Package cc.redberry.rings.poly

Class AlgebraicNumberField<E extends IUnivariatePolynomial<E>>

java.lang.Object

cc.redberry.rings.ARing<E>

cc.redberry.rings.poly.SimpleFieldExtension<E>

cc.redberry.rings.poly.AlgebraicNumberField<E>

All Implemented Interfaces:

IParser<E>, Stringifiable<E>, IPolynomialRing<E>, Ring<E>, Serializable, Iterable<E>, Comparator<E>

public class AlgebraicNumberField<E extends IUnivariatePolynomial<E>>
extends SimpleFieldExtension<E>

Algebraic number field F(α) represented as a simple field extension, for details see SimpleFieldExtension.

Since:

2.5

See Also:

SimpleFieldExtension, FiniteField, Rings.AlgebraicNumberField(IUnivariatePolynomial), Serialized Form

Constructor Summary

Constructors

Constructor	Description
AlgebraicNumberField(E minimalPoly)	Constructs a simple field extension F(α) generated by the algebraic number α with the specified minimal polynomial.

Method Summary

Modifier and Type	Method	Description
E[]	divideAndRemainder(E a, E b)	Returns quotient and remainder of dividend / divider
E	gcd(E a, E b)	Returns the greatest common divisor of two elements
boolean	isField()	Returns whether this ring is a field
boolean	isUnit(E element)	Tests whether specified element is a ring unit
Iterator<E>	iterator()	Returns iterator over ring elements (for finite rings, otherwise throws exception)
E	normalizer(E element)	Gives an element C(element) of this field extension with the property that element * C(element) is in the base field.
E	remainder(E dividend, E divider)	Returns the remainder of dividend / divider

Methods inherited from class cc.redberry.rings.poly.SimpleFieldExtension

add, addMutable, asMultipleExtension, cardinality, characteristic, compare, conjugatesProduct, copy, createArray, createArray2d, createArray2d, degree, equals, factor, factory, generator, getMinimalPolynomial, getMinimalPolynomialRef, getOne, getZero, hashCode, isEuclideanRing, isInTheBaseField, isOne, isZero, minimalPolynomial, multiply, multiplyMutable, negate, negateMutable, norm, normOfPolynomial, normOfPolynomial, nVariables, parse, randomElement, reciprocal, shouldReduceFast, subtract, subtractMutable, toString, toString, toString, trace, valueOf, valueOf, valueOfBigInteger, variable

Methods inherited from class cc.redberry.rings.ARing

isPerfectPower, perfectPowerBase, perfectPowerExponent

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.util.Comparator

reversed, thenComparing, thenComparing, thenComparing, thenComparingDouble, thenComparingInt, thenComparingLong

Methods inherited from interface cc.redberry.rings.poly.IPolynomialRing

mkCoder, parse, signum

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface cc.redberry.rings.Ring

abs, add, createArray, createArray, createArray, createZeroesArray, createZeroesArray2d, decrement, divideExact, divideExactMutable, divideOrNull, extendedGCD, factorial, factorSquareFree, fillZeros, firstBezoutCoefficient, gcd, gcd, getNegativeOne, increment, isFinite, isFiniteField, isMinusOne, isPerfectPower, isUnitOrZero, lcm, lcm, lcm, max, min, multiply, multiply, multiply, perfectPowerBase, perfectPowerExponent, pow, pow, pow, quotient, randomElement, randomElementTree, randomElementTree, randomNonZeroElement, setToValueOf, valueOf

Constructor Detail

AlgebraicNumberField

public AlgebraicNumberField(E minimalPoly)

Constructs a simple field extension F(α) generated by the algebraic number α with the specified minimal polynomial.

NOTE: irreducibility test for the minimal polynomial is not performed here, use IrreduciblePolynomials.irreducibleQ(IUnivariatePolynomial) to test irreducibility.

Parameters:

minimalPoly - the minimal polynomial

Method Detail

isField

public boolean isField()

Description copied from interface: Ring

Returns whether this ring is a field

Returns:

whether this ring is a field

isUnit

public boolean isUnit(E element)

Description copied from interface: Ring

Tests whether specified element is a ring unit

Parameters:

element - the ring element

Returns:

whether specified element is a ring unit

See Also:

Ring.isOne(Object)

gcd

public E gcd(E a,
             E b)

Description copied from interface: Ring

Returns the greatest common divisor of two elements

Parameters:

a - the first element

b - the second element

Returns:

gcd

divideAndRemainder

public E[] divideAndRemainder(E a,
                              E b)

Description copied from interface: Ring

Returns quotient and remainder of dividend / divider

Parameters:

a - the dividend

b - the divider

Returns:

{quotient, remainder}

remainder

public E remainder(E dividend,
                   E divider)

Description copied from interface: Ring

Returns the remainder of dividend / divider

Parameters:

dividend - the dividend

divider - the divider

Returns:

the remainder of dividend / divider

normalizer

public E normalizer(E element)

Gives an element C(element) of this field extension with the property that element * C(element) is in the base field.

iterator

public Iterator<E> iterator()

Description copied from interface: Ring

Returns iterator over ring elements (for finite rings, otherwise throws exception)