#8446: avoid 0^0 in number fields
-----------------------------+----------------------------------------------
   Reporter:  rlm            |       Owner:  davidloeffler
       Type:  defect         |      Status:  needs_review 
   Priority:  major          |   Milestone:  sage-4.3.4   
  Component:  number fields  |    Keywords:               
     Author:  Robert Miller  |    Upstream:  N/A          
   Reviewer:                 |      Merged:               
Work_issues:                 |  
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Description changed by rlm:

Old description:

> In the case of a trivial number field, such as
> {{{
> K.<a> = NumberField(polygen(QQ))
> }}}
> the Selmer group function doesn't work, since the generator `a` of the
> number field is 0, and when we're constructing polynomials we use the
> form `coeff*a**i`. However, if `i==0`, we get an `ArithmeticError` since
> Sage does not have conventions for `0^0`.

New description:

 In the case of a trivial number field, such as
 {{{
 K.<a> = NumberField(polygen(QQ))
 }}}
 the Selmer group function doesn't work, since the generator `a` of the
 number field is 0, and when we're constructing polynomials we use the form
 `coeff*a**i`. However, if `i==0`, we get an `ArithmeticError` since Sage
 does not have conventions for `0^0`.

 I found several places where this comes up, and I've fixed them where I
 can.

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8446#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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