#20103: Some clean up in simplicial complexes
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Reporter: jhpalmieri | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-7.1
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers:
Authors: John Palmieri | Work issues:
Report Upstream: N/A | Commit:
Branch: u/jhpalmieri | 6fb881a4de6cfa94cad0481120cbd2c48d3ee077
/complex-cleanup | Stopgaps:
Dependencies: |
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Description changed by jhpalmieri:
Old description:
> This in some sense a followup to #6102 and in some sense a precursor a
> future ticket for simplicial sets. This mainly involves some
> reorganization, not much new.
>
> - Add a `reduced` keyword to the `homology` method, to make it easy to
> compute unreduced homology. (Computing reduced homology has always been
> the default, but it was a little inconvenient to compute the unreduced
> homology before.)
> - Add an `is_acyclic` method for cell complexes.
> - Instead of having a single `algebraic_topological_model` method for all
> cell complexes, broken into cases depending on the complex, instead each
> class which inherits from `GenericCellComplex` should implement its own
> method.
> - Similarly, cell complexes should have an `alexander_whitney` method.
> This helps to clean up the cup product code; that code should be easy to
> maintain if we add more types of cell complexes.
> - Change `__cmp__` to `__eq__` etc., for all types of cells and
> complexes. My understanding is that `__cmp__` is no longer used in Python
> 3, so we should eliminate it.
> - For simplicial complexes, define a `face` method: then `K.face(sigma,
> i)` will return the ith face of `sigma` in `K`. This is not really useful
> on its own, but it gets used in the `Sq` method in
> `homology_vector_space_with_basis`. The point is, we could define cell
> complexes (like the current Delta complexes, and like simplicial sets) in
> which you can only compute the face of a cell by knowing about the
> complex in which it lives, and we might want to extend the `Sq` method to
> work with such complexes.
New description:
This in some sense a followup to #6102 and in some sense a precursor for a
future ticket for simplicial sets. This mainly involves some
reorganization, not much new.
- Add a `reduced` keyword to the `homology` method, to make it easy to
compute unreduced homology. (Computing reduced homology has always been
the default, but it was a little inconvenient to compute the unreduced
homology before.)
- Add an `is_acyclic` method for cell complexes.
- Instead of having a single `algebraic_topological_model` method for all
cell complexes, broken into cases depending on the complex, instead each
class which inherits from `GenericCellComplex` should implement its own
method.
- Similarly, cell complexes should have an `alexander_whitney` method.
This helps to clean up the cup product code; that code should be easy to
maintain if we add more types of cell complexes.
- Change `__cmp__` to `__eq__` etc., for all types of cells and complexes.
My understanding is that `__cmp__` is no longer used in Python 3, so we
should eliminate it.
- For simplicial complexes, define a `face` method: then `K.face(sigma,
i)` will return the ith face of `sigma` in `K`. This is not really useful
on its own, but it gets used in the `Sq` method in
`homology_vector_space_with_basis`. The point is, we could define cell
complexes (like the current Delta complexes, and like simplicial sets) in
which you can only compute the face of a cell by knowing about the complex
in which it lives, and we might want to extend the `Sq` method to work
with such complexes.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/20103#comment:3>
Sage <http://www.sagemath.org>
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