Re: Re: Limit[(x - Log[Cosh ]) SinIntegral , x -> Infinity]
- To: mathgroup at smc.vnet.net
- Subject: [mg86989] Re: [mg86947] Re: Limit[(x - Log[Cosh ]) SinIntegral , x -> Infinity]
- From: "Szabolcs HorvÃt" <szhorvat at gmail.com>
- Date: Fri, 28 Mar 2008 03:16:00 -0500 (EST)
- References: <20080326082007.401$ci@newsreader.com>
On Thu, Mar 27, 2008 at 3:04 PM, Daniel Lichtblau <danl at wolfram.com> wrote: > Szabolcs Horvát wrote: > > On Wed, Mar 26, 2008 at 1:20 PM, David W. Cantrell > > > > Actually a ClearSystemCache[] is enough, but since cached results can > > affect the success of calculations, probably it would be better if > > Mathematica did not cache the "result" that it *cannot* calculate > > something. > > [...] > > I beg to differ. If that nonevaluation result is time consuming to > compute, and is something that might show up in a context where > recomputation is an issue, then caching can save considerable time. > > Limits tend to be recomputed when one does, say, a definite integral > requiring several different tactics. Caching them thus can reduce > timings of Integrate, a notoriously slow function. That is a very good point. But I am still curious about why Mathematica can compute the two limits separately but not the limit of their product. I could imagine that Limit[] has some built-in constraints, e.g. it only tries a limited number of transformations on the expression, or it has some internal time constraints. If I understood correctly, Bob Hanlon reported that Mathematica does give an answer on his computer---this could be explained by time constraints and a faster computer. If this is really the case, is there a way to ask Mathematica to work "harder" (perhaps try longer), so that it will be able to give an answer? (For example, Simplify has the option TimeConstraint.) Szabolcs Horvát