#17804: Cleanup of sage.graphs.pq_trees
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   Reporter:  ncohen        |            Owner:
       Type:  enhancement   |           Status:  new
   Priority:  major         |        Milestone:  sage-6.6
  Component:  graph theory  |         Keywords:
  Merged in:                |          Authors:  Nathann Cohen
  Reviewers:                |  Report Upstream:  N/A
Work issues:                |           Branch:
     Commit:                |     Dependencies:
   Stopgaps:                |
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 While fixing the bug reported at #17787, I noticed several things in
 `sage.graphs.pq_trees` that should be cleaned. Some misnamed functions,
 hard-to-read documentation, and also a couple of simple but useful missing
 features that can be very helpful when debugging code.

 This branch consists of several commits which do the following:

 - Rename `.cardinality` to `.number_of_children`: the `PQ`-trees encode a
 set of permutations, and the 'cardinality' function should represent that,
 instead of what it represents now.

 - Add a real `.cardinality` function, which can be used to compute the
 number of different representations of an interval graph

 - Add a `.orderings` function, which lists all possibles representations
 of an interval graph

 - remove `.is_P` and `.is_Q`. These functions were barely used in the code
 itself, and can be replaced with `isinstance(x,P)` and `isinstance(x,Q)`.

 - Move the documentation of class PQ-tree, which actually explains how the
 main algorithm works, into the module's doc. It is also rewritten, and
 hopefully easier to understand.

 - Some one-line changes that improve readability or add links.

 Nathann

--
Ticket URL: <http://trac.sagemath.org/ticket/17804>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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