19
$\begingroup$

Fixed in 11.3


I have the following issue, trying to evaluate an integral. Mathematica tells me

Integrate[x^2 (1 + x^2)^(1/2) + y + z, {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]

(* 1/2 π (3 Sqrt[2] - Log[2 (2 + Sqrt[2])]) *)

By the way, it also gives me

Integrate[x^2 (1 + x^2)^(1/2), {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]

(* 1/4 π (6 Sqrt[2] + Log[3 - 2 Sqrt[2]]) *)

And, of course,

Integrate[y + z, {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]

(* 0 *)

You can check that the two results are not equal (they differ by $\frac{3\pi}{8}\log 2$); therefore the linearity of the integral is not respected. How can I explain this fact?

Thank you in advance! This is really puzzling me up.

$\endgroup$
  • 3
    $\begingroup$ Same behavior here on Mathematica 11.0.1 on macos 10.12.6. I would classify that as a bug. Note that this does not happen with NIntegrate which has some other issues instead. $\endgroup$ – Henrik Schumacher Nov 25 '17 at 15:52
  • $\begingroup$ Thank you for quick answer. By the way, do you know what is the bug caused by? So that one can at least try to avoid it. $\endgroup$ – Simone Melchiorre Chiarello Nov 25 '17 at 15:56
  • 2
    $\begingroup$ I have absolutely no idea. Personally, I mostly avoid everything provided by Mathematica related to two dimensional MeshRegions; mostly for the reason that many features haven't been implemented yet. But this issue is really striking. Would you please be so kind and send a bug report to Wolfram Research? $\endgroup$ – Henrik Schumacher Nov 25 '17 at 16:47
  • $\begingroup$ Same behavior for 11.2 on Windows 10. Bug. $\endgroup$ – bbgodfrey Nov 25 '17 at 21:44
  • 1
    $\begingroup$ confirm it is fixed in 11.3 !Mathematica graphics $\endgroup$ – Nasser Mar 10 '18 at 21:31
11
$\begingroup$

This is a bug introduced in 10.4.0 and persisting through 11.2.0. It is already fixed in our internal development build, so it should be fixed in our next release.

I haven't tracked down the cause, but based on the different answers over various versions, it is probably either a simplification bug, or a branch cut issue.

$\endgroup$
  • $\begingroup$ Upvoting for saving me the time tracking down the actual cause... $\endgroup$ – Daniel Lichtblau Nov 27 '17 at 20:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.