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:

AbelianGroupI, GroupI, RingI

Direct Known Subclasses:

AlgebraicExtension

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

protected RingI	baseRing
protected Complex	rootVal
protected java.lang.String	symbol
protected FreeGroupElement	tPoly
protected FreeGroupElement	unitPoly
protected FreeGroupElement	zeroPoly

Constructor Summary

FreeGroup(RingI K, java.lang.String symbol)
Create the ring K(t) where t is a solution of the monic polynomial p.

Method Summary

java.lang.Number	add(java.lang.Number a, java.lang.Number b) Get sum of the numbers
void	addStandardConstants(JEP j) adds the standard constants for this group
boolean	equals(java.lang.Number a, java.lang.Number b) whether two numbers are equal
RingI	getBaseRing() Returns the base ring of this extension.
java.lang.Number	getInverse(java.lang.Number a) Get Inverse of a number
java.lang.Number	getONE() Get multiplicative identity i.e. 1.
Complex	getRootVal() Returns an aproximation to the value of the root as a complex number.
java.lang.String	getSymbol() Returns the symbol used to denote the generator.
java.lang.Number	getZERO() Returns the identity element under +
java.lang.Number	mul(java.lang.Number a, java.lang.Number b) Returns the product of two numbers, a*b
void	setRootVal(Complex complex) Sets the value used to aproximate the root as a complex number.
java.lang.Number	sub(java.lang.Number a, java.lang.Number b) Get the difference of the numbers.
java.lang.String	toString()
java.lang.Number	valueOf(java.lang.Number[] coeffs)
java.lang.Number	valueOf(java.lang.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 java.lang.String symbol

rootVal

protected Complex rootVal

Constructor Detail

FreeGroup

public FreeGroup(RingI K,
                 java.lang.String symbol)

Create the ring K(t) where t is a solution of the monic polynomial p.

Throws:

java.lang.IllegalArgumentException - if the base ring of the poly is not the same.

java.lang.IllegalArgumentException - if the polynomial is not monic.

Method Detail

add

public java.lang.Number add(java.lang.Number a,
                            java.lang.Number b)

Description copied from interface: GroupI

Get sum of the numbers

Specified by:

add in interface GroupI

sub

public java.lang.Number sub(java.lang.Number a,
                            java.lang.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 java.lang.Number mul(java.lang.Number a,
                            java.lang.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(java.lang.Number a,
                      java.lang.Number b)

Description copied from interface: GroupI

whether two numbers are equal

Specified by:

equals in interface GroupI

valueOf

public java.lang.Number valueOf(java.lang.String s)

Description copied from interface: GroupI

returns number given by the string

Specified by:

valueOf in interface GroupI

valueOf

public java.lang.Number valueOf(java.lang.Number[] coeffs)

getZERO

public java.lang.Number getZERO()

Description copied from interface: GroupI

Returns the identity element under +

Specified by:

getZERO in interface GroupI

getONE

public java.lang.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

getInverse

public java.lang.Number getInverse(java.lang.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 interface: GroupI

adds the standard constants for this group

Specified by:

addStandardConstants in interface GroupI

Overrides:

addStandardConstants in class Group

toString

public java.lang.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 aproximate the root as a complex number.

getRootVal

public Complex getRootVal()

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

getSymbol

public java.lang.String getSymbol()

Returns the symbol used to denote the generator.