 +0200 asked a question Elliptic Integral Bug?


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

2018-03-19 16:35:06 +0200 asked a question Error when making it a function

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')
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)
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2015-10-22 02:24:13 +0200 commented answer How to use matrices with @interact

thanks a lot.

2015-10-21 02:00:58 +0200 commented answer How to use matrices with @interact

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.

2015-10-21 01:18:34 +0200 commented answer How to use matrices with @interact

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

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2015-10-20 22:50:23 +0200 asked a question How to use matrices with @interact

I found the following example here.

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?

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2015-10-17 17:01:02 +0200 asked a question Is this a known bug with integral()

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):

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:

while we get that when replacing 1 by 2: