#2329: add interface to Pari's rnfisnorm
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Reporter: craigcitro | Owner: craigcitro
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6.1
Component: number fields | Keywords: editor_craigcitro
Author: Craig Citro, Marco Streng | Upstream: N/A
Reviewer: Nick Alexander, David Loeffler | Merged:
Work_issues: |
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Description changed by jdemeyer:
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`.
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`.
See #10430 for some needed PARI bugfixes.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2329#comment:23>
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