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]]