Re: CVS: seriesprecision too large

[Igor Schein <igor@txc.com>]

On Mon, May 12, 2003 at 05:08:38PM -0700, Ilya Zakharevich wrote:
> On Sat, May 10, 2003 at 03:29:23PM -0700, Ilya Zakharevich wrote:
> > ? default(seriesprecision,9)
> >    seriesprecision = 9 significant terms
> > ? sin(x+y)
> >       /     1 3    1  5    1   7     1    9     10  \
> > %2 =  | y - -y  + ---y  - ----y  + ------y + O(y  ) | +
> >       \     6     120     5040     362880           /
> > /     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            /
> 
> OK, I can believe it is an artefact of the used algorithm.  But watch this:
> 
> ? sin(x*y/(x+y))
>   ***   division by zero in gdiv, gdivgs or ginv

I am not getting this error (fresh session):

          GP/PARI CALCULATOR Version 2.2.6 (development CHANGES-1.749)
            i686 running linux (ix86/GMP-4.1 kernel) 32-bit version
       compiled: May  1 2003, gcc-3.2 20020903 (Red Hat Linux 8.0 3.2-7)
                (readline v4.3 enabled, extended help available)
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
? sin(x*y/(x+y))
               / -1 2     \
               | --y  + 1 |      /   2     \      /  4       2       \
         1 2   | 6        |  3   | -y  + 2 |  4   | y  - 120y  + 120 |  5
%3 = x - -x  + | -------- | x  + | ------- | x  + | ---------------- | x  + 
         y     |     2    |      |     3   |      |          4       |
               \    y     /      \  -2y    /      \      120y        /
/   4      2      \      /   6       4         2        \
| -y  + 40y  - 24 |  6   | -y  + 630y  - 12600y  + 5040 |  7
| --------------- | x  + | ---------------------------- | x  +
|         5       |      |                 6            |
\      24y        /      \            5040y             /
/  6       4        2       \
| y  - 210y  + 2520y  - 720 |  8
| ------------------------- | x  +
|               7           |
\           720y            /
/  8        6          4           2          \
| y  - 2016y  + 211680y  - 1693440y  + 362880 |  9      10
| ------------------------------------------- | x  + O(x  )
|                         8                   |
\                  362880y                    /
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Igor