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I've noticed a strange behavior of Mathematica's ArcTan function with two arguments. If both arguments are 0 or 0., Mathematica evaluates the ArcTan to Indeterminate.

ArcTan[0, 0]

During evaluation of In[1]:= ArcTan::indet: Indeterminate expression ArcTan[0,0] encountered. >>
Indeterminate

ArcTan[0., 0.]

During evaluation of In[2]:= ArcTan::indet: Indeterminate expression ArcTan[0.,0.] encountered. >>
Indeterminate

However, I get different results if only one argument is using machine precision:

ArcTan[0., 0]

0

ArcTan[0, 0.]

π/2

No warning is displayed. This inconsistent behavior is causing problems in my code. Is it a bug or is it intentional? Why does this happen?

J. M.'s missing motivation
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shrx
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1 Answers1

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To Mathematica, 0. means "somewhere in the vicinity of zero". 0 means "exactly zero", much stronger. So, when you mix them, the stronger condition wins.

John Doty
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