#9400: modify the NumberField constructor to pass in optional integer B such 
that
all the internal pari routines will replace the discriminant by its gcd
with B, making some things massively faster.
-----------------------------+----------------------------------------------
   Reporter:  was            |       Owner:  davidloeffler
       Type:  enhancement    |      Status:  needs_review 
   Priority:  major          |   Milestone:  sage-4.6     
  Component:  number fields  |    Keywords:               
     Author:                 |    Upstream:  N/A          
   Reviewer:                 |      Merged:               
Work_issues:                 |  
-----------------------------+----------------------------------------------

Comment(by jdemeyer):

 I attached a big reviewer patch (to be applied on top of
 9400_maximize_at_primes.patch) changing:
  * the PARI functions {{{nfbasis()}}} and {{{nfinit()}}}: document and fix
 implementation.
  * change {{{pari_nf()}}} to always use {{{integral_basis()}}} (this means
 that all the {{{maximize_at_primes}}} code can be moved out of
 {{{pari_nf()}}}).
  * rename {{{_compute_integral_basis}}} to {{{_pari_integral_basis}}} and
 don't convert from PARI to Sage.
  * make the code for CyclotomicField more analogous to NumberField_generic
 (such that only {{{_pari_integral_basis}}} needs to be specialized, not
 {{{integral_basis()}}}.

 Since the purpose of {{{_pari_init_()}}} is very unclear to me, I'm not
 sure what to do with that.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9400#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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