#14990: Implement algebraic closures of finite fields
-------------------------------------+-------------------------------------
       Reporter:  pbruin             |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-5.13
      Component:  algebra            |   Resolution:
       Keywords:  finite field       |    Merged in:
  algebraic closure                  |    Reviewers:
        Authors:  Peter Bruin        |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:  u/pbruin/14990     |  dbc331bb85d634cb9cb6c75ad8dd82764c066f39
   Dependencies:  #14958, #13214     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by vdelecroix):

 * commit:   => dbc331bb85d634cb9cb6c75ad8dd82764c066f39


Comment:

 Hi,

 In order to speed up a bit, you could add the following lines at the very
 begining of the method _to_common_subfield(self, x, y) (lines 561-580)
 {{{
 if x._level == y._level:
     return x._value, y._value
 }}}
 (when the level is the same I go from 3ms to 0.8ms)

 What do you think about what I suggest in comment:15 namely, implementing
 .is_finite() (returning False) and do something for Zmod(3) ?
 ----
 Last 10 new commits:
 ||[[http://git.sagemath.org/sage.git/commit/?id=dbc331b|dbc331b]]||rename
 _coerce_2 to _to_common_subfield; cosmetic changes||
 ||[[http://git.sagemath.org/sage.git/commit/?id=ac93a01|ac93a01]]||remove
 the optional name from algebraic_closure examples||
 ||[[http://git.sagemath.org/sage.git/commit/?id=2432102|2432102]]||allow
 no argument for .algebraic_closure()||
 ||[[http://git.sagemath.org/sage.git/commit/?id=a197d0d|a197d0d]]||Merge
 branch 'u/vdelecroix/14990' of ssh://trac.sagemath.org:2222/sage into
 14990||
 ||[[http://git.sagemath.org/sage.git/commit/?id=f232993|f232993]]||fix the
 parent in pth_root and pth_power||
 ||[[http://git.sagemath.org/sage.git/commit/?id=0f4b895|0f4b895]]||add
 examples to .cardinality()||
 ||[[http://git.sagemath.org/sage.git/commit/?id=d95f57f|d95f57f]]||more
 methods to algebraic elements||
 ||[[http://git.sagemath.org/sage.git/commit/?id=081c096|081c096]]||Trac
 14990: implement algebraic closures of finite fields||
 ||[[http://git.sagemath.org/sage.git/commit/?id=31045f7|31045f7]]||fix the
 parent in pth_root and pth_power||
 ||[[http://git.sagemath.org/sage.git/commit/?id=3d88af6|3d88af6]]||add
 examples to .cardinality()||

--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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