AlgebraicExtension

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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.

See Also:

AlgebraicExtensionElement

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

All Methods Instance Methods Concrete Methods
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
equals, 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

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Jas4pp 1.5 © Java Analysis Studio for Particle Physics