integrate returns undefined .. Bug in zero denominator?

I like exact results too.  Proofs are important to be able to do in Maxima 
in my opinion.

Rich

----- Original Message ----- 
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: "'Richard Hennessy'" <rvh2007 at comcast.net>
Cc: <maxima at math.utexas.edu>
Sent: Wednesday, September 10, 2008 1:44 PM
Subject: RE: [Maxima] integrate returns undefined .. Bug in zero 
denominator?


>I think that a computer program should provide a correct answer (even if it
> is complicated),
> whenever it is asked.  The compromise is not between simple&maybe-wrong 
> vs.
> complicated.
> The compromise is inherent in the approach: "this is the best we could
> figure out with the algorithms and
> information currently implemented" vs. "this answer is certified correct".
> Sometimes the algorithms
> DO provide what amounts to a proof of correctness, especially in cases 
> where
> you are doing formal
> algebra in well-known rings, fields, etc.
> RJF
>
>
>> -----Original Message-----
>> From: Richard Hennessy [mailto:rvh2007 at comcast.net]
>> Sent: Wednesday, September 10, 2008 9:53 AM
>> To: fateman at EECS.Berkeley.EDU; Raymond Toy
>> Cc: maxima at math.utexas.edu
>> Subject: Re: [Maxima] integrate returns undefined .. Bug in
>> zero denominator?
>>
>> If you are not going to allow anything other than 100%
>> correct answers, that
>> would make answers much more complicated wouldn't it?  In
>> engineering you
>> have to compromise between an ideal answer verses a 100%
>> correct one.  I
>> suppose that has already been done in Maxima, so I take it back.
>>
>> Rich
>>
>>
>>
>>
>> ----- Original Message ----- 
>> From: "Richard Fateman" <fateman at cs.berkeley.edu>
>> To: "'Richard Hennessy'" <rvh2007 at comcast.net>
>> Cc: <maxima at math.utexas.edu>
>> Sent: Wednesday, September 10, 2008 11:38 AM
>> Subject: RE: [Maxima] integrate returns undefined .. Bug in zero
>> denominator?
>>
>>
>> > The result from solve is clearly not a solution.  But your proposed
>> > solution
>> > is not right because
>> > x= y+n*%pi,  n integer and nonzero IS a solution.
>> >
>> > The point I was trying to make is that you cannot say it is ok to be
>> > just a little slipshod because you yourself
>> > will be aware of something  (like a denominator being zero).
>> >
>> > There are enough subtle problems with detecting zero that
>> you can't always
>> > do it.
>> > But that's not a positive feature.
>> >
>> > Once you are aware of a "feature" that is really a bug, you
>> can construct
>> > many erroneous
>> > results, as Vladimir Bondarenko does, on sci.math.symbolic.
>> >
>> > RJF
>> >
>> >
>> >> -----Original Message-----
>> >> From: Richard Hennessy [mailto:rvh2007 at comcast.net]
>> >> Sent: Wednesday, September 10, 2008 8:23 AM
>> >> To: fateman at EECS.Berkeley.EDU
>> >> Cc: maxima at math.utexas.edu
>> >> Subject: Re: [Maxima] integrate returns undefined
>> >>
>> >> Rich,
>> >>
>> >> Automatic taking of limits is not always the answer for
>> many people.
>> >> Personnally I would like this feature
>> >> (%i1) solve (sin(x-y)/(x-y)=0,x);
>> >> (%o1) []
>> >>
>> >> since I think a "solution" that makes the demominator zero is
>> >> never "right".
>> >>
>> >> Rich
>> >>
>> >>
>> >> ----- Original Message ----- 
>> >> From: "Richard Fateman" <fateman at cs.berkeley.edu>
>> >> To: "'Richard Hennessy'" <rvh2007 at comcast.net>
>> >> Cc: <maxima at math.utexas.edu>
>> >> Sent: Wednesday, September 10, 2008 11:04 AM
>> >> Subject: RE: [Maxima] integrate returns undefined
>> >>
>> >>
>> >> > Your saying that something is not a bug does not mean
>> >> everyone will agree
>> >> > with you.
>> >> > Or even that it will result in non-buggy results.  Many
>> >> "bugs" reported on
>> >> > sci.math.symbolic
>> >> > by one writer as bugs in "integrate"  in Maple, are bugs in
>> >> > simplification,
>> >> > sometimes
>> >> > just like this "obvious" but sometimes wrong feature.
>> >> >
>> >> > In particular, you may not need reminding about a=0 in this
>> >> case, but what
>> >> > about
>> >> > in other cases, where Maxima just goes ahead without you... e.g.
>> >> > solve (sin(x-y)/(x-y)=0,x)
>> >> >
>> >> > returns x=y;
>> >> > but this is not a solution, which can be seen either by direct
>> >> > substitution
>> >> > or
>> >> > taking a limit.
>> >> >
>> >> > RJF
>> >> >
>> >> >
>> >> >
>> >> >
>> >> >
>> >> >
>> >> >
>> >> >> -----Original Message-----
>> >> >> From: Richard Hennessy [mailto:rvh2007 at comcast.net]
>> >> >> Sent: Wednesday, September 10, 2008 7:26 AM
>> >> >> To: fateman at EECS.Berkeley.EDU; 'John Pye';
>> maxima at math.utexas.edu
>> >> >> Cc: 'Edwin Woollett'
>> >> >> Subject: Re: [Maxima] integrate returns undefined
>> >> >>
>> >> >> This is not a bug, this simplifies to 1
>> >> >>
>> >> >> a/a -> 1
>> >> >>
>> >> >> with no assumptions made.  I have noticed that in general
>> >> >> radcan(expr1/expr1) simplifies to 1 and Maxima never says
>> >> >> except when expr1
>> >> >> = 0.  Which I find useful since I know about the possibility
>> >> >> that expr1
>> >> >> could be zero but I don't really need to be reminded of
>> >> this case.  I
>> >> >> definitely would not want to be asked is expr1 = zero all the
>> >> >> sime when
>> >> >> cancelling terms.  That would be annoying.
>> >> >>
>> >> >> Rich
>> >> >>
>> >> >>
>> >> >> ----- Original Message ----- 
>> >> >> From: "Richard Fateman" <fateman at cs.berkeley.edu>
>> >> >> To: "'John Pye'" <john.pye at anu.edu.au>; <maxima at math.utexas.edu>
>> >> >> Cc: "'Edwin Woollett'" <woollett at charter.net>
>> >> >> Sent: Tuesday, September 09, 2008 11:56 PM
>> >> >> Subject: Re: [Maxima] integrate returns undefined
>> >> >>
>> >> >>
>> >> >> > Not so clear a bug.
>> >> >> > (n-m)/(n-m) simplifies to 1.
>> >> >> > But if you know n=m, then you have 0/0.  So is it a bug if
>> >> >> (n-m)/(n-m) -->
>> >> >> > 1?
>> >> >> >
>> >> >> > Answer: maybe. But not clear :)
>> >> >> >
>> >> >> > RJF
>> >> >> >
>> >> >> >
>> >> >> >> -----Original Message-----
>> >> >> >> From: maxima-bounces at math.utexas.edu
>> >> >> >> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of John Pye
>> >> >> >> Sent: Tuesday, September 09, 2008 6:47 PM
>> >> >> >> To: maxima at math.utexas.edu
>> >> >> >> Cc: Edwin Woollett
>> >> >> >> Subject: Re: [Maxima] integrate returns undefined
>> >> >> >>
>> >> >> >> I can confirm that behaviour; it looks like a clear
>> bug to me.
>> >> >> >>
>> >> >> >> Cheers
>> >> >> >> JP
>> >> >> >>
>> >> >> >> Edwin Woollett wrote:
>> >> >> >> > integrate(..) returns undefined when it
>> >> >> >> > should know the answer.
>> >> >> >> >
>> >> >> >> > (%i1) declare( [ m, n ], integer )$
>> >> >> >> > (%i2) assume ( m > 0,  n > 0 )$
>> >> >> >> > (%i3) integrate( cos(m*x)^2, x, 0, 2*%pi );
>> >> >> >> > (%o3)                                 %pi
>> >> >> >> > (%i4) integrate( cos(m*x)*cos(n*x), x, 0, 2*%pi  );
>> >> >> >> > Is  n - m  positive, negative, or zero?
>> >> >> >> >
>> >> >> >> > zero;
>> >> >> >> > (%o4)                              undefined
>> >> >> >> >
>> >> >> >> > Is this a known bug?
>> >> >> >>
>> >> >> >> _______________________________________________
>> >> >> >> Maxima mailing list
>> >> >> >> Maxima at math.utexas.edu
>> >> >> >> http://www.math.utexas.edu/mailman/listinfo/maxima
>> >> >> >>
>> >> >> >
>> >> >> > _______________________________________________
>> >> >> > Maxima mailing list
>> >> >> > Maxima at math.utexas.edu
>> >> >> > http://www.math.utexas.edu/mailman/listinfo/maxima
>> >> >>
>> >> >>
>> >> >
>> >>
>> >>
>> >
>>
>>
>