another example of simplicial complex : the K3 surface

[fchapoton]

I propose to add to the list of simplicial complexes the minimal triangulation of the K3 surface, which has 16 vertices and 288 facets.

sage: simplicial_complexes.K3_surface()
Simplicial complex with vertex set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16) and 288 facets

This is can either be defined by storing the data or by recovering it using a group action. What should I prefer ?

Reference : Combinatorial properties of the K3 surface:
Simplicial blowups and slicings by Jonathan Spreer & Wolfgang Kühnel

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Apply

• attachment: trac_11703-simplicial_K3_surface-fc.patch and attachment: trac_11703-referee.patch.

CC: @sagetrac-sage-combinat

Component: algebraic topology

Keywords: simplicial complex

Author: Frédéric Chapoton

Reviewer: John Palmieri

Merged: sage-4.7.2.alpha3

Issue created by migration from https://trac.sagemath.org/ticket/11703

[jhpalmieri]

comment:1

Adding the K3 surface would be great. Can you describe what's involved for the two approaches (storing the data or using the group action)? Then I could make a better suggestion about which to use here.

[vbraun]

comment:2

That would be nice! If there is some reasonably easy way to construct the complex from a group action then it should be done that way so that others can learn from the source code. But just listing raw data would be fine with me, too.

[fchapoton]

comment:3

Here is the code with the group (of size 240) and the orbit closure. The other option is just a long list.

def K3_surface():
    """
    Returns the minimal triangulation of the K3 surface. This is a simplicial complex with 16 vertices and 288 facets.

    EXAMPLES::
        sage: K3=simplicial_complexes.K3_surface() ; K3
        Simplicial complex with vertex set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16) and 288 facets
        sage: K3.f_vector()
        [1, 16, 120, 560, 720, 288]

    REFERENCES:
        - Combinatorial properties of the K3 surface: Simplicial blowups and slicings by Jonathan Spreer & Wolfgang Kühnel
        - M. Casella and W. K¨uhnel, A triangulated K3 surface with the minimum number of vertices, Topology 40 (2001), 753–772.
    """
    G = PermutationGroup([[(1,3,8,4,9,16,15,2,14,12,6,7,13,5,10)],[(1,11,16),(2,10,14),(3,12,13),(4,9,15),(5,7,8)]])
    gen1=(1,2,3,8,12)      
    gen2=(1,2,5,8,14)
    liste=[tuple([g(i) for i in gen1]) for g in G]+[tuple([g(i) for i in gen2]) for g in G]
    return SimplicialComplex(liste)

[jhpalmieri]

comment:4

The group action approach looks good to me. Can you post a patch?

[kcrisman]

comment:5

Can I "like" this?

Also, don't forget the sage developer guide for some nitpicky things about the docstring - this will save the reviewer (presumably jhpalmieri himself) some effort.

[fchapoton]

comment:6

Here is a patch, ready for review. I have tried to do my best with respect to coding conventions.

[fchapoton]

Author: Frédéric Chapoton

[jhpalmieri]

Reviewer: John Palmieri

[jhpalmieri]

comment:7

Attachment: trac_11703-simplicial_K3_surface-fc.patch.gz

This mostly looks good. I'm attaching a referee patch:

• only import PermutationGroup where it's needed, not at the top-level.
• add a sentence to the documentation.
• format the references correctly.

If you're happy with these changes, then the whole ticket can get a positive review.

[jhpalmieri]

apply on top of other patch

[fchapoton]

comment:8

Attachment: trac_11703-referee.patch.gz

This is ok for me. The only point (very minor one) is that the bot does not give a green light, but I guess it does not work very smoothly yet.

[jhpalmieri]

comment:9

The failures reported by the bot don't seem to have anything to do with this ticket.

[nexttime]

Merged: sage-4.7.2.alpha3

[nexttime]

comment:12

Jeroen's script should be smart enough to collapse multiple spaces into a single one... 8/

P.S.:

Frédéric, you could add yourself to http://trac.sagemath.org/sage_trac/wiki#AccountNamesMappedtoRealNames.

[nexttime]

Changed author from Frédéric Chapoton to Frédéric Chapoton