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]]