#19496: Improve FiniteStateMachine.number_of_words
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   Reporter:  cheuberg               |            Owner:
       Type:  defect                 |           Status:  new
   Priority:  major                  |        Milestone:  sage-6.10
  Component:  finite state machines  |         Keywords:
  Merged in:                         |          Authors:  Clemens Heuberger
  Reviewers:                         |  Report Upstream:  N/A
Work issues:                         |           Branch:
     Commit:                         |     Dependencies:
   Stopgaps:                         |
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 Improve `FiniteStateMachine.number_of_words`:
 - provide a parameter `base_ring` (currently, `QQbar` is always used)
 - remove `assert` statements (may produce `DivisionByZero` due to
 evaluation for small `n`)
 - add doctest for eigenvalue zero
 - compute in `base_ring` as long as possible and move to symbolic ring as
 late as possible
 - do not compute inverses, but solve linear systems of equations

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Ticket URL: <http://trac.sagemath.org/ticket/19496>
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