Package dk.jonaslindstrom.ruffini.common.abstractions

Interface Semigroup<E>

Type Parameters:

E - Element type.

All Superinterfaces:

Set<E>

All Known Subinterfaces:

EuclideanDomain<E>, Field<E>, Group<E>, Monoid<E>, Ring<E>, SemiRing<E>

All Known Implementing Classes:

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

public interface Semigroup<E>
extends Set<E>

A semigroup is a set with an associative multiplication operation.

Method Summary

Modifier and Type	Method	Description
E	multiply(E a, E b)	Return the result of the product ab in this group.
default E	multiply(E a, E b, E c)	Return the result of the product abc in this group.
default E	multiply(E a, E b, E c, E d)	Return the result of the product abcd in this group.

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

equals, toString

Method Details

multiply

E multiply(E a,
 E b)

Return the result of the product ab in this group.

multiply

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

Return the result of the product abc in this group.

multiply

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

Return the result of the product abcd in this group.