I just installed V11.3. However, when I am doing numerical calculations, which is a summation. V11.3 would give answers in complex number while I only get answers in real field in any earlier versions, e.g., V11.1 and V11.2. Of course, my input is a real number. Although the imaginary part is extremely small, I am curious how the machine could get a complex number now. Is there any changes in the algorithm for summations in V11.3?
Please see my attachment.
Thanks in advance.
It's from terms like Gamma[100 - 5/0.015`200].
Gamma[100 - 5/0.015`200]
Yes, I found that too. Thank you.
However, I am wondering what leads to this change?
I don't know for sure. I can see that the result is the same as Exp@LogGamma[100 - 5/0.015`200]. Gamma is negative, so LogGamma is complex. Gamma[100 - 5/0.015`] (machine precision) now underflows to 0., with an error message, in V11.3. In V11.2, it automatically is promoted to an arbitrary-precision number that can handle such small numbers. This change in handling underflows is a big change in V11.3. It suggests to me that it might be the reason for the difference in your computation, that they changed how Gamma is computed in general to handle the change in machine precision computation.
Exp@LogGamma[100 - 5/0.015`200]
Gamma[100 - 5/0.015`]