#13101: enumerate_totallyreal_fields bug fix
-----------------------------+----------------------------------------------
   Reporter:  jvoight        |             Owner:  davidloeffler
       Type:  defect         |            Status:  new          
   Priority:  major          |         Milestone:  sage-5.1     
  Component:  number fields  |          Keywords:               
Work issues:                 |   Report Upstream:  N/A          
  Reviewers:  citro          |           Authors:               
  Merged in:                 |      Dependencies:               
   Stopgaps:                 |  
-----------------------------+----------------------------------------------
 sage: enumerate_totallyreal_fields_all(8, 10^8)
 ---------------------------------------------------------------------------
 IndexError                                Traceback (most recent call
 last)

 /home/jvoight/sage-4.2/devel/sage-main/sage/rings/number_field/<ipython
 console> in <module>()

 /usr/local/share/sage-5.0/local/lib/python2.7/site-
 packages/sage/rings/number_field/totallyreal_rel.pyc in
 enumerate_totallyreal_fields_all(n, B, verbose, return_seqs)
     887                     print "Taking F =", Sds[i][1]
     888                 F = NumberField(ZZx(Sds[i][1]), 't')
 --> 889                 T = enumerate_totallyreal_fields_rel(F, n/d, B,
 verbose=verbose, return_seqs=return_seqs)
     890                 if return_seqs:
     891                     for i in range(3):

 /usr/local/share/sage-5.0/local/lib/python2.7/site-
 packages/sage/rings/number_field/totallyreal_rel.pyc in
 enumerate_totallyreal_fields_rel(F, m, B, a, verbose, return_seqs)
     726         T.incr(f_out,verbose)
     727     else:
 --> 728         T.incr(f_out)
     729
     730     Fx = PolynomialRing(F, 'xF')

 /usr/local/share/sage-5.0/local/lib/python2.7/site-
 packages/sage/rings/number_field/totallyreal_rel.pyc in incr(self, f_out,
 verbose, haltk)
     542                         # New bounds from Lagrange multiplier in
 degree 3.

     543                         bminmax =
 [lagrange_degree_3(m,v(self.a[m-1]),v(self.a[m-2]),v(self.a[m-3])) for v
 in self.Foo]
 --> 544                         self.b_lower = [bminmax[i][0] for i in
 range(len(bminmax))]
     545                         self.b_upper = [bminmax[i][1] for i in
 range(len(bminmax))]
     546

 IndexError: list index out of range

 The fix is easy: we just need to add the lines

     if len(z4minmax) < 1:
         z4minmax = [0.0, -1.0]
 [    return z4minmax ]

 before line 295 of sage/rings/number_field/totallyreal_data.pyx.  (Yes,
 I'm still intimidated by creating a patch.)

 The issue was that when the lagrange multipliers gives contradictory
 bounds (a good thing, since it says the enumeration can stop in that
 branch), it was not sending a pair of bounds, just a single element,
 causing a type error.

 JV

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13101>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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