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Re: Replacement Rule with Sqrt in denominator. Also Bug in Series

On 12/8/2010 3:40 AM, Bill Rowe wrote:
> On 12/7/10 at 6:45 AM, fateman at (Richard Fateman)
> wrote:
>> On 12/6/2010 3:14 AM, Bill Rowe wrote: ...
>>> I don't agree the behavior of replacement rules reflects an error
>>> in design.
>> Aha, but you don't answer the question.  Let us say that the
>> designer put in something you truly thought was wrong, for example
>> the designer truly thought that Cot[x] could be simplified to
>> 1/x*Tan[x].
>> If this is not a bug, perhaps you would call it a BLUNDER?
> This is a meaningless strawman of your own making which has no
> bearing on the discussion.

OK, you want some examples that have occurred, and whose resolution has
changed, from version to version of Mathematica?  How would you
characterize a situation in which version N replies True but version
N+1 replies False?  Did version N+1 fix a bug? a blunder? or exhibit
just some chronologico-mathematical time warp?

If you want to argue about such things, just look at the brouhaha
regarding whether sqrt(x^2) is abs(x),  or the difference between
0^0 and 0.0^0.0 .   or whether integral of x^n is 1/(n+1)*x^(n+1),
which is arguably false if n=-1.

> Or is it you are arguing someone
> designing software to do mathematics would intentionally create
> a design to return 1/x*Tan[x] as a result for Cot[x]?

I set this up so that you and I would agree that the designer was
indeed mistaken, regardless of his sincerity in believing this.
I have no idea of your view of whether  sqrt(x^2) is x, -x, {-x,x}, 
abs(x), rootof(), ...

I cannot
> believe anyone designing software to do mathematics would argue
> getting 1/x*Tan[x] as the result for Cot[x] was intentional design.

You can't?  You cannot believe that anyone designing software might
have gotten some formula wrong?  So much of computer algebra
system design includes a portion of "you might not like it but I have
my own reason for doing it this way."

> You have made it abundantly clear you do not like the current
> design of Mathematica with respect to how replacement rules
> work.

> And that is fine. You are clearly entitled to your own
> preferences with respect to how anything in Mathematica works or
> doesn't work for that matter.
  I merely point out your dislike of
> the design that results in the behavior of replacement rules
> does not make that behavior a bug nor a design error.
nor does your apparent enjoyment of the behavior constitute a
proof that it is by some objective criterion, correct.

As for why this appears repeatedly -- as I have pointed out in
private mail to DanL,  the history of questions on this newsgroup
is inaccessible to many newsreaders. Someone asks, the usual
crowd of hangers-on tell him that he is wrong to believe that
I->-I is an effective rule, etc. And some people tell him he
is right to complain.

Perhaps there should be a database , even a FAQ of some sort.

As for Andrzej's assertion that no one agrees with my perspective,
I suppose it is sufficient to point out that Andrzej would have
no way of knowing that. And to some extent it is pointless to
support my perspective (on this newsgroup)  as long as I am willing to 
do so myself.
So far as I know, Andrzej does not have access to my personal email, 
though who knows what Wikileaks will release in the future.

I do agree that crowd-sourcing of mathematical theorems or
opinions on the design of Mathematica seems less useful than
using expert(s) in general.

I might point out that in almost all the reported problems, we have
a rule or sub-part of a rule, which has a constant,  like 2, or I,
which fails to match an expression like -2 or or 1/2 or  -I.
You, and others seem to thing that the
effects of allowing this match would be confusing, or inefficient, or
would break things. In my view it would be simple enough to completely
define the changes necessary, document them, and implement them.
I took the trouble to write a paper and a sample implementation.
It responds to certain customers' issues.

Your view, shared by some others, is that such a change is unthinkable, 
and that the customer is wrong.  But the argument you offer is
fundamentally is the Peewee Herman refrain .. "I meant to do that".



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