id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
2329 Add interface to PARI's rnfisnorm() craigcitro craigcitro "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)" enhancement closed blocker sage-4.7 number fields fixed editor_craigcitro pari ncalexan mstreng jdemeyer sage-4.7.alpha2 Craig Citro, Marco Streng, Francis Clarke, Jeroen Demeyer Nick Alexander, David Loeffler, Jeroen Demeyer, David Kirkby N/A