I had some useful confirmation from Karim.
The pari library always and only measures precision in
number-of-codewords, and the prec parameter in pari library functions
always denotes this.
For the gp interface (to pari) decimal precisions are used, as they
are supposed to make more sense to humans (which they do).
Sage interfaces with *both* libpari and gp, in different places. When
it interfaces with libpari it needs to work with word lengths; for
example in a function like the elliptic curve function pari_curve(),
it makes no sense at all for the prec parameter of that function to be
in decimal in the belief that that is what the pari library wants.
It should be in bits, as in the rest of Sage, and that function can
convert it to word-precision before calling the pari library function.
It seems that #4064, which most of you ignored as it was about
elliptic curves ;) has some far-reaching consequences (since the pari
library is used all over the place). I think a new ticket is
therefore required (and I don't mind trying to take care of it). Or
am I making a mountain out of a molehill?
John
2008/9/5 John Cremona <[EMAIL PROTECTED]>:
> I think this is at the heart of the precision weirdness in converting
> to/from pari reals.
>
> Example:
>
> sage: E = EllipticCurve('37a')
> sage: E_pari = E.pari_curve()
> sage: om = E_pari.omega()[0]
> sage: om
> 2.9934586462319596298320099794525081778
> sage: om.precision()
> 19
> sage: om.python()
> 2.99345864623195962983200997945250817779758379137013298534052337856325035698668290412039406739705147343584052710494728819414438723737202525437537667109326137530433325059652462521644730690726945107490578063656104457817258171351824279342631324889800869424380208704316693154446424015476558450847785954700795671977773461040730510763
> sage: om.python().prec()
> 1088
> sage: 1088 == (19-2)*64
> True
>
> The pari_curve object has been created with a *decimal* precision of
> 19 *decimal* digits, but the conversion back to python reals has
> interpreted this as 19 *words*, which is 1088 bits.
>
> This is behind #4064 and who knows what else...
>
> John
>
> ---------- Forwarded message ----------
> From: Bill Allombert <[EMAIL PROTECTED]>
> Date: 2008/9/5
> Subject: Re: precision() in pari
> To: John Cremona <[EMAIL PROTECTED]>
> Cc: Karim Belabas <[EMAIL PROTECTED]>
>
>
> On Fri, Sep 05, 2008 at 03:13:44PM +0100, John Cremona wrote:
>> Am I right in thinking that in the pari library, if x is a t_REAL,
>> precision0(x) returns the decimal digit precision of x, just as the gp
>> function precision (without the 0), while precision(x) returns the
>> word length?
>
> Yes! Actually there is the relation:
> precision0(x)=(precision(x)-2)*log(2^32)/log(10)
> (or 2^64 on a 64bit system)
>
> Cheers,
> Bill.
>
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