Cell -- the class of all cells in cell complexes

Description

This class represents a single cell in a cell complex. A cell has a boundary, a dimension, and a label. In most cases, the label should be a monomial. But the cells in this package may be anything. However for functions such as complex to work, the labels should be either monomials, ideals, or modules. In the monomial case, we can view the label as a module by taking the submodule generated by the monomial in the ring. There should be canonical inclusions maps from the label on any cell to the labels of the cells in its boundary.

Functions and methods returning a cell:

newCell -- creates a new cell
newSimplexCell -- create a new cell

Methods that use a cell:

boundary(Cell) -- see boundary -- returns the boundary cells along with relative orientations
boundaryCells(Cell) -- see boundaryCells -- returns the boundary cells of the given cell
cellLabel(Cell) -- see cellLabel -- return the label of a cell
dim(Cell) -- compute the dimension of a cell
isSimplex(Cell) -- see isSimplex -- check if a cell is a simplex
isWellDefined(Cell) -- checks if a cell is well defined
net(Cell) (missing documentation)

For the programmer

The object Cell is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in CellularResolutions/doc.m2:63:0.

Cell -- the class of all cells in cell complexes

Description

See also

Functions and methods returning a cell:

Methods that use a cell:

For the programmer