Ring

interface Ring<T> : Group<T> , RingOperations<T>

Represents ring, i.e. algebraic structure with two associative binary operations called "addition" and "multiplication" and their neutral elements.

Parameters

the type of element of this ring.

Functions

add

common

abstract fun add(a: T, b: T): T

Addition of two elements.

binaryOperation

common

open fun binaryOperation(operation: String, left: T, right: T): T

Dynamically invokes a binary operation with the certain name.

binaryOperationFunction

common

open override fun binaryOperationFunction(operation: String): (T, T) -> T

Dynamically dispatches a binary operation with the certain name.

bindSymbol

common

open fun bindSymbol(value: String): T

Wraps a raw string to T object.

equals

common

open operator fun equals(other: Any?): Boolean

hashCode

common

open fun hashCode(): Int

minus

common

open operator fun T.minus(b: T): T

Subtraction of two elements.

multiply

common

abstract fun multiply(a: T, b: T): T

Multiplies two elements.

plus

common

open operator fun T.plus(b: T): T

Addition of two elements.

times

common

open operator fun T.times(b: T): T

Multiplies this element by scalar.

toString

common

open fun toString(): String

unaryMinus

common

abstract operator fun T.unaryMinus(): T

The negation of this element.

unaryOperation

common

open fun unaryOperation(operation: String, arg: T): T

Dynamically invokes an unary operation with the certain name.

unaryOperationFunction

common

open override fun unaryOperationFunction(operation: String): (T) -> T

Dynamically dispatches an unary operation with the certain name.

unaryPlus

common

open operator fun T.unaryPlus(): T

Returns this value.

Properties

one

common

abstract val one: T

neutral operation for multiplication

zero

common

abstract val zero: T

The neutral element of addition.

Inheritors

FunctionalExpressionRing

NDRing

Field

IntRing

ShortRing

ByteRing

LongRing

JBigIntegerField

Extensions

power

common

fun <T> Ring<T>.power(arg: T, power: Int): T

Raises arg to the natural power power.

ringExpression

common

inline fun <T> Ring<T>.ringExpression(block: FunctionalExpressionRing<T, Ring<T>>.() -> Expression<T>): Expression<T>

Creates a functional expression with this Ring.