Mathematica 12 crashes upon taking the Log of a double series

Question

Bug introduced in 11.1 and fixed in 12.1

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I recently upgraded from Mathematica 10.4 to 12.0. Unfortunately, I am now experiencing crashes with code that was stable in 10.4. The code involves extensive manipulation of the Series function with 2 variables. The culprit seems to be when the logarithm of such a series is taken.

Here is an example:

Log[SeriesData[p,DirectedInfinity[1],List[SeriesData[e,0,List[1,0,Rational[-3,2]],0,3,1],0,SeriesData[e,0,List[3,0,Rational[-3,2]],0,3,1],0,SeriesData[e,0,List[Rational[9,2],0,12],0,3,1],0,SeriesData[e,0,List[Rational[27,2],0,63],0,3,1],0,SeriesData[e,0,List[Rational[405,8],0,Rational[5499,16]],0,3,1]],0,9,2]]

On Mathematica 10.4, this (rapidly) evaluates to another series in (1/p) and e, while on Mathematica 12.0, it stalls for several seconds and then crashes. Simple workarounds using "Normal" inside the Log and then taking another Series are not ideal, as I need Mathematica to track the appropriate orders automatically, rather than having to set all the orders manually.

Is this a bug, or a side effect of some new functionality? Is there a simple way to achieve the 10.4 behavior?

Answer 1

This bug has been fixed as of version 12.1.0

In[1]:= $Version                                                                                                                               

Out[1]= 12.1.0 for Linux x86 (64-bit) (March 18, 2020)

In[2]:= Log[SeriesData[p,DirectedInfinity[1],List[SeriesData[e,0,List[1,0,Rational[-3,2]],0,3,1],0,SeriesData[e,0,List[3,0,Rational[-3,2]],0,3,
1],0,SeriesData[e,0,List[Rational[9,2],0,12],0,3,1],0,SeriesData[e,0,List[Rational[27,2],0,63],0,3,1],0,SeriesData[e,0,List[Rational[405,8],0,R
ational[5499,16]],0,3,1]],0,9,2]]                                                                                                              

                   2            2        2             2
                3 e     3 (1 + e )   39 e    9 (2 + 9 e )       -4
Out[2]= Log[1 - ----] + ---------- + ----- + ------------ + O[p]
                 2          p           2           3
                                     4 p         2 p

Answer 2

I am not a nerd as others but to me it seems at first glance and mistake in using e as a variable.

Change to another name of the variable. Then start with

SeriesData[p, DirectedInfinity[1], 
 List[SeriesData[x, 0, List[1, 0, Rational[-3, 2]], 0, 3, 1], 0, 
  SeriesData[x, 0, List[3, 0, Rational[-3, 2]], 0, 3, 1], 0, 
  SeriesData[x, 0, List[Rational[9, 2], 0, 12], 0, 3, 1], 0, 
  SeriesData[x, 0, List[Rational[27, 2], 0, 63], 0, 3, 1], 0, 
  SeriesData[x, 0, List[Rational[405, 8], 0, Rational[5499, 16]], 0, 
   3, 1]], 0, 9, 2]

This is

Mathematica the suggests to truncate the higher-order terms with Normal:

This is a sum that can be brought to denominator 16 p^4.

The Log can than be developed further into a Series:

I am using

$Version

12.0.0 for Mac OS X x86 (64-bit) (April 7, 2019)

All that is probably not done in 12.0.0 is the development into a Series of the Log on a Series. That is different from the evaluation in other versions of Mathematica but it is to me not really an error.

I admit this is not a Laurent expansion of complex numbers. The problem of the given expansion form @ilan for the Log is that it does not turn to positive exponents.

The example in the Mathematica documentation demonstration for a Laurent expansion this general behavior for finite type of singularities.

The solution in Mathematica for a Series of Log is:

Series[Log[x], {x, 0, 3}]

SeriesData[x, 0, {
Log[x]}, 0, 4, 1]