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MathGroup Archive 2006

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Bugs--Limit bug in version 5+ ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66570] Bugs--Limit bug in version 5+ ?
  • From: itamar0 at gmail.com
  • Date: Sat, 20 May 2006 04:47:38 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

The following seems to be a (strange) bug in "Limit":


Notebook[{

Cell[CellGroupData[{
Cell[BoxData[{
    \(Limit[Log[x + I] - Log[x - I], 
      x \[Rule] \(-Infinity\)]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \  (*\ \ \ \ \ 1\ \ \ \ \ \ *) \), "\[IndentingNewLine]", \

    \(Limit[Log[x + I*Exp[\(-3\)]] - Log[x - I*Exp[\(-3\)]], 
      x \[Rule] \(-Infinity\)]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\  (*\ \ \ \ \ 2\ \ \ \ \ \ *) \), "\[IndentingNewLine]", 
    \(Limit[Log[x + I*s] - Log[x - I*s], x \[Rule] \(-Infinity\), 
      Assumptions \[Rule] 
        s \[Equal] 
          1]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \  (*\ \ \ \ \ 3\ \ \ \ \ \ *) \
\[IndentingNewLine]\), "\[IndentingNewLine]", 
    \(Limit[Log[x + I*s] - Log[x - I*s], x \[Rule] \(-Infinity\), 
      Assumptions \[Rule] 
        s \[Equal] 
          Exp[\(-3\)]]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\  (*\ \ \ \ \ 4\ \ \ \ \ \ *) \), "\[IndentingNewLine]", 
    \(Limit[Log[x + I*s] - Log[x - I*s], 
      x \[Rule] \(-Infinity\)]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ \ \ \
\ \ 5\ \ \ \ \ \ *) \), "\[IndentingNewLine]", 
    \(Limit[Log[x + I*s] - Log[x - I*s], x \[Rule] \(-Infinity\), 
      Assumptions \[Rule] 
        s > 0]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \  (*\ \ \ \ \ 6\ \ \ \ \ \ *) \
\[IndentingNewLine]\), "\[IndentingNewLine]", 
    \(N[ReplaceAll[Log[x + I] - Log[x - I], x \[Rule] \(-Exp[100]\)], 
      10]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \  (*\ \ \ \ \ 7\ \ \ \ \ \ *) \[IndentingNewLine]\), "\
\[IndentingNewLine]", 
    \(\)}], "Input"],

Cell[BoxData[
    \(2\ \[ImaginaryI]\ \[Pi]\)], "Output"],

Cell[BoxData[
    \(2\ \[ImaginaryI]\ \[Pi]\)], "Output"],

Cell[BoxData[
    \(2\ \[ImaginaryI]\ \[Pi]\)], "Output"],

Cell[BoxData[
    \(0\)], "Output"],

Cell[BoxData[
    \(0\)], "Output"],

Cell[BoxData[
    \(0\)], "Output"],

Cell[BoxData[
    \(0``9.352335129473877 + 
      6.2831853071795864769`10.150514997831994\ \[ImaginaryI]\)], \
"Output"]
}, Open  ]]
},
FrontEndVersion->"5.2 for Microsoft Windows",
ScreenRectangle->{{0, 1024}, {0, 689}},
WindowSize->{1020, 655},
WindowMargins->{{Automatic, 0}, {Automatic, 0}}
]


Lines 1,2,3 are obviously correct limits. Lines 4,6 are wrong answers (line 4 is especially puzzling to me, but maybe "Assumptions" is not meant to be used this way). Line 5 is not a well defined limit (absent assumptions). The last line is a numerical check of sorts (haven't figured out how to use NLimit yet).

This was run on Mathematica 5.2 for Students on a P4 D820 (dual core) with XP-PRO EN SP2. I've also had the same problem on a number of other configurations including v5.0. This thing took me a month to sort out as part of a really nasty expression so I'd appreciate any feedback. 

Link to the forum page for this post:
http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Special:Forum_ViewTopic&pid=10468#p10468
Posted through http://www.mathematica-users.org [[postId=10468]]



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