Re: Polynomial/Series Precision

[Gerhard Niklasch <nikl@mathematik.tu-muenchen.de>]

In response to:
> Message-ID: <Pine.LNX.4.33.0107030248160.11392-100000@math.Princeton.EDU>
> Date: Tue, 3 Jul 2001 02:59:54 -0400 (EDT)
> From: "Jonathan P. Hanke" <jonhanke@Math.Princeton.EDU>
> 
> It's very possible that this is a silly question, but I was having some
> trouble working with large exponents in polynomials.  In particular, I
> would like to work with powers larger than x^65532, but when I try I
> recieve a "*** degree overflow" error.

With a 32-bit gp executable, we only have 16 bits to represent an
exponent - or more precisely, since the representation doesn't take
sparseness into account, we only have 16 bits to represent the length
of the vector of coefficients  (including a few words for internal
administrative business).  Thus x^(2^16) cannot be represented in
the internal format, giving rise to the degree overflow message.

A 64-bit executable  (on platforms which support this)  will get around
this limitation, but will still consume enormous amounts of memory
when handling polynomials of this size  (and spend rather a lot of
time in doing so).

> I have tried changing the seriesprecision with \ps and default, but it
> doesn't help the error.

(Polynomials aren't series -- the seriesprecision determines at which
term a power series will be truncated by default.  This applies e.g.
when you enter cos(x) and look at the resulting series output.)

Hope this helps,
Gerhard