edu.stanford.math.plex4.homology.chain_basis

Class Simplex

java.lang.Object

edu.stanford.math.plex4.homology.chain_basis.Simplex

All Implemented Interfaces:

PrimitiveBasisElement

public class Simplex
extends java.lang.Object
implements PrimitiveBasisElement

This class implements the functionality of a simplex. A simplex is an n-dimensional polytope which is the convex hull of its vertices. For our purposes, we simply represent a simplex by its vertices which are labeled by integers. For example, a 2-simplex could be [0, 5, 9].

The vertices of a simplex are specified by non-negative integers. It uses an array implementation to store the indices of the vertices of the simplex.

This class is designed to be a standard implementation of the PrimitiveBasisElement interface. It is also immutable and implements value semantics.

Author:

Andrew Tausz

Constructor Summary

Constructors

Constructor and Description
Simplex(int[] vertices) This constructor initializes the simplex from a supplied array of integers.

Method Summary

Methods

Modifier and Type	Method and Description
boolean	equals(java.lang.Object obj)
Simplex[]	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.
int[]	getVertices() This function returns an array containing the vertices of the simplex.
int	hashCode()
static Simplex	makeSimplex(int... args)
java.lang.String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Simplex

public Simplex(int[] vertices)

This constructor initializes the simplex from a supplied array of integers.

Parameters:

vertices - the vertices to

Method Detail

makeSimplex

public static Simplex makeSimplex(int... args)

getDimension

public int getDimension()

Description copied from interface: PrimitiveBasisElement

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.

Specified by:

getDimension in interface PrimitiveBasisElement

Returns:

the geometric dimension of this object

getVertices

public int[] getVertices()

This function returns an array containing the vertices of the simplex.

Returns:

an array containing the vertices of the simplex

getBoundaryArray

public Simplex[] getBoundaryArray()

Description copied from interface: PrimitiveBasisElement

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.

Specified by:

getBoundaryArray in interface PrimitiveBasisElement

Returns:

the boundary of the current object

getBoundaryCoefficients

public int[] getBoundaryCoefficients()

Description copied from interface: PrimitiveBasisElement

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.

Specified by:

getBoundaryCoefficients in interface PrimitiveBasisElement

Returns:

the coefficients of the boundary elements

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object