com.perisic.ring
Class UniversalCyclotomicField

java.lang.Object
  |
  +--com.perisic.ring.Ring
        |
        +--com.perisic.ring.UniversalRing
              |
              +--com.perisic.ring.UniversalCyclotomicField

public class UniversalCyclotomicField

extends UniversalRing

The infinite algebraic extension of Q which contains all unit roots.

• Last Change: 13.12.2003: GPL MC.
• 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.

Fields inherited from class com.perisic.ring.Ring

C, F2, Q, R, Z

Constructor Summary

UniversalCyclotomicField(java.lang.String unitRootPrefix)
Construct the universal cyclotomic field by the prefix for the variable.

Method Summary

Ring	findRing() A suitable ring able to map 0 (and 1).
Ring	findRing(RingElt a) Returns the ring of the argument a if this a Cyclotomic field or Q.
Ring	findRing(RingElt a, RingElt b) Returns cyaclotomic field which contains both a and b.
boolean	isField() returns true, as this is a field.
static void	main(java.lang.String[] args) This is for testing this class only.
RingElt	map(int n, java.lang.String str) maps the string str into the n-th cyclotomic field
RingElt	map(RingElt r) The following Rings are mapped: Cyclotomic fields, where the variable is of the form z* where z ist the preifx of the variable and * is a number; Polynomial rings and Quotient fields over Polynomial rings where the variables are of the form z*; the usual suspects (Z, Q).
RingElt	map(java.lang.String str) Strings denoting Rational functions (elements of Quotient fields of Polynomial rings) over variables of the form z* where z ist the preifx of the variable and * is a number; are mapped.
java.lang.String	toString()

Methods inherited from class com.perisic.ring.UniversalRing

add, ediv, equalZero, gcd, inv, mod, mult, neg, one, tdiv, zero

Methods inherited from class com.perisic.ring.Ring

div, eltToString, equal, evaluatePolynomial, isEuclidian, isUFD, map, map, map, pow, pow, sub

Methods inherited from class java.lang.Object

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

Constructor Detail

UniversalCyclotomicField

public UniversalCyclotomicField(java.lang.String unitRootPrefix)

Construct the universal cyclotomic field by the prefix for the variable. That means, when the parameter is "z" the unit roots are denoted as z3, z5, z15, z24, etc. meaning a primitive third, fifth, 15th, 24th, etc. unit root. The relationship between the unitroots is zn^n/d=zd.

Method Detail

isField

public boolean isField()

returns true, as this is a field.

Overrides:

isField in class Ring

toString

public java.lang.String toString()

Overrides:

toString in class UniversalRing

Returns:

"CYC(z*)" where R is the coefficient ring and z the prefix of the variable.

map

public RingElt map(int n,
                   java.lang.String str)

maps the string str into the n-th cyclotomic field

map

public RingElt map(RingElt r)

The following Rings are mapped: Cyclotomic fields, where the variable is of the form z* where z ist the preifx of the variable and * is a number; Polynomial rings and Quotient fields over Polynomial rings where the variables are of the form z*; the usual suspects (Z, Q).

Overrides:

map in class UniversalRing

map

public RingElt map(java.lang.String str)

Strings denoting Rational functions (elements of Quotient fields of Polynomial rings) over variables of the form z* where z ist the preifx of the variable and * is a number; are mapped.

Overrides:

map in class UniversalRing

findRing

public Ring findRing()

Description copied from class: UniversalRing

A suitable ring able to map 0 (and 1).

Overrides:

findRing in class UniversalRing

Returns:

the rational numbers.

findRing

public Ring findRing(RingElt a)

Returns the ring of the argument a if this a Cyclotomic field or Q. Otherwise a RingException is thrown.

Overrides:

findRing in class UniversalRing

Throws:

RingException -

findRing

public Ring findRing(RingElt a,
                     RingElt b)

Returns cyaclotomic field which contains both a and b. If a is a ring of the n-th cyclotomic field and b of the m-th cyclotomic field, then the k-th cyclotomic field with k = lcm(n,m) (least common multiple) is returned.

Overrides:

findRing in class UniversalRing

main

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

This is for testing this class only.