#2329: Add interface to PARI's rnfisnorm()
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Reporter: craigcitro |
Owner: craigcitro
Type: enhancement |
Status: needs_review
Priority: blocker |
Milestone: sage-4.7
Component: number fields |
Keywords: editor_craigcitro pari
Author: Craig Citro, Marco Streng, Francis Clarke, Jeroen Demeyer |
Upstream: N/A
Reviewer: Nick Alexander, David Loeffler, Jeroen Demeyer |
Merged:
Work_issues: fix on 32-bit |
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Changes (by jdemeyer):
* status: needs_work => needs_review
Old description:
> This patch adds support to solve norm equations via PARI.
>
> Quick summary: given an element `x` of any number field (even `QQ`),
> `x.is_norm(L)` will return `True` if and only if `x` is a norm from `L`.
> It is also able to return an element of `L` whose norm is `x`.
>
> The data used by PARI to compute whether or not an element is a norm can
> be computed once for each extension `L/K`. The function
> `pari_rnfnorm_data` computes exactly this, and hopefully in a later
> version its result can be passed to `is_norm` to avoid recomputing it
> each time in the case that `K != QQ`. If `K` is `QQ`, there is no need to
> save any such data -- the only data needed is that of `K.pari_bnf()`,
> which is used instead, and is already cached by `K`.
>
> '''Dependencies''': #10677
>
> '''Apply''':
> 1. [attachment:trac_2329_rnfisnorm5.patch]
> 1. [attachment:2329_reviewer.patch]
> 1. [attachment:2329_selmer.patch]
New description:
This patch adds support to solve norm equations via PARI.
Quick summary: given an element `x` of any number field (even `QQ`),
`x.is_norm(L)` will return `True` if and only if `x` is a norm from `L`.
It is also able to return an element of `L` whose norm is `x`.
The data used by PARI to compute whether or not an element is a norm can
be computed once for each extension `L/K`. The function
`pari_rnfnorm_data` computes exactly this, and hopefully in a later
version its result can be passed to `is_norm` to avoid recomputing it each
time in the case that `K != QQ`. If `K` is `QQ`, there is no need to save
any such data -- the only data needed is that of `K.pari_bnf()`, which is
used instead, and is already cached by `K`.
'''Dependencies''': #10677
'''Apply''':
1. [attachment:trac_2329_rnfisnorm5.patch] (positive_review)
1. [attachment:2329_reviewer.patch] (positive_review)
1. [attachment:2329_selmer.patch] (needs_review)
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2329#comment:54>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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