org.lsmp.djep.groupJep.groups

Class FreeGroup

java.lang.Object

org.lsmp.djep.groupJep.groups.Group

org.lsmp.djep.groupJep.groups.FreeGroup

All Implemented Interfaces:

GroupI, AbelianGroupI, RingI

Direct Known Subclasses:

ExtendedFreeGroup

public class FreeGroup
extends Group
implements RingI

A free group generated by a symbol t.

Author:

Rich Morris Created on 09-Mar-2004

Field Summary

Fields

Modifier and Type	Field and Description
protected RingI	baseRing
protected Complex	rootVal
protected String	symbol
protected FreeGroupElement	tPoly
protected FreeGroupElement	unitPoly
protected FreeGroupElement	zeroPoly

Constructor Summary

Constructors

Constructor and Description
FreeGroup(RingI K, String symbol) Create the ring K(t) where t is a free variable.

Method Summary

Modifier and Type	Method and Description
Number	add(Number a, Number b) Get sum of the numbers
void	addStandardConstants(JEP j) adds the standard constants for this group.
boolean	equals(Number a, Number b) whether two numbers are equal
RingI	getBaseRing() Returns the base ring of this extension.
Number	getInverse(Number a) Get Inverse of a number
Number	getONE() Get multiplicative identity i.e.
Complex	getRootVal() Returns an approximation to the value of the root as a complex number.
String	getSymbol() Returns the symbol used to denote the generator.
Number	getTPoly()
Number	getZERO() Returns the identity element under +
boolean	isConstantPoly(Number poly) Whether the given polynomial is constant.
Number	mul(Number a, Number b) Returns the product of two numbers, a*b
void	setRootVal(Complex complex) Sets the value used to approximate the root as a complex number.
boolean	setRootVal(String sym, Complex val) Sets the root value for given symbol.
Number	sub(Number a, Number b) Get the difference of the numbers.
String	toString()
Number	valueOf(Number[] coeffs)
Number	valueOf(String s) returns number given by the string

Methods inherited from class org.lsmp.djep.groupJep.groups.Group

addStandardFunctions, getNumberFactory

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.lsmp.djep.groupJep.GroupI

addStandardFunctions, getNumberFactory

Field Detail

baseRing

protected RingI baseRing

zeroPoly

protected FreeGroupElement zeroPoly

unitPoly

protected FreeGroupElement unitPoly

tPoly

protected FreeGroupElement tPoly

symbol

protected String symbol

rootVal

protected Complex rootVal

Constructor Detail

FreeGroup

public FreeGroup(RingI K,
                 String symbol)

Create the ring K(t) where t is a free variable.

Parameters:

K - the Ring this is an extension of.

symbol - the name of the free variable.

Method Detail

add

public Number add(Number a,
                  Number b)

Description copied from interface: GroupI

Get sum of the numbers

Specified by:

add in interface GroupI

sub

public Number sub(Number a,
                  Number b)

Description copied from interface: GroupI

Get the difference of the numbers. i.e. a + (-b)

Specified by:

sub in interface GroupI

mul

public Number mul(Number a,
                  Number b)

Description copied from interface: RingI

Returns the product of two numbers, a*b

Specified by:

mul in interface RingI

equals

public boolean equals(Number a,
                      Number b)

Description copied from interface: GroupI

whether two numbers are equal

Specified by:

equals in interface GroupI

valueOf

public Number valueOf(String s)

Description copied from interface: GroupI

returns number given by the string

Specified by:

valueOf in interface GroupI

valueOf

public Number valueOf(Number[] coeffs)

getZERO

public Number getZERO()

Description copied from interface: GroupI

Returns the identity element under +

Specified by:

getZERO in interface GroupI

getONE

public Number getONE()

Description copied from interface: RingI

Get multiplicative identity i.e. 1. Strictly speaking a ring need not have a mul indentity. However most useful ones do, and they are not all integral domains.

Specified by:

getONE in interface RingI

getTPoly

public Number getTPoly()

getInverse

public Number getInverse(Number a)

Description copied from interface: GroupI

Get Inverse of a number

Specified by:

getInverse in interface GroupI

addStandardConstants

public void addStandardConstants(JEP j)

Description copied from class: Group

adds the standard constants for this group. By default does nothing.

Specified by:

addStandardConstants in interface GroupI

Overrides:

addStandardConstants in class Group

toString

public String toString()

Overrides:

toString in class Group

getBaseRing

public RingI getBaseRing()

Returns the base ring of this extension.

setRootVal

public void setRootVal(Complex complex)

Sets the value used to approximate the root as a complex number.

setRootVal

public boolean setRootVal(String sym,
                          Complex val)

Sets the root value for given symbol.

Parameters:

sym - the symbol to set

val - the complex value

Returns:

true is sym is a symbol for either this group or its baseRing or the basrRing's baseRing etc.

getRootVal

public Complex getRootVal()

Returns an approximation to the value of the root as a complex number.

getSymbol

public String getSymbol()

Returns the symbol used to denote the generator.

isConstantPoly

public boolean isConstantPoly(Number poly)

Whether the given polynomial is constant.

Specified by:

isConstantPoly in interface GroupI

Overrides:

isConstantPoly in class Group