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
> >> >>
> >> >>
> >> >
> >>
> >>
> > 
> 
>