Changes between Version 24 and Version 33 of Ticket #2329
 Timestamp:
 12/10/10 13:00:53 (11 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

Ticket #2329

Property
Status
changed from
needs_review
toneeds_work

Property
Milestone
changed from
sage2.10.4
tosage4.6.2

Property
Summary
changed from
add interface to Pari's rnfisnorm
toAdd interface to PARI's rnfisnorm()

Property
Reviewers
changed from
Nick Alexander, David Loeffler
toNick Alexander, David Loeffler, Jeroen Demeyer

Property
Status
changed from

Ticket #2329 – Description
v24 v33 1 This patch adds support to solve norm equations via P ari.1 This patch adds support to solve norm equations via PARI. 2 2 3 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 The data used by P arito 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`.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`. 6 6 7 7 See #10430 for some related PARI bugfixes (not strictly required as the patch here contains a workaround).