Re: Some bugs in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg59680] Re: Some bugs in Mathematica
- From: "Alex" <akhmel at hotmail.com>
- Date: Wed, 17 Aug 2005 04:00:31 -0400 (EDT)
- References: <dds9e5$91q$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Bill Rowe wrote:
>
> Your "logic" doesn't follow. If you agree with the point I was making, then >you must realize two different programmers are likely to include different >transforms simply because of differences design considerations or programming >style. That is, not including a specific transform is not evidence of sloppy >programming.
Those are general phrases, which actually mean nothing. The issue is
Mathematica couldn't compute a very elementary integral. There is no
excuse for that.
>
> I believe that to be an unreasonable expectation.
>
It's more than reasonable. There are not that many substitutions. I can
name 3 or 4. Can you name 125?
> Although I do not work for Wolfram nor do I have access to the source code of >Mathematica, I am reasonably confident the process Mathematica goes through is >what you've outlined above. Probably the only real difference is how big >the "huge ... table of integrals" is which would be a design consideration.
>
Even the smallest table of integrals has the integral I used as
example. So, this excuse doesn't work.
Here is another proof that either Mathematica doesn't have tables or
has a very inadequate one. Consider an example
Integrate[BesselJ[1, a x] Sin[b x], {x, 0, \[Infinity]}]
Mathematica gives only one-sided result, b/a < 1 while in any table of
integrals, the result for b/a > 1 is well known. So, whatever is the
case, Mathematica was designed in a sloppy manner.
>
> And your basis for this assertion is ....?
I addressed it before, the substitutions are simple and the number of
different substitutions is very limited. I tried several substitutions
myself and got result of simplification practically immediately. And my
computer is 5 years old, so it is not fast at all. Can you imagine how
a fast computer would behave?
>
> How is "appearance" of an integrad to be defined for a system like >Mathematica? I am confident algorithm needed to define "appearance" will lead >to unacceptable performance if every possible grouping of variables in an >arbritrary complex expression is considered.
>
> In essence, you've made an unsupported assertion which I suspect indicates a >lack of experience with creating complex programs. It is very easy to >criticize the programmer for not including what you see as desireable but not >very easy to create the tool yourself.
You cannot have it both ways: you claim that Mathematica has a table of
integrals, it means that they have managed to write a table in
computer-readable and computer-searchable form. And now you are telling
me that this just cannot be done! Now, which one is right?
>
>
> I agree there is a vast difference between "not perfect" and "inadequate". I >strongly disagree that Mathematica is "inadequate". If Mathematica is >inadequate for your needs, you are certainly free to use some other software.
Please give me your definition of inedequate. Would you for example
call a system inadequate when it cannot integrate a rational
expression? Would you call it inadequate when it cannot integrate x dx?
How far would you go? Where do you draw the line? I draw the line in
undergraduate calculus. Am I wrong?
> I make no claim to being able to always get a particular result from >Mathematica or reduce the result from every "elementary" integral with >Mathematica into some specifiec form. Nor do I see any real advantage to >having a symbolic result specified in terms of ArcTanh versus some other form. >In either case, I can plot the results, evaluate the results to a number once >the various parameters are assigned numerical values etc.
...
> Although this isn't in terms of ArcTanh, it is in terms of common functions. >And there is probably a way to re-write the integrand to get the result in >terms of ArcTanh. Perhaps someone else may be interested enough to demonstrate.
You wrote a lot of things, which proves absolutely nothing, instead of
honestly admitting that this is Mathematica's fault, which needs to be
corrected.
I noticed that you published over 100 postings, each of them can be
summarized as follows: "Mathematica is right. Even when Mathematica is
wrong, it is still right to be wrong". Why is this so?
Kozlowski published over 1000 postings; all of them are of the same
kind. Have any of you ever encountered Mathematica having a bug,
Mathematica being inedequate in certain sense? Never?
Both you and Kozlowski are trying to make user feel inedequate,
"blind", stupid, etc. It doesn't look good. It doesn't look good at all.
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