Re: VM machine: A CAS answer 25,000,000+ times longer than it is
- From: rjf <fateman@xxxxxxxxx>
- Date: Wed, 10 Dec 2008 11:47:48 -0800 (PST)
Maxima gives, for n=13,
(594914320*sqrt(3)*%pi-3198743379)/526126590
and gets slower as n increases.
Again, VB has probably cloaked the nature of the bug in obscurity.
One would think that the bug has to do with integration, but it is
more likely that it has to do with simplification and evaluation of a
limit involving atan and a polynomial.
As for the bug in length, it seems that Maple is using a fixed-length
counter that is not long enough.
It should be fixed, but really not a compelling problem.
I recall, many many years ago, a primitive computer display at a
children's museum that invited visitors to
enter two numbers into a keypad, and it would "instantly" multiply
them and display the answer. It worked
fine for 2,3,4, digit numbers, but children were not prevented from
entering numbers with far more digits.
The computer did not correctly multiply 20 digit numbers. So?
VB is doing the same kind of testing on CAS.
Since one can easily represent a problem whose solution, displayed
explicitly, would not fit on any existing
display device, (with, say, more terms than there are believed to be
electrons in this universe [10^79?], and requiring
more time to compute than the age of the universe [14 billion
years?]), how is one to judge whether the defect observed
or predicted to occur is interesting or not?
As another trivial example, consider the sequence of problems
a+1;
aa+1;
aaa+1;
.....
etc . If there are enough letter a's in the identifier, something
will break. Will Maple accommodate 10^9 a's?
Which will break first, the lexical analysis for input, the symbol
table, the simplifier, the memory, the user interface,...
There are enough real defects to find that discussing such artificial
ones constitute more of a distraction than anything else.
RJF
.
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- From: Robert H. Lewis
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