[with patch, positive review] Sets enumerated by exploring a search space with a (lazy) tree or graph structure

[nthiery]

This patches extend the sage.combinat.backtrack library with other generic tools for constructing large sets whose elements can be enumerated by exploring a search space with a (lazy) tree or graph structure.

• SearchForest?: Depth first search through a tree descrived by a child function
• GenericBacktracker?: (was readilly there) Depth first search through a tree descrived by a child function, with branch pruning, ...
• TransitiveIdeal?: Depth first search through a graph described by a neighbours relation
• TransitiveIdealGraded?: Breath first search through a graph described by a neighbours relation

Todo: the names are crappy and inconsistent, because they come from different point of views. We need to find a good naming scheme!!!

Do we want to emphasize the underlying graph/tree structure? The branch&bound aspect? The transitive closure of a relation point of view?

Todo: which interface do we want:

• TransitiveIdeal?(relation, generators)
• TransitiveIdeal?(generators, relation)

The code needs to be standardized once the choice is done.

[rbeezer]

Apply on top of main patch

[rbeezer]

Passes tests: ./sage -t devel/sage-backtrack/sage/combinat/

Reviewer patch adds two doctests, and some general cleanup, so apply on top of the main patch.

In the case of a search tree (not a graph), options for "leaves only" would be useful. Then the generators could be checked for a first element when using a search tree for existence questions.

Building a single function to call these routines as variants might ease the question of names and interfaces.

Positive review.

[mhansen]

Merged in 4.0.1.alpha0.