7
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Fixed in 13.1


I believe the following two integrals should have the same value, since the Boole[] expression always evaluates to 1 in the given range. However, for some reason the first one returns 0.

Is this a bug? Or am I missing something about how integrals work in Mathematica?

In[1]:= Integrate[Boole[u0 <= 1]/(
 Sqrt[u0] Sqrt[u1] Sqrt[u2]), {u0, u1, u2} \[Element] 
  Simplex[{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}]]

Out[1]= 0

In[2]:= Integrate[1/(
 Sqrt[u0] Sqrt[u1] Sqrt[u2]), {u0, u1, u2} \[Element]
  Simplex[{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}]]

Out[2]= 2 Sqrt[3] \[Pi]

Or with a screenshot for better formatting enter image description here

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2
  • $\begingroup$ Integrate[ Simplify[Boole[u0 <= 1]/(Sqrt[u0] Sqrt[u1] Sqrt[u2]), Assumptions -> u0 <= 1], {u0, u1, u2} \[Element] Simplex[{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}]] returns 2 Sqrt[3] \[Pi] so this is not a big bug. $\endgroup$
    – user64494
    Mar 16, 2022 at 8:54
  • 2
    $\begingroup$ Yes looks like a bug to me. $\endgroup$
    – Roman
    Mar 16, 2022 at 10:18

1 Answer 1

6
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Bug fixed in 13.1. Screen shot below

enter image description here

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