Triangulation.polyhedral_complex, boundary_simplicial_complex, boundary_polyhedral_complex

[mkoeppe]

polyhedral_complex creates a geometric polyhedral complex corresponding to the triangulation.

boundary_simplicial_complex and boundary_polyhedral_complex are combinations of boundary (which gives a set of simplices) with simplicial_complex (which gives an abstract simplicial complex) and polyhedral_complex, respectively

CC: @yuan-zhou @jhpalmieri

Component: geometry

Author: Matthias Koeppe

Branch/Commit: 65134f1

Reviewer: Yuan Zhou, John Palmieri

Issue created by migration from https://trac.sagemath.org/ticket/33586

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Branch: u/mkoeppe/triangulation_polyhedral_complex

[mkoeppe]

New commits:

65b7cfe

Triangulation.polyhedral_complex: New

[mkoeppe]

Commit: 65b7cfe

[sagetrac-git]

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

fff67c3

Triangulation.boundary_{simplicial,polyhedral}_complex: New

[sagetrac-git]

Changed commit from 65b7cfe to fff67c3

[jhpalmieri]

comment:8

The docstring for boundary_simplicial_complex ends with

The boundary of every convex set is a topological sphere::

[mkoeppe]

comment:9

Thanks! I'll add the missing example

[sagetrac-git]

Changed commit from fff67c3 to 0a09ca4

[sagetrac-git]

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

0a09ca4

src/sage/geometry/triangulation/element.py: Add missing example

[yuan-zhou]

comment:12

Would it be possible to illustrate that boundary_simplicial_complex is a sub complex of simplicial_complex?

[sagetrac-git]

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

0845f03

Triangulation.boundary_simplicial_complex: Expand example

[sagetrac-git]

Changed commit from 0a09ca4 to 0845f03

[sagetrac-git]

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

80165ba

Triangulation.boundary_polyhedral_complex: Expand example

[sagetrac-git]

Changed commit from 0845f03 to 80165ba

[mkoeppe]

comment:15

Replying to @yuan-zhou:

Would it be possible to illustrate that boundary_simplicial_complex is a sub complex of simplicial_complex?

Good idea, done

[mkoeppe]

comment:16

It looks like abstract simplicial complexes don't have an is_subcomplex method. Should we add one?

[mkoeppe]

comment:17

Cubical complexes also define is_subcomplex.

[yuan-zhou]

comment:18

Defining is_subcomplex for abstract simplicial complexes is probably beyond the scope of the current ticket. I think that polyhedral complex has the method is_subcomplex, so it can at least be added to the doctests of polyhedral_complex or boundary_polyhedral_complex.
Replying to @mkoeppe:

It looks like abstract simplicial complexes don't have an is_subcomplex method. Should we add one?

[mkoeppe]

comment:19

Yes, I'm already using it

[mkoeppe]

comment:20

Replying to @yuan-zhou:

Defining is_subcomplex for abstract simplicial complexes is probably beyond the scope of the current ticket.

OK, I've opened #34294 for it

[yuan-zhou]

comment:21

In the docstring of Triangulation.__init__, it says "In the second case, the point indices of the maximal simplices of the triangulation", which needs rephrasing.

[yuan-zhou]

comment:22

It would be nice to point out that the polyhedral complex and boundary polyhedral complex are actually simplicial complexes. The difference is that they are not abstract.

[yuan-zhou]

comment:23

Never mind.
Replying to @yuan-zhou:

It would be nice to point out that the polyhedral complex and boundary polyhedral complex are actually simplicial complexes. The difference is that they are not abstract.

[yuan-zhou]

comment:24

Does it make sense to compare Triangulation.boundary_polyhedral_complex and PolyhedralComplex.boundary_subcomplex?

[mkoeppe]

comment:25

Replying to @yuan-zhou:

Does it make sense to compare Triangulation.boundary_polyhedral_complex and PolyhedralComplex.boundary_subcomplex?

I decided to stay away from that for this ticket because there's a bit of confusion regarding "boundary" vs "relative boundary"

[yuan-zhou]

comment:26

The code on this ticket (other than comment:21) looks good to me.

[sagetrac-git]

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

65134f1

src/sage/geometry/triangulation/element.py: Docstring improvements

[sagetrac-git]

Changed commit from 80165ba to 65134f1

[mkoeppe]

comment:28

I've rephrased it, please take a look

[yuan-zhou]

Reviewer: Yuan Zhou, John Palmieri

[mkoeppe]

comment:30

Thanks!

[vbraun]

Changed branch from u/mkoeppe/triangulation_polyhedral_complex to 65134f1