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Class math.alg.PowerSeries.NCseries 

java.lang.Object
   |
   +----math.alg.PowerSeries.NCseries
public class NCseries
extends Object
This class represents infinite power series with integer coefficients, in an arbitrary number of non-commuting variables, and provides various methods to implement elmentary algebraic and other manipulations.

Version:
$Id: NCseries.java,v 1.2 1999/02/12 20:40:26 djun Exp djun $

Variable Index

o DefaultTruncDegree
o numvars
The number of variables involved in this series.

Constructor Index

o NCseries(Vector)
Creates a new Non-commutative Power Series in the given variables.

Method Index

o addTerm(Term)
Adds a term to this NCseries.
o collect()
Collects like terms in this NCseries.
o compare(NCseries, NCseries)
Compares two NCseries: returns $-1$ if the first is $<$ the second, 0 if they're equal, and 1 if the first is $>$ the second.
o compare_to(NCseries)
Compares this NCseries with the given NCseries: returns $-1$ if this is < the given NCseries, 0 if they're equal, and 1 if this > the given NCseries.
o divided_by(NCseries)
Returns the result of dividing this NCseries by the given NCseries.
o getLength()
Gets the length (number of terms) of this NCseries.
o getTruncDeg()
Gets the truncation degree of this NCseries.
o getVariableOrder()
Returns the variable order of this NCseries, as a vector.
o Identity(Vector)
Returns an NCseries with the given variable order, representing the identity series.
o insertTerm(Term)
Inserts the given Term into this NCseries in proper order.
o invert(NCseries)
Returns the result of inverting the given NCseries.
o minus(NCseries)
Returns the result of subtracting a given series from this NCseries.
o plus(NCseries)
Returns the result of adding ps to this NCseries.
o setTruncDeg(int)
Sets the truncation degree of this NCseries.
o sort()
Sorts the terms of this NCseries into ascending order, first by total degree of the terms, then by lexicographic order, based on the given order of variables.
o times(NCseries)
Returns the product of this NCseries times the given NCseries.
o toMagnus(Vector, intArray)
Returns the non-commutative power series (with variable order given by vars) giving the Magnus representation of word in the free group.
o toString()
Formats this NCseries as a string and returns the result.
o trunc(int)
Returns the result of truncating this NCseries after terms of total degree deg.

Variables

o DefaultTruncDegree 
 public static final int DefaultTruncDegree
o numvars 
 public int numvars
The number of variables involved in this series.

Constructors

o NCseries 
 public NCseries(Vector variables) throws VariableOrderException
Creates a new Non-commutative Power Series in the given variables. The variables should be in the form of a vector of $N$ contiguous integers between one and $N$. The variables will be ordered in ascending order according to the order in which they are given. For example, the input 4/3/1/2 corresponds to an ordering $X_4 < X_3 < X_1 < X_2$.

Throws: VariableOrderException
Thrown whenever the variables given are not in the form of a vector of $N$ contiguous integers between one and $N$.

Methods

o getVariableOrder 
 public Vector getVariableOrder()
Returns the variable order of this NCseries, as a vector.

o addTerm 
 public void addTerm(Term term)
Adds a term to this NCseries.

o plus 
 public NCseries plus(NCseries ps)
Returns the result of adding ps to this NCseries.

Parameters:
$ps$ - must have the same variables and order as this series
o minus 
 public NCseries minus(NCseries ps)
Returns the result of subtracting a given series from this NCseries.

Parameters:
$ps$ - must have the same variables and order as this NCseries.
o divided_by 
 public NCseries divided_by(NCseries ps2)
Returns the result of dividing this NCseries by the given NCseries.

Parameters:
$ps2$ - must have the same variables and order as this series.
o times 
 public NCseries times(NCseries ps2)
Returns the product of this NCseries times the given NCseries.

Parameters:
$ps2$ - must have the same variables and order as this NCseries
o getLength 
 public int getLength()
Gets the length (number of terms) of this NCseries.

o getTruncDeg 
 public int getTruncDeg()
Gets the truncation degree of this NCseries.

o setTruncDeg 
 public void setTruncDeg(int truncDeg)
Sets the truncation degree of this NCseries.

o trunc 
 public NCseries trunc(int deg)
Returns the result of truncating this NCseries after terms of total degree deg. Assumes this NCseries is sorted.

o insertTerm 
 public void insertTerm(Term t)
Inserts the given Term into this NCseries in proper order. Assumes that this NCseries is sorted.

o compare_to 
 public int compare_to(NCseries ps)
Compares this NCseries with the given NCseries: returns $-1$ if this is < the given NCseries, 0 if they're equal, and 1 if this > the given NCseries.

o sort 
 public void sort()
Sorts the terms of this NCseries into ascending order, first by total degree of the terms, then by lexicographic order, based on the given order of variables.

o collect 
 public void collect()
Collects like terms in this NCseries.

o toString 
 public String toString()
Formats this NCseries as a string and returns the result.

Overrides:
toString in class Object
o toMagnus 
 public static NCseries toMagnus(Vector vars,
                                 intArray word)
Returns the non-commutative power series (with variable order given by vars) giving the Magnus representation of word in the free group.

o compare 
 public static int compare(NCseries ps1,
                           NCseries ps2)
Compares two NCseries: returns $-1$ if the first is $<$ the second, 0 if they're equal, and 1 if the first is $>$ the second.

o invert 
 public static NCseries invert(NCseries ps)
Returns the result of inverting the given NCseries.

o Identity 
 public static NCseries Identity(Vector variables)
Returns an NCseries with the given variable order, representing the identity series. 

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