#17903: Wrong approximation for taylor series of L-series for elliptic curves
on 32
bits architecture.
-----------------------------------+------------------------
Reporter: tmonteil | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
-----------------------------------+------------------------
Description changed by tmonteil:
Old description:
> On 32-bits systems, #16997 introduces the following behaviour:
>
> {{{
> sage: L = EllipticCurve('37a').lseries()
> sage: L.taylor_series(10)
> 0.990010459847588 + 0.0191338632530789*z - 0.0197489006172923*z^2 +
> 0.0137240085327618*z^3 - 0.00703880791607153*z^4 +
> 0.00280906165766519*z^5 + O(z^6)
> }}}
>
> Which is very far from the value before #16997 (which stay unchanged on
> 64 bits architecture).
>
> Note the following gap when increasing the precision by 1 bit:
>
> {{{
> sage: L.taylor_series(10, prec=53)
> 0.990010459847588 + 0.0191338632530789*z - 0.0197489006172923*z^2 +
> 0.0137240085327618*z^3 - 0.00703880791607153*z^4 +
> 0.00280906165766519*z^5 + O(z^6)
>
> sage: L.taylor_series(10, prec=54)
> 0.997997869801216 + 0.00140712894524909*z - 0.000498127610959923*z^2 +
> 0.000118835596665833*z^3 - 0.0000215906522442074*z^4 +
> (3.20363155415891e-6)*z^5 + O(z^6)
> }}}
>
> Direct evaluation leads to the same problem:
>
> {{{
> sage: L.dokchitser(prec=53)(10)
> 0.990010459847588
> sage: L.dokchitser(prec=54)(10)
> 0.997997869801216
> }}}
New description:
On 32-bits systems, #16997 introduces the following behaviour:
{{{
sage: L = EllipticCurve('37a').lseries()
sage: L.taylor_series(10)
0.990010459847588 + 0.0191338632530789*z - 0.0197489006172923*z^2 +
0.0137240085327618*z^3 - 0.00703880791607153*z^4 + 0.00280906165766519*z^5
+ O(z^6)
}}}
Which is very far from the value before #16997 (which stay unchanged on 64
bits architecture).
Note the following gap when increasing the precision by 1 bit (at 54 bits,
the value coincides with the one before #16997):
{{{
sage: L.taylor_series(10, prec=53)
0.990010459847588 + 0.0191338632530789*z - 0.0197489006172923*z^2 +
0.0137240085327618*z^3 - 0.00703880791607153*z^4 + 0.00280906165766519*z^5
+ O(z^6)
sage: L.taylor_series(10, prec=54)
0.997997869801216 + 0.00140712894524909*z - 0.000498127610959923*z^2 +
0.000118835596665833*z^3 - 0.0000215906522442074*z^4 +
(3.20363155415891e-6)*z^5 + O(z^6)
}}}
Direct evaluation leads to the same problem:
{{{
sage: L.dokchitser(prec=53)(10)
0.990010459847588
sage: L.dokchitser(prec=54)(10)
0.997997869801216
}}}
--
--
Ticket URL: <http://trac.sagemath.org/ticket/17903#comment:1>
Sage <http://www.sagemath.org>
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