Package dk.jonaslindstrom.ruffini.common.abstractions

Interface EuclideanDomain<E>

Type Parameters:

E - Element type.

All Superinterfaces:

AdditiveGroup<E>, CommutativeMonoid<E>, Monoid<E>, Ring<E>, Semigroup<E>, SemiRing<E>, Set<E>

All Known Implementing Classes:

BigIntegers, Integers, MultivariatePolynomialRing, PolynomialRing, PolynomialRingKaratsuba, TestUtils.TestBigIntegers, TestUtils.TestIntegers

public interface EuclideanDomain<E>
extends Ring<E>

A Euclidean domain is a ring with Euclidean division.

Method Summary

Modifier and Type	Method	Description
default E	abs(E a, Comparator<E> ordering)	Return a if a ≥ 0 according to the given ordering, otherwise return -a.
default Pair<E,E>	divide(E a, int b)	Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see norm(E) for this domain.
Pair<E,E>	divide(E a, E b)	Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see norm(E) for this domain.
default E	divideExact(E a, int b)	Compute a/b and throw and exception if the division is not exact.
default E	divideExact(E a, E b)	Compute a/b and throw and exception if the division is not exact.
default boolean	divides(E a, E b)
default E	mod(E a, int m)
default E	mod(E a, E m)
BigInteger	norm(E a)	The euclidean function is a multiplicative map that maps elements of the domain to the integers and is used in the division of divide(E, E).

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.AdditiveGroup

doubling, isZero, negate, scale, scale, subtract, sum

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.CommutativeMonoid

add, add, add, zero

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Monoid

identity, isIdentity, power

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Semigroup

multiply, multiply, multiply

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.SemiRing

integer, multiply, multiply

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Set

equals, toString

Method Details

divide

Pair<E,E> divide(E a,
 E b)

Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see norm(E) for this domain.

divide

default Pair<E,E> divide(E a,
 int b)

Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see norm(E) for this domain.

divideExact

default E divideExact(E a,
 E b)

Compute a/b and throw and exception if the division is not exact.

divideExact

default E divideExact(E a,
 int b)

Compute a/b and throw and exception if the division is not exact.

mod

default E mod(E a,
 E m)

mod

default E mod(E a,
 int m)

abs

default E abs(E a,
 Comparator<E> ordering)

Return a if a ≥ 0 according to the given ordering, otherwise return -a.

norm

BigInteger norm(E a)

The euclidean function is a multiplicative map that maps elements of the domain to the integers and is used in the division of divide(E, E).

divides

default boolean divides(E a,
 E b)