Ilya Zakharevich on Sun, 07 Feb 2010 12:03:47 +0100

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Re: PARI stable release 2.3.5 (for real now)

On Sat, Feb 06, 2010 at 11:16:45AM +0100, wrote:
> Dear Ilya,
> Sorry, my mistake. Indeed, the exponential decrease would be
> [[1],3/2]. But a decrease in x^(-3/2) or x^(-2) is an ordinary
> slow decrease,

If it is "ordinary", why provide a special flag for it?  And how would
user understand what is "ordinary", and what is not?

> so I maintain that one should use [[1],0], or
> equivalently simply [1].

> I must admit that I do not remember what
> [[1],-3/2] would mean, but certainly not X^(-3/2), so on that point
> the doc is wrong. Perhaps "very slowly decreasing like X^(-z)"
> in the doc should be replaced by "very slowly decreasing like
> 1/(X\log(X)^z)", but I am not sure, need to be checked.

Well, "documentation being wrong" is a very convenient excuse in this
case.  ;-)

However, no matter what the correct semantic of this limit is, in the
first few calculations of the integrated function, libpari DOES NOT
YET KNOW that the specified "speed of decrease" is wrong (even if it
is).  So the fact that it uses negative argument when the lower limits
is [0, -1/2] must be a bug.

  [IMO, even just emiting "error: unsupported combination of limits"
   is way better than what one gets now.  However, I would prefer it
   to auto-split in such cases...]