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java.lang.Object com.perisic.ring.Ring com.perisic.ring.ModularRing com.perisic.ring.CyclotomicField
public class CyclotomicField
This class implements a cyclotomic field.
Field Summary |
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Fields inherited from class com.perisic.ring.Ring |
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C, F2, Q, R, Z |
Constructor Summary | |
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CyclotomicField(int n,
java.lang.String variable)
Constructs the algebraic number field which contains all n th
roots of unity. |
Method Summary | |
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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 |
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add, displayMod, eltToString, equalZero, getHideMod, getModulus, getValue, hideMod, inv, map, mult, neg, one, setHideMod, zero |
Methods inherited from class com.perisic.ring.Ring |
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div, ediv, equal, evaluatePolynomial, gcd, isEuclidian, isUFD, map, map, map, mod, pow, pow, sub, tdiv |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
Constructor Detail |
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public CyclotomicField(int n, java.lang.String variable)
n
th
roots of unity.
Method Detail |
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public boolean isField()
isField
in class Ring
public int getN()
public java.lang.String toString()
toString
in class java.lang.Object
public static RingElt getCyclotomicPolynomial(Ring F, int n, java.lang.String variable)
n
-th cyclotomic polynomial over the ring F as a
polynomial in the variable variable
.
public RingElt map(RingElt a)
map
in class ModularRing
public static void main(java.lang.String[] args)
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