Package dk.jonaslindstrom.ruffini.common.abstractions

Interface SemiRing<E>

Type Parameters:

E - Element type.

All Superinterfaces:

CommutativeMonoid<E>, Monoid<E>, Semigroup<E>, Set<E>

All Known Subinterfaces:

EuclideanDomain<E>, Field<E>, Ring<E>

All Known Implementing Classes:

AlgebraicFieldExtension, BigElements, BigFiniteField, BigIntegers, BigIntegersModuloN, BigPrimeField, BigRationals, ComplexNumbers, ConstructiveReals, FieldOfFractions, FiniteField, GaussianRationals, Integers, IntegersModuloN, MatrixRing, MultivariatePolynomialRing, MultivariatePolynomialRingOverRing, NullSafeRing, PerformanceLoggingField, PerformanceLoggingRing, PolynomialRing, PolynomialRingFFT, PolynomialRingKaratsuba, PolynomialRingOverRing, PrimeField, QuadraticField, QuotientRing, Rationals, RealNumbers, TestUtils.TestBigIntegers, TestUtils.TestField, TestUtils.TestIntegers

public interface SemiRing<E>
extends Monoid<E>, CommutativeMonoid<E>

A semiring is a set with an associative and commutative addition operation and an associative multiplication operation. It is not required that each element has an additive inverse.

Method Summary

Modifier and Type	Method	Description
default E	integer(int a)	Return the element in this ring equal to 1 + ⋯ + 1 where 1 is added to it self a times.
default E	multiply(int a, E b)	Return the element in this ring equal to ab.
default E	multiply(int a, E b, E c)	Return the element in this ring equal to abc.

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.Set

equals, toString

Method Details

integer

default E integer(int a)

Return the element in this ring equal to 1 + ⋯ + 1 where 1 is added to it self a times. If this is a ring, a are allowed to be negative, in which case it is equal to the additive inverse of 1 is added to it self -a times

multiply

default E multiply(int a,
 E b)

Return the element in this ring equal to ab.

multiply

default E multiply(int a,
 E b,
 E c)

Return the element in this ring equal to abc.