sage: integral(integral(integral(x^2+2*y*z, (z, y, (2-x-2*y)/3)), (y, x, (2-x)/2)), (x, -1, 2))
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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:Is there a way to easily perform this operation even in sage?
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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'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?
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