Re: CVS: seriesprecision too large

[Ilya Zakharevich <ilya@Math.Berkeley.EDU>]

On Sun, May 11, 2003 at 07:24:42PM +0200, Bill Allombert wrote:
> I think it is 2.2.5 F22:
>    22- for transcendental function f and polynomial p, f(p) only gave
>        seriesprecision significant terms when val(p) = 0

It is not clear why good behaviour w.r.t. multiplication is prefered
to good behaviour w.r.t. addition.  Of course, one needs to make a
choice, but *why* this one?

(unless for series with negative valuation we still keep
"seriesprecision" positive terms.)

> ? sin(x)
> %1 = x - 1/6*x^3 + 1/120*x^5 - 1/5040*x^7 + 1/362880*x^9 - 1/39916800*x^11 + 1/6227020800*x^13 - 1/1307674368000*x^15 + O(x^17)
> 
> instead of
> 
> %1 = x - 1/6*x^3 + 1/120*x^5 - 1/5040*x^7 + 1/362880*x^9 - 1/39916800*x^11 + 1/6227020800*x^13 - 1/1307674368000*x^15 + O(x^16)

Did not you notice

/     1 2   1  4    1  6     1   8      1    10     11  \
| 1 - -y  + --y  - ---y  + -----y  - -------y  + O(y  ) | x +
\     2     24     720     40320     3628800            /

with seriesprecision==9?

Ilya