ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 10 Feb 2021 12:37:36 +0100cell complexes vs simplicial complexeshttps://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/I have spent several days googling, but am not able to find any basic information for working with cell complexes in sage. I am using windows 10 , sage 9.1 where the help function doesn't work.
What I need to be able to do is to enter a cell complex, add cells, delete cells and subdivide. I already have functions defined that could be used to specify the gluing maps.
There seems to be slightly more information available for working with simplicial complexes. If I were to subdivide my cell complex, I would get a simplicial complex; there are no exotic gluing maps. However, because the cells are high dimensional, the number of simplicies is huge after subdivision, and I am not sure I could correctly enter all that information by hand.
Any suggestions would be very appreciated! If anyone has a file to share in which they have worked with cell complexes or simplicial complexes, that would also be really helpful to me to learn the syntax.Tue, 09 Feb 2021 06:41:25 +0100https://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/Answer by jipilab for <p>I have spent several days googling, but am not able to find any basic information for working with cell complexes in sage. I am using windows 10 , sage 9.1 where the help function doesn't work.</p>
<p>What I need to be able to do is to enter a cell complex, add cells, delete cells and subdivide. I already have functions defined that could be used to specify the gluing maps.
There seems to be slightly more information available for working with simplicial complexes. If I were to subdivide my cell complex, I would get a simplicial complex; there are no exotic gluing maps. However, because the cells are high dimensional, the number of simplicies is huge after subdivision, and I am not sure I could correctly enter all that information by hand.
Any suggestions would be very appreciated! If anyone has a file to share in which they have worked with cell complexes or simplicial complexes, that would also be really helpful to me to learn the syntax.</p>
https://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/?answer=55634#post-id-55634I would recommend you to have a look at the documentation:
[For general cell complexes](https://doc.sagemath.org/html/en/reference/homology/sage/homology/cell_complex.html)
[For simplicial complexes](https://doc.sagemath.org/html/en/reference/homology/sage/homology/simplicial_complex.html)
Note that they have different methods available and that they might not offer the state-of-the-art methods for what you mean, but it is worth trying!Tue, 09 Feb 2021 11:53:56 +0100https://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/?answer=55634#post-id-55634Comment by Ingrid for <p>I would recommend you to have a look at the documentation:</p>
<p><a href="https://doc.sagemath.org/html/en/reference/homology/sage/homology/cell_complex.html">For general cell complexes</a>
<a href="https://doc.sagemath.org/html/en/reference/homology/sage/homology/simplicial_complex.html">For simplicial complexes</a></p>
<p>Note that they have different methods available and that they might not offer the state-of-the-art methods for what you mean, but it is worth trying!</p>
https://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/?comment=55657#post-id-55657Thanks, both of you, for confirming what I was beginning to be afraid of. I don't know how to describe continuous functions in sage, but for all the examples I can think of, the maps can be described as being piecewise linear.Wed, 10 Feb 2021 12:37:36 +0100https://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/?comment=55657#post-id-55657Answer by John Palmieri for <p>I have spent several days googling, but am not able to find any basic information for working with cell complexes in sage. I am using windows 10 , sage 9.1 where the help function doesn't work.</p>
<p>What I need to be able to do is to enter a cell complex, add cells, delete cells and subdivide. I already have functions defined that could be used to specify the gluing maps.
There seems to be slightly more information available for working with simplicial complexes. If I were to subdivide my cell complex, I would get a simplicial complex; there are no exotic gluing maps. However, because the cells are high dimensional, the number of simplicies is huge after subdivision, and I am not sure I could correctly enter all that information by hand.
Any suggestions would be very appreciated! If anyone has a file to share in which they have worked with cell complexes or simplicial complexes, that would also be really helpful to me to learn the syntax.</p>
https://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/?answer=55641#post-id-55641From the documentation for generic cell complexes cited by @jpilab:
> This module defines a class of
> abstract finite cell complexes. This
> is meant as a base class from which
> other classes (like SimplicialComplex,
> CubicalComplex, and DeltaComplex)
> should derive. As such, most of its
> properties are not implemented. It is
> meant for use by developers producing
> new classes, not casual users.
In particular, there is no way for a Sage user to use a "cell complex"; you can instead work with a simplicial complex, a Delta complex, or a simplicial set. There are plenty of examples of all of those [in the documentation](https://doc.sagemath.org/html/en/reference/homology/index.html).
Simplicial sets can be very efficient; to define a 10-dimensional sphere, for example, you only have to specify a 10-dimensional simplex and a 0-dimensional simplex. Delta complexes are somewhat more efficient, and simplicial complexes are the least efficient, in terms of numbers of simplices required.
(Here's a question: if Sage were to implement CW complexes, for example, how should it encode the gluing maps? Is there a good way to describe a continuous function in a computer algebra system like Sage? With a good answer to this, we could think about how to handle the rest of the implementation.)
Tue, 09 Feb 2021 17:34:19 +0100https://ask.sagemath.org/question/55631/cell-complexes-vs-simplicial-complexes/?answer=55641#post-id-55641