[Maxima-bugs] [ maxima-Bugs-3276461 ] Inaccurate Limit Evaluation

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Bugs item #3276461, was opened at 2011-04-05 13:41
Message generated for change (Comment added) made by dgildea
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Category: Lisp Core - Limit
Group: None
>Status: Closed
>Resolution: Fixed
Priority: 5
Private: No
Submitted By: eEniquEe (bonoxofut)
>Assigned to: Dan Gildea (dgildea)
Summary: Inaccurate Limit Evaluation

Initial Comment:
Hi,
While working on my project on Limit Problem Generation, I've encountered a bug. The following limit is evaluated incorrectly!!!
(%i1) limit((-4*x^2-10*x+24)/((4*x+8)^(1/3)+2), x, -4);
(%o1) 0

The result should be 66 instead.

It's pretty strange, because Maxima can evaluate another limit of the same type correctly:
(%i2) limit((-2*x^2-15*x-25)/((-4*x-21)^(1/3)+1), x, -5);
(%o2) -15/4

tlimit returns the correct value as expected. I just wondered what was wrong with limit function. :(

Thanks guys very much for all your efforts to maintain Maxima,

Keep up the good work,

And have a great day, :)

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>Comment By: Dan Gildea (dgildea)
Date: 2011-10-12 14:59

Message:
Fixed in limit.lisp - add radcan before zero check in simplimsubst.

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Comment By: eEniquEe (bonoxofut)
Date: 2011-04-07 13:35

Message:
Hi again,

It appears that in some specific cases, limit.lisp seems to act weirdly. I
don't know why, but it appears that Maxima fails to evaluate this limit:

(%i1) limit((16*x^3+16*x^2-32*x-32)/(-16*x^3-20*x^2+32*x+40), x,
-sqrt(2))
(%o1) -(15569*2^(5/2)-88072)/(68725*sqrt(2)-97192)

The result given by tlimit is even more monstrous:
(%i2) tlimit((16*x^3+16*x^2-32*x-32)/(-16*x^3-20*x^2+32*x+40), x,
-sqrt(2));
(%o2)
-(28587895628423267593*2^(5/2)-161717558869690800084)/(7887067287668281425*2^(9/2)-178463960409114635249)

The result should be:
(-16*sqrt(2)+16)/(16*sqrt(2)-20) instead.

The 2 expressions (the correct result, and the result given by limit
function) are pretty much identical when we take the float value of it. 
But however, in fact, they are not the same!!!

The above limit can be easily found either by L'Hopital's Rule, or by
factoring out (x^2 - 2), which makes both numerator and denominator tend to
0.

----------------------------------

I'm not very familiar with programming, (well, in fact, I do have some
basic programming, scripting skill, I can create small applicants: small
games, and auto stuff), but I really want to help you guys in modifying the
limit.lisp. I don't really know how. :(

I just wanna ask, if I w ant to modify the Lisp(s) in Maxima, which
programming language should I consider?

Thanks very much in advance, :)

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