Changes between Initial Version and Version 13 of Ticket #2329
 Timestamp:
 08/17/10 14:04:06 (11 years ago)
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Ticket #2329

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Status
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new
toassigned

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Authors
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Craig Citro, Marco Streng
 Property Cc ncalexan mstreng added

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Report Upstream
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N/A

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Component
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number theory
tonumber fields

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Summary
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[with patch, needs review] add interface to Pari's rnfisnorm
to[with patch, pending another patch] add interface to Pari's rnfisnorm

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Priority
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minor
tomajor
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Milestone
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sage2.11
tosage2.10.4
 Property Owner changed from was to craigcitro

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Reviewers
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Nick Alexander

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Ticket #2329 – Description
initial v13 1 1 This patch adds support to solve norm equations via Pari. 2 2 3 Quick summary: given an element `x` of any number field (even `QQ`), `x.is_norm(L)` will return ` False` if `x` is not a norm from `L`, and if `x` is a norm from `L`, willreturn an element of `L` whose norm is `x`.3 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`. 4 4 5 According to the Pari documentation, these functions depend on GRH when `L/K` is not known to be Galois, and work independent of any such hypothesis otherwise (at least, that's what I got from reading the Pari manual). 6 7 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 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`. 5 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`.