Re: limits at infinity Re: Maple bug the long liver, 1992--2007--? (limit)
- From: Daniel Lichtblau <danl@xxxxxxxxxxx>
- Date: Fri, 15 Jun 2007 12:41:25 -0700
On Jun 15, 12:12 am, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
On Jun 14, 4:32 pm, Daniel Lichtblau <d...@xxxxxxxxxxx> writes:
DL> I see nothing to suggest triviality.
From the algorithmic viewpoint, I fully agree with you. It is,
however, not exactly what I meant.
The formal old good definition of a bug as kind of a defect
in logics etc is old, narrow, and much misleading as it fully
ignores and masks the ECONOMIC nature of software bug.
Software bugs indeed have an economic aspect. From everything I have
seen in this forum, there is little or no commonality to our opinions
on what those economic impact/consequences might be.
Software does not exist in vacuum. It lives within a market.
It is like a waiter at table. It serves customers, their
needs, their expectations.
Chances are if the food or service are not what the customers want or
expect, they'll not return. If they come in at all.
If a high school teacher on Monday preaches that
sin(z)^2+cos(z)^2 = 1 (long live Pythagoras!)
now on Tuesday the pupil starts Maple 11 and discovers
that
limit(1/(sin(z)^2+cos(z)^2), z= infinity);
undefined
thus killing cruelly the same Pythagoras on the spot, --
He's already dead (kinda like Elvis...)
this can be an emotional shock for his young mind strong
enough to undermine or even fully destroy his interest in
mathematics (or software).
I think this is a stretch.
It's simply morally wrong. In a sense, it's a potential murder.
If we have a market, and 5 competitors can handle something
but the 6th fails, for this the 6th case IS a bug -- no matter
is there an algorithm for handling this or whatever.
DL> providing an algorithm to handle such limits in a general
DL> way.
This would require yet another Dominic Gruntz & Gaston Gonnet.
Or even probably an improved version of them, of more math
powers...
But the CAS customers should NOT care much if there is an
algorithm to handle or a heuristics has been applied.
This statement is the main rason I am replying to the thread.
Heuristics are a great thing (admittredly, that's a self-serving
remark, because I use them frequently). But heuristics, even ones that
strike me as clever, are frequently the cause of the sort of "bugs"
you have posted. I might add that unforseen limitations of bona fide
algorithms are also a cause of such behaviors. The symbolic
computation community generally bears these issues in mind in terms of
future development. But they are not something for which I think we
need or ought be apologetic: if all this stuff was simple, we'd
probably be doing something else.
The capital goal of the customer is to save his time and
effort, this is (almost) all (...well, plus enjoy a nice
result).
DL> uncharted territory.
Yes, this is right. Still Mathematica 6 handles these
test cases without any effort
I believe someone in a related thread showed some parts of the effort.
I'd say Limit used considerable resources (i.e. some intermediate
simplification).
In[1] := Limit[z (Sin[z]^2 + Cos[z]^2), z -> Infinity]
Out[1] = Infinity
In[2] := Limit[1/(Sin[z]^2 + Cos[z]^2), z -> Infinity]
Out[2] = 1
This is about care of the customer. I do enjoy this.
It looks to be about one particular customer.
Daniel Lichtblau
Wolfram Research
.
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