Representation: The repreesentation of complexes¶
- class simplicial.Representation¶
The base class for implementations of simplicial complexes.
This class defines the interface to be implemented by representations, plus some housekeeping functions.
- Parameters
c – the complex we’re representing
Complex¶
- Representation.setComplex(c)¶
Set the complex we’re representing. This allows the representation to make use of the complex’s more flexible operations if required.
- Parameters
c (
SimplicialComplex) – the complex
Adding and deleting simplices¶
- Representation.addSimplex(fs, id, attr)¶
Add a simplex to the complex whose faces are the elements of fs.
- Parameters
fs (
List[Any]) – (optional) a list of faces of the simplexid (
Any) – (optional) name for the simplexattr (
Dict[str,Any]) – (optional) dict of attributes
- Returns
the name of the new simplex
- Representation.newSimplex(d)¶
Generate a new unique identifier for a simplex.
- Parameters
d (
int) – dimension of the simplex to be identified- Return type
str- Returns
an identifier not currently used in the complex
- Representation.forceDeleteSimplex(s)¶
Delete a simplex without sanity checks.
- Parameters
s (
Any) – the simplex
- Representation.relabelSimplex(s, q)¶
Relabel a simplex.
- Parameters
s (
Any) – the simplex to renameq (
Any) – the new name
Retrieving simplices¶
- Representation.simplices(reverse)¶
Return all the simplices in the complex, in order: the low orders first (unless reverse is True), and in canonical order within each order.
- Parameters
reverse (
bool) – (optional) reverse the sort order if True- Return type
List[Any]- Returns
a list of simplices
- Representation.simplicesOfOrder(k)¶
Return all the simplices of the given order. The simplices are returned in “canonical” order, meaning the order they appear in the boiundary operator matrices.
- Parameters
k (
int) – the desired order- Return type
List[Any]- Returns
a set of simplices, which may be empty
- Representation.containsSimplex(s)¶
Test whether the complex contains the given simplex.
- Parameters
s (
Any) – the simplex- Return type
bool- Returns
True if the simplex is in the complex
- Representation.maxOrder()¶
Return the largest order of simplices in the complex.
- Return type
int- Returns
the largest order that contains at least one simplex, or -1
Details of individual simplices¶
- Representation.orderOf(s)¶
Return the order of a simplex.
- Parameters
s (
Any) – the simplex- Return type
int- Returns
the order of the simplex
- Representation.indexOf(s)¶
Return the inmdex of a simplex.
- Parameters
s (
Any) – the simplex- Return type
int- Returns
an index
- Representation.getAttributes(s)¶
Return the attributes associated with the given simplex.
- Parameters
s (
Any) – the simplex- Return type
Dict[str,Any]- Returns
a dict of attributes
- Representation.setAttributes(s, attr)¶
Set the attributes associated with a simplex.
- Parameters
s (
Any) – the simplexattr (
Dict[str,Any]) – a dict of attributes
- Representation.faces(s)¶
Return the faces of a simplex.
- Parameters
s (
Any) – the simplex- Return type
Set[Any]- Returns
a set of faces
- Representation.cofaces(s)¶
Return the simplices the given simnplex is a face of.
- Parameters
s (
Any) – the simplex- Return type
Set[Any]- Returns
a list of simplices
- Representation.basisOf(s)¶
Return the basis of a simplex.
- Parameters
s (
Any) – the simplex- Return type
Set[Any]- Returns
the set of 0-simplices that form the basis of s
Topological information¶
- Representation.boundaryOperator(k)¶
Return the boundary operator of the k-simplices.
- Parameters
k (
int) – the order of simplices- Return type
ndarray- Returns
the boundary matrix