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Class math.topol.Braid.CurveDiagram.CutSequence 

java.lang.Object
   |
   +----math.topol.Braid.CurveDiagram.CutSequence
public class CutSequence
extends Object
implements Cloneable
Implements a geometric cut sequence, as defined in "Ordering the Braid Groups", by Fenn, Green, Rolfsen, Rourke, and Wiest, to appear in Pacific Journal of Mathematics.

Version:
$Id: CutSequence.java,v 1.10 1999/02/12 20:37:54 djun Exp djun $ Copyright (c)1998-1999 Djun Kim. The author reserves all rights.

Variable Index

o braidword
o ColArray
The sequence of colors used to differentiate images of the original intervals under the braid automorphism.
o end
o start

Constructor Index

o CutSequence(int)
Returns a new, empty cutsequence of the given index.

Method Index

o append(CutPoint)
Appends the given CutPoint to this CutSequence.
o delete(CutPoint)
Delete the CutPoint del.
o getIndex()
o insertAfter(CutPoint, CutPoint)
Insert the CutPoint newpoint after CutPoint here.
o insertBefore(CutPoint, CutPoint)
Insert the CutPoint newpoint before CutPoint here.
o prepend(CutPoint)
Prepends the given CutPoint to this CutSequence.
o PSOutput()
Writes PostScript code which draws the Canonical Curve Diagram for this CutSequence to System.out.
o reduce()
Reduce a curve diagram.
o setHole(CutPoint, int)
o setInterval(Interval, int)
o toString()
Returns a String representing this CutSequence.
o trivial(int)
Returns the "trivial" CutSequence for the given index.
o twistBy(int)
Returns the result of acting on this CutSequence by the elementary braid $\sigma_k$.

Variables

o start 
 public CutPoint start
o end 
 public CutPoint end
o braidword 
 public String braidword
o ColArray 
 public static Color ColArray[]
The sequence of colors used to differentiate images of the original intervals under the braid automorphism.

Constructors

o CutSequence 
 public CutSequence(int index)
Returns a new, empty cutsequence of the given index.

Methods

o setHole 
 public void setHole(CutPoint entry,
                     int index)
o setInterval 
 public void setInterval(Interval entry,
                         int index)
o getIndex 
 public int getIndex()
o trivial 
 public static CutSequence trivial(int index)
Returns the "trivial" CutSequence for the given index.

o twistBy 
 public CutSequence twistBy(int k)
Returns the result of acting on this CutSequence by the elementary braid $\sigma_k$. Permitted values of $k$ are -braidIndex + 1 .. braidIndex - 1. A value of 0 indicates the identity braid.

o reduce 
 public void reduce()
Reduce a curve diagram.

o append 
 public void append(CutPoint tail)
Appends the given CutPoint to this CutSequence.

o prepend 
 public void prepend(CutPoint head)
Prepends the given CutPoint to this CutSequence.

o delete 
 public void delete(CutPoint del)
Delete the CutPoint del.

o insertAfter 
 public void insertAfter(CutPoint newpoint,
                         CutPoint here)
Insert the CutPoint newpoint after CutPoint here.

o insertBefore 
 public void insertBefore(CutPoint newpoint,
                          CutPoint here)
Insert the CutPoint newpoint before CutPoint here.

o toString 
 public String toString()
Returns a String representing this CutSequence.

Overrides:
toString in class Object
o PSOutput 
 public void PSOutput()
Writes PostScript code which draws the Canonical Curve Diagram for this CutSequence to System.out. 

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