Changes between Version 24 and Version 33 of Ticket #2329


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Timestamp:
12/10/10 13:00:53 (11 years ago)
Author:
jdemeyer
Comment:

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  • Ticket #2329

    • Property Status changed from needs_review to needs_work
    • Property Milestone changed from sage-2.10.4 to sage-4.6.2
    • Property Summary changed from add interface to Pari's rnfisnorm to Add interface to PARI's rnfisnorm()
    • Property Reviewers changed from Nick Alexander, David Loeffler to Nick Alexander, David Loeffler, Jeroen Demeyer
  • Ticket #2329 – Description

    v24 v33  
    1 This patch adds support to solve norm equations via Pari.
     1This patch adds support to solve norm equations via PARI.
    22
    33Quick 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`.
    44
    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`.
     5The 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`.
    66
    77See #10430 for some related PARI bugfixes (not strictly required as the patch here contains a workaround).