#7735: [with patch] incorrect sage exponentiation in interreduced_basis '^' vs
'**'
-----------------------------------------------------------+----------------
   Reporter:  lftabera                                     |       Owner:  
AlexGhitza                
       Type:  defect                                       |      Status:  new  
                     
   Priority:  major                                        |   Milestone:  
sage-4.3                  
  Component:  algebra                                      |    Keywords:  
interreduced_basis, python
Work_issues:                                               |      Author:  Luis 
Felipe Tabera        
   Upstream:  Not yet reported upstream; Will do shortly.  |    Reviewer:       
                     
     Merged:                                               |  
-----------------------------------------------------------+----------------
 There is a bug in the code of interreduced_basis in

 sage/rings/polynomial/multi_polynomial_ideal.py

 {{{
 sage: R=QQ['t'].fraction_field()['x,y']
 sage: R.inject_variables()
 Defining x, y
 sage: I=x*R
 sage: I.interreduced_basis()
 ---------------------------------------------------------------------------
 RuntimeError                              Traceback (most recent call
 last)

 /home/luisfe/<ipython console> in <module>()

 /opt/SAGE/sage/local/lib/python2.6/site-
 packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in
 wrapper(*args, **kwds)
     362         """
     363         with RedSBContext():
 --> 364             return func(*args, **kwds)
     365
     366     from sage.misc.sageinspect import sage_getsource

 /opt/SAGE/sage/local/lib/python2.6/site-
 packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in
 interreduced_basis(self)
    1542                 for f in self._singular_().interred():
    1543                     f = R(f)
 -> 1544                     ret.append(f.lc()^(-1)*f) # lead coeffs are
 not reduced by interred
    1545                 s.option("set",o)
    1546             except TypeError:

 /opt/SAGE/sage/local/lib/python2.6/site-packages/sage/structure/element.so
 in sage.structure.element.Element.__xor__
 (sage/structure/element.c:4469)()

 RuntimeError: Use ** for exponentiation, not '^', which means xor
 in Python, and has the wrong precedence.

 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7735>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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