LatticePoset: add sublattice()

[jmantysalo]

Add a function to get smallest sublattice of the lattice containing given elements.

[jmantysalo]

Slooow. Better than nothing. Needs review.

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New commits:

​6b9a03b	Added a function.
​54d912c	Removed spaces.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​34a588d

Arghs, should return a lattice, not a poset.

[deinst]

I think there is a typo. I've changed the code to what I think is correct. The previous code did the following:

sage: L = Posets.BooleanLattice(3)
sage: L.sublattice([3,5,6,7])
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-14-837853635c8a> in <module>()
----> 1 L.sublattice([Integer(3),Integer(5),Integer(6),Integer(7)])

/Users/davideinstein/projects/sage/local/lib/python2.7/site-packages/sage/combinat/posets/lattices.pyc in sublattice(self, elms)
    881                     elms.append(m)
    882                     n=True
--> 883         return LatticePoset(self.subposet(elms))
    884 
    885 ############################################################################

/Users/davideinstein/projects/sage/local/lib/python2.7/site-packages/sage/combinat/posets/lattices.pyc in LatticePoset(data, *args, **options)
    406     P = Poset(data, *args, **options)
    407     if not P.is_lattice():
--> 408         raise ValueError("Not a lattice.")
    409 
    410     return FiniteLatticePoset(P, category = FiniteLatticePosets(), facade = P._is_facade)

ValueError: Not a lattice.

Also, could you put whitespace around = as suggested by ​http://doc.sagemath.org/html/en/developer/coding_basics.html#python-code-style

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New commits:

​47f2ce7

Fixed probable typo

[deinst]

Otherwise it looks good to me.

[jmantysalo]

Thanks! And yes, there was a stupid typo. I'll try to remember spaces from now on. (A promise I have made before...)

So, who's going to review this?

[ncohen]

Yo !

I added a commit at public/18515 which improves the algorithm a bit. In general, try to avoid using 'Subsets' (or any combinat stuff) if you can avoid it: they implement their code to deal with infinitely more abstraction than you usually need (categories, parents, elements, ...).

sage: type(Subsets([1,2,3],2).an_element())
<class 'sage.sets.set.Set_object_enumerated_with_category'>

When you only need to enumerate pairs of points, the better is to use itertools:

sage: from itertools import combinations
sage: list(combinations([1,2,3],2))
[(1, 2), (1, 3), (2, 3)]

Simple, and more efficient.

So, who's going to review this?

We can review each other's commits, it is not forbidden. For as long as everything is doubled checked, no problem.

Nathann

[jmantysalo]

Seems good, but of course doesn't make that much difference than totally other algorithm mentioned in the note. I'll check the code of Nathann and then put this to positive review. (Assuming that deinst doesn't do it before that.)

[jmantysalo]

Works.

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New commits:

​a86919a

trac #18515: A less wasteful algorithm

[ncohen]

;-)