com.perisic.ring
Class CyclotomicField

java.lang.Object
  com.perisic.ring.Ring
      com.perisic.ring.ModularRing
          com.perisic.ring.CyclotomicField

public class CyclotomicField
extends ModularRing

This class implements a cyclotomic field.

• Last Change: 20.01.2003, Mapping from cyclotomic field to cyclotomic field added.
• Last Change: 13.12.2003: GPL.
• Copyright: (c) Marc Conrad, 2002, 2003
• Email: ring@perisic.com. Please let me know if you use this software.
• WWW: www.ring.perisic.com
• The com.perisic.ring library is distributed under the terms of the GNU Lesser General Public License (LGPL).
• If you require the package under a different licence please contact me.
• disclaimer: The classes are provided "as is". There is no warranty implied by using the com.perisic.ring package.

Field Summary

Fields inherited from class com.perisic.ring.Ring

C, F2, Q, R, Z

Constructor Summary

CyclotomicField(int n, java.lang.String variable)
Constructs the algebraic number field which contains all nth roots of unity.

Method Summary

static RingElt	getCyclotomicPolynomial(Ring F, int n, java.lang.String variable) Constructs the n-th cyclotomic polynomial over the ring F as a polynomial in the variable variable.
int	getN() returns the n if this is the nth cyclotomic field
boolean	isField() returns true.
static void	main(java.lang.String[] args) A very simple tester for this class.
RingElt	map(RingElt a) If the ring of the argument is of a dth cyclotomic field and d a divisor of n we embed via the mapping zd -> znn/d where zn denotes a fixed nth root of unity.
java.lang.String	toString() returns CYC(n).

Methods inherited from class com.perisic.ring.ModularRing

add, displayMod, eltToString, equalZero, getHideMod, getModulus, getValue, hideMod, inv, map, mult, neg, one, setHideMod, zero

Methods inherited from class com.perisic.ring.Ring

div, ediv, equal, evaluatePolynomial, gcd, isEuclidian, isUFD, map, map, map, mod, pow, pow, sub, tdiv

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

CyclotomicField

public CyclotomicField(int n,
                       java.lang.String variable)

Constructs the algebraic number field which contains all nth roots of unity.

Method Detail

isField

public boolean isField()

returns true.

Overrides:

isField in class Ring

getN

public int getN()

returns the n if this is the nth cyclotomic field

toString

public java.lang.String toString()

returns CYC(n).

Overrides:

toString in class java.lang.Object

getCyclotomicPolynomial

public static RingElt getCyclotomicPolynomial(Ring F,
                                              int n,
                                              java.lang.String variable)

Constructs the n-th cyclotomic polynomial over the ring F as a polynomial in the variable variable.

map

public RingElt map(RingElt a)

If the ring of the argument is of a dth cyclotomic field and d a divisor of n we embed via the mapping z_d -> z_n^n/d where z_n denotes a fixed nth root of unity.
If the ring is not a cycltomic field the map() method of the parent class is invoked.

Overrides:

map in class ModularRing

main

public static void main(java.lang.String[] args)

A very simple tester for this class.