org.lsmp.djep.groupJep.groups

Class AlgebraicExtension

java.lang.Object

org.lsmp.djep.groupJep.groups.Group

org.lsmp.djep.groupJep.groups.FreeGroup

org.lsmp.djep.groupJep.groups.ExtendedFreeGroup

org.lsmp.djep.groupJep.groups.AlgebraicExtension

All Implemented Interfaces:

GroupI, AbelianGroupI, HasDivI, HasPowerI, RingI

public class AlgebraicExtension
extends ExtendedFreeGroup
implements RingI

An Algebraic Extension of a Ring. The ring generated by {1,t,...,t^n-1} where t is an algebraic number i.e t is be a root of a monic polynomial equation.

Author:

Rich Morris Created on 09-Mar-2004

See Also:

AlgebraicExtensionElement

Field Summary

Fields inherited from class org.lsmp.djep.groupJep.groups.FreeGroup

baseRing, rootVal, symbol, tPoly, unitPoly, zeroPoly

Constructor Summary

Constructors

Constructor and Description
AlgebraicExtension(RingI K, Polynomial poly) Create the ring K(t) where t is a solution of the monic polynomial p.

Method Summary

Modifier and Type	Method and Description
Polynomial	getPoly() Returns the polynomial defining the algebraic number.
Polynomial	getSubsPoly() Returns the polynomial -a_(n-1) t^(n-1) + ...
String	toString()
Number	valueOf(Number[] coeffs)

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

div, pow

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

add, addStandardConstants, equals, getBaseRing, getInverse, getONE, getRootVal, getSymbol, getTPoly, getZERO, isConstantPoly, mul, setRootVal, setRootVal, sub, valueOf

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.interfaces.RingI

getONE, mul

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

add, addStandardConstants, addStandardFunctions, equals, getInverse, getNumberFactory, getZERO, isConstantPoly, sub, valueOf

Constructor Detail

AlgebraicExtension

public AlgebraicExtension(RingI K,
                          Polynomial poly)

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

Parameters:

K - the Ring this is an extension of.

poly - A monic polynomial whose solution gives an algebraic number which is used to generate this group.

Throws:

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

IllegalArgumentException - if the polynomial is not monic.

Method Detail

valueOf

public Number valueOf(Number[] coeffs)

Overrides:

valueOf in class FreeGroup

toString

public String toString()

Overrides:

toString in class FreeGroup

getPoly

public Polynomial getPoly()

Returns the polynomial defining the algebraic number.

getSubsPoly

public Polynomial getSubsPoly()

Returns the polynomial -a_(n-1) t^(n-1) + ... + a_0. This polynomial is used in reducing the equation t^n