#895 limit x->inf sin(100/x)*x very slow

[Stavros Macrakis]

limit(sin(a/x)*x,x,inf),a=100 takes about 90 seconds on
a 1Ghz machine, whereas for a=5 it takes 0.1 seconds,
and for unbound a, it takes 0.4 sec.

I am guessing that limit calls trigexpand or some such,
leading to completely unnecessary blowup in the
intermediate results.

[Barton Willis]

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Yes, it seems that limit calls trigexpand (I traced
trigexpand).

One observation: tlimit is very fast on this problem.
Is tlimit often better (faster, fewer bugs, ...)
than limit? I didn't know about tlimit for years
and I still forget about it.

Barton

[Raymond Toy]

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One workaround is to set trigexpandtimes:false. Then it's
very fast.

[Barton Willis]

The function lhospital calls expand-trigs. And expand-trigs calls trigexpand.

I commented out the call to expand-trigs in lhospital. Additionally, I also eliminated the call to tansc

      ;(setq n (expand-trigs (tansc n) var))
      ;(setq d (expand-trigs (tansc d) var))

Less drastically, the call to tansc could remain. Another idea would be to locally set
trigexpandtimes to false (as Raymond observed).

My change didn't cause any problems with the testsuite, but my version of the limit code has a few other changes in it. Maybe others can try this experiment.