#14746: Clean up S-class group, S-unit and Selmer group code
-------------------------------------------------+-------------------------
       Reporter:  pbruin                         |         Owner:
           Type:  enhancement                    |  davidloeffler
       Priority:  major                          |        Status:
      Component:  number fields                  |  needs_review
       Keywords:  S-class group, S-units,        |     Milestone:
  Selmer group                                   |  sage-5.11
        Authors:  Peter Bruin                    |    Resolution:
Report Upstream:  N/A                            |     Merged in:
         Branch:                                 |     Reviewers:
       Stopgaps:                                 |   Work issues:
                                                 |  Dependencies:  #14489
-------------------------------------------------+-------------------------

Comment (by vbraun):

 Test failure in my 32-bit VM:
 {{{
 [vbraun@localhost hg]$ sage -t
 sage/rings/polynomial/polynomial_quotient_ring.py  # 2 doctests failed
 Running doctests with ID 2013-07-18-21-23-12-2dbc373e.
 Doctesting 1 file.
 sage -t sage/rings/polynomial/polynomial_quotient_ring.py
 **********************************************************************
 File "sage/rings/polynomial/polynomial_quotient_ring.py", line 987, in
 
sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_class_group
 Failed example:
     S.S_class_group([])
 Expected:
     [((1/4*xbar^2 + 31/4, (-1/8*a + 1/8)*xbar^2 - 31/8*a + 31/8,
 1/16*xbar^3 + 1/16*xbar^2 + 31/16*xbar + 31/16, -1/16*a*xbar^3 + (1/16*a +
 1/8)*xbar^2 - 31/16*a*xbar + 31/16*a + 31/8), 6, 1/16*xbar^3 - 5/16*xbar^2
 + 31/16*xbar - 139/16), ((-1/4*xbar^2 - 23/4, (1/8*a - 1/8)*xbar^2 +
 23/8*a - 23/8, -1/16*xbar^3 - 1/16*xbar^2 - 23/16*xbar - 23/16,
 1/16*a*xbar^3 + (-1/16*a - 1/8)*xbar^2 + 23/16*a*xbar - 23/16*a - 23/8),
 6, 1/16*xbar^3 + 3/16*xbar^2 + 23/16*xbar + 85/16), ((-5/4*xbar^2 - 115/4,
 5/4*a*xbar^2 + 115/4*a, -5/16*xbar^3 + 5/16*xbar^2 - 115/16*xbar + 115/16,
 1/16*a*xbar^3 + 7/16*a*xbar^2 + 23/16*a*xbar + 161/16*a), 2, 5/16*xbar^3 +
 37/16*xbar^2 + 115/16*xbar + 867/16)]
 Got:
     [((1/4*xbar^2 + 31/4, (-1/8*a + 1/8)*xbar^2 - 31/8*a + 31/8,
 1/16*xbar^3 + 1/16*xbar^2 + 31/16*xbar + 31/16, -1/16*a*xbar^3 + (1/16*a +
 1/8)*xbar^2 - 31/16*a*xbar + 31/16*a + 31/8), 6, -1/16*xbar^3 +
 1/16*xbar^2 - 31/16*xbar + 47/16), ((-1/4*xbar^2 - 23/4, (1/8*a -
 1/8)*xbar^2 + 23/8*a - 23/8, -1/16*xbar^3 - 1/16*xbar^2 - 23/16*xbar -
 23/16, 1/16*a*xbar^3 + (-1/16*a - 1/8)*xbar^2 + 23/16*a*xbar - 23/16*a -
 23/8), 6, 1/16*xbar^3 + 3/16*xbar^2 + 23/16*xbar + 85/16), ((-5/4*xbar^2 -
 115/4, 5/4*a*xbar^2 + 115/4*a, -5/16*xbar^3 + 5/16*xbar^2 - 115/16*xbar +
 115/16, 1/16*a*xbar^3 + 7/16*a*xbar^2 + 23/16*a*xbar + 161/16*a), 2,
 5/16*xbar^3 + 37/16*xbar^2 + 115/16*xbar + 867/16)]
 **********************************************************************
 File "sage/rings/polynomial/polynomial_quotient_ring.py", line 1063, in
 
sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.class_group
 Failed example:
     S.class_group()
 Expected:
     [((2, -a + 1, 1/2*xbar + 1/2, -1/2*a*xbar + 1/2*a + 1), 6, -1/2*xbar +
 3/2)]
 Got:
     [((2, -a + 1, 1/2*xbar + 1/2, -1/2*a*xbar + 1/2*a + 1), 6, 1/2*xbar -
 3/2)]
 **********************************************************************
 2 items had failures:
    1 of  23 in
 
sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_class_group
    1 of  25 in
 
sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.class_group
     [357 tests, 2 failures, 6.25 s]
 ----------------------------------------------------------------------
 sage -t sage/rings/polynomial/polynomial_quotient_ring.py  # 2 doctests
 failed
 ----------------------------------------------------------------------
 Total time for all tests: 6.4 seconds
     cpu time: 5.8 seconds
     cumulative wall time: 6.2 seconds
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/14746#comment:12>
Sage <http://www.sagemath.org>
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