Re: Why does Limit sometimes just return what I input?

*To*: mathgroup at smc.vnet.net*Subject*: [mg44605] Re: Why does Limit sometimes just return what I input?*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Mon, 17 Nov 2003 03:38:40 -0500 (EST)*Organization*: The University of Western Australia*References*: <bp28u9$351$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <bp28u9$351$1 at smc.vnet.net>, jmonk <jmonk at hep.man.ac.uk> wrote: > I am trying to find the limit of some gamma matrix traces when a small > parameter \[Epsilon]->0. I am using the package Tracer.m Note that I picked up an error/omission in this package when I loaded it in. In the SortLine routine there is the following: If[ list === rlist, , If[ Sort[list] === Sort[rlist], Now, since the (extended) syntax of If is If[condition, t, f, u] gives u if condition evaluates to neither True nor False. then the meaning associated with the repeated comma is rather important. I note that the pakcage at http://library.wolfram.com/infocenter/MathSource/2987/ has a revision date of 1991. > and I define 4 lines: > > Spur[l1, l2]; > line11 = G[l1, p1, p3, G5, n, {Î½}, (p1 + k), {Î¼}]; > line12 = G[l1, p1, p3, G5, n, {Î¼}, (p3 - k), {Î½}]; > line21 = G[l2, p2, p4, G5, np, {Î»}, (p2 - k), {Î¼}]; > line22 = G[l2, p2, p4, G5, np, {Î¼}, (p4 + k), {Î»}]; Your message came through with some very strange characters. Perhaps you could re-post in a readable format? > The vectors n and np are well defined by > > OnShell[on,{n, xx_,\[Chi]1. xx + Î»\_1**\[Chi2p.xx]}, > {np, xx_, lim[Î¶1 . xx + Î»\_\[Zeta]2p.¹*¶xx}]; > > with \[Chi]1, \[Chi]2p, Î¶1and\[Zeta]2p similarly defined. The momenta > p1...p4 also have their dot products defined. n and np depend on a small > parameter \[Epsilon], and it turns out that the highest order terms in the > lines line11...line22 are of order 1/\[Epsilon]. > > I want to take the limit e.g. > > Limit[line11*\[Epsilon],\[Epsilon]->0,Direction->-1] Instead of taking the limit (using Limit), it is usually preferable to perform a series expansion using Series. > and then contract the 2 lines on the \[Mu] Lorentz index, but usually when > I try to take the limit it just returns the limit unevaluated. > Sometimes, however, it does return the limit. I can use the function > Residue to get the answer, but I want to know why Limit does not work. Well, Residue (or Series) may be more appropriate anyway. In my experience, Limit is not "as solid" as Series. > The expressions for the lines are quite long - there are 338 terms, so I > wonder if it is too long for mathematica to cope with unless all of the > computer resources are available to it. I am running Mathematica 5.0 on > Mac Os X, G4 1Ghz 256 Mb. > > The full script I have is too long to include, but I could forward it if > requested. Perhaps you could post the relevant input expressions or give a URL to where the Notebook can be obtained. Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul