Re: Re: New version, new bugs
- To: mathgroup at smc.vnet.net
- Subject: [mg42541] Re: [mg42537] Re: New version, new bugs
- From: Andrzej Kozlowski <andrzej at lineone.net>
- Date: Mon, 14 Jul 2003 05:42:10 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Sunday, July 13, 2003, at 01:53 am, Maxim wrote:
> 2) still cannot give answers for Sum and Product in conditional form;
> doesn't even indicate that the series is divergent in cases like
>
> In[1]:= Sum[I^k, {k, 0, Infinity}]
>
> Out[1]=
> 1/2 + I/2
Since this answer is exactly the Abel (and Cesaro) sum of this
divergent series it may be deliberate. This is hard to tell since the
Mathematica book does not say anything about the way divergent series
are handled. In fact Version 4.2 gives the correct Abel sum (1/2) for
Sum[Cos[x], {x, 0, Infinity, Pi}] (as discussed on this list recently)
but Mathematica 5.0 simply says that the series is divergent. Certainly
we have at least an inconsistency here.
> In[1]:= FullSimplify[2^(4*n + 1) - 16^n]
>
> Out[1]=
> 2^(1 + 4*n) - 16^n
This one may be rather hard to make work the way one would like since
Mathematica never transforms 2^(1 + 4*n) to 2 2^(4n), or rather, if it
did it would immediately transform it back into the original form. To
get the obvious simplification one needs to to do something like
ReleaseHold[Simplify[Hold[2]*2^(4*n) - 16^n]]
16^n
While it would not be impossible to write a Simplify that used this
sort of approach it may be prohibitively expensive in terms of
computational time.
>
> I haven't looked closely at the Version 5's new features yet, but I
> have a
> suspicion those modules won't be any more reliable:
>
> In[1]:= Reduce[Sin[x + Pi/5] + Cos[x - Pi/10] == 0, x]
>
> Out[1]=
> False
>
> (general solution is x -> (7*Pi)/10 + Pi*C[1]).
However, the following works correctly:
In[30]:=
FullSimplify[Reduce[Sin[x + Pi/5] + Cos[x - Pi/10] == 0, x, Reals]]
Out[30]=
C[1] $B":(B Integers && (x == Pi*(-(3/10) + 2*C[1]) || x == Pi*(7/10 +
2*C[1]))
I agree that the other bugs you mention are awful and ought to have
been fixed long ago. Some of them at least seem pretty trivial to fix
and it seems that the only reason why they haven't been fixed is that
they were never recorded on a "to be done" list. I feel that something
is seriously amiss when a reported bug that does not require a major
re-write of the kernel is not fixed: at least the person who reported
it ought to be given an explanation why it has not been done. It looks
to me that Wolfram's entire bug-reporting system needs a serious
reconsideration.
As for Mathematica 5, my early impression is that whether it is worth
the price of the upgrade or not depends on what you use if for.
Personally I do not care at all for Integrate, I have never found it
useful to know a "closed form" formula for any integral I could not
evaluate by hand. Numerical integration is much more useful, but what
makes for me Mathematica 5 easily worth the upgrade price is the new
abilities of NDSolve, particularly in numerical solutions of PDE's. I
think the new abilities put this version in a different class from the
previous ones in this respect. If this is what interests you than I
strongly recommend this upgrade.
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/