edu.stanford.math.plex4.homology.chain_basis

Interface PrimitiveBasisElement

All Known Implementing Classes:

Cell, Simplex, SimplexPair

public interface PrimitiveBasisElement

This interface defines the functionality of a primitive basis element type for a chain complex. The two main implementing classes are designed to be the Simplex and Cell classes. We refer to these as "primitive" basis types since they are not built from other any other types. Whereas, we may also construct a chain complex on a basis consisting of objects derived from other basis types. An example of this is when we construct the tensor product of two chain complexes - the basis type consists of tensors of elements. We require that the implementing class provide the hashCode and equals functions.

Author:

Andrew Tausz

Method Summary

Methods

Modifier and Type	Method and Description
PrimitiveBasisElement[]	getBoundaryArray() This function returns the boundary of the current basis element.
int[]	getBoundaryCoefficients() This function returns the coefficients of the elements of the boundary array.
int	getDimension() This function returns the dimension of the basis element.

Method Detail

getDimension

int getDimension()

This function returns the dimension of the basis element. Note that this is the actual geometric dimension of the simplex or cell. For example, for a simplex this would be one less than the number of indices in it.

Returns:

the geometric dimension of this object

getBoundaryArray

PrimitiveBasisElement[] getBoundaryArray()

This function returns the boundary of the current basis element. As with the dimension, this actually obtains the geometric boundary of this object. Note that this function only returns the the objects in the boundary, but not their coefficients.

Returns:

the boundary of the current object

getBoundaryCoefficients

int[] getBoundaryCoefficients()

This function returns the coefficients of the elements of the boundary array. It is implemented as a separate function, since this interface is designed to be agnostic to its algebraic environment. In the case of the Simplex class this will return the array consisting of alternating signs [1, -1, 1, ...]. However, in the case of the Cell class it will return the degrees of the composite attaching maps used to compute cellular homology.

Returns:

the coefficients of the boundary elements