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Sep 6, 2020, 4:09:53 AM9/6/20

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On Sun, Sep 6, 2020 at 8:25 AM Teodoro Coluccio

<teodoro....@gmail.com> wrote:

>

> Can I perform triple integrals in a region of space I define? I'm trying to migrate from mathematica to sage, and in mathematica I could go and define a region of space (with various limitations) and then perform the integral of a function on it. Here is an explanatory image:

> https://ibb.co/H74hgVS

> Is there a way to easily perform this operation even in sage?

>

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Please do not post links with ads here (in particular the sort of ads

that basically obscure the important part - after I opened your link I

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(https://remarkablemark.org/blog/2016/06/16/how-to-add-image-to-gist/).

On Sun, Sep 6, 2020 at 8:25 AM Teodoro Coluccio

<teodoro....@gmail.com> wrote:

>

> Can I perform triple integrals in a region of space I define? I'm trying to migrate from mathematica to sage, and in mathematica I could go and define a region of space (with various limitations) and then perform the integral of a function on it. Here is an explanatory image:

> https://ibb.co/H74hgVS

> Is there a way to easily perform this operation even in sage?

>

> --

> You received this message because you are subscribed to the Google Groups "sage-support" group.

> To unsubscribe from this group and stop receiving emails from it, send an email to sage-support...@googlegroups.com.

> To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/6692345e-f559-4637-9e4e-b679e9bbdc37n%40googlegroups.com.

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Sep 12, 2020, 7:23:56 AM9/12/20

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Can I perform triple integrals in a region of space I define? I'm trying to migrate from mathematica to sage, and in mathematica I could go and define a region of space (with various limitations) and then perform the integral of a function on it. Here is an explanatory image:

Sep 12, 2020, 8:05:17 AM9/12/20

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1) You have to integrate wrt z first, which I don't know whether Mma would understand without being told.

sage: integral(integral(integral(x^**2**+**2***y*z, (z, y, (**2**-x-**2***y)/**3**)), (y, x, (**2**-x)/**2**)), (x, -**1**, **2**))

1681/320

2) Using sympy (in sage, but I used https://live.sympy.org/):

(x, y, z)(x, y, z)

>>> integrate(x*x+2*y*z, (z, y, (2-x-2*y)/3), (y, x, (2-x)/2), (x, -1, 2))

1681/320

3) You can also do this in maxima (also included in sage). See

for an example of how to use the syntax.

4) Instead of reposting the same question 3 times , it would be helpful to others with the same question just

to keep the question in one thread.

5) Is this a homework problem for a math class?

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Sep 13, 2020, 6:30:09 AM9/13/20

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On Sun, Sep 6, 2020 at 10:03 AM Teodoro Coluccio <teodoro....@gmail.com> wrote:

Can I perform triple integrals in a region of space I define? I'm trying to migrate from mathematica to sage, and in mathematica I could go and define a region of space (with various limitations) and then perform the integral of a function on it.

in general, there are no exact algorithms known for such a task. Mathematica does implement some heuristics, it's not clear which ones.

In your example you're integrating a polynomial over a polytope, for this case it's known how to do this exactly:

triangulate the region into simplices, then use an explicit formula for each simplex. Perhaps that's

what Mathematica doing, they don't tell us.

Not implemented in Sage, but it would be a nice addition.

Here is an explanatory image:Is there a way to easily perform this operation even in sage?

--

Sep 13, 2020, 9:23:38 PM9/13/20

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Le dimanche 13 septembre 2020 12:30:09 UTC+2, Dima Pasechnik a écrit :

On Sun, Sep 6, 2020 at 10:03 AM Teodoro Coluccio <teodoro...@gmail.com> wrote:Can I perform triple integrals in a region of space I define? I'm trying to migrate from mathematica to sage, and in mathematica I could go and define a region of space (with various limitations) and then perform the integral of a function on it.in general, there are no exact algorithms known for such a task. Mathematica does implement some heuristics, it's not clear which ones.In your example you're integrating a polynomial over a polytope, for this case it's known how to do this exactly:triangulate the region into simplices, then use an explicit formula for each simplex. Perhaps that'swhat Mathematica doing, they don't tell us.Not implemented in Sage, but it would be a nice addition.Here is an explanatory image:Is there a way to easily perform this operation even in sage?

Note: also asked on Ask Sage:

- Triple integrals in a specific region of space

I posted an answer there.

Sep 15, 2020, 11:27:22 AM9/15/20

to sage-support

Thanks, right, I forgot the meaning of "int" in latte_int, sorry.

Indeed, this looks like one can actually do better than Mathematica, if latte_int is installed.

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