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

The same as bindSymbolOrNull but throws an error if symbol could not be bound

bindSymbolOrNull

common

open fun bindSymbolOrNull(value: String): T?

Wraps a raw string to T object.

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.

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 a unary operation with the certain name.

unaryOperationFunction

common

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

Dynamically dispatches a unary operation with the certain name.

unaryPlus

common

open operator fun T.unaryPlus(): T

Returns this value.

Properties

one

common

abstract val one: T

The neutral element of multiplication

zero

common

abstract val zero: T

The neutral element of addition.

Inheritors

FunctionalExpressionRing

MstRing

RingND

Field

NumbersAddOperations

IntRing

ShortRing

ByteRing

LongRing

JBigIntegerField

Extensions

abs

common

fun <T : Comparable<T>> Ring<T>.abs(value: T): T

Absolute of the comparable value

power

common

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

Raises arg to the non-negative integer power exponent.

sum

common

fun <T> Ring<T>.sum(data: Iterable<T>): T

Returns the sum of all elements in the iterable in this Ring.

fun <T> Ring<T>.sum(data: Sequence<T>): T

Returns the sum of all elements in the sequence in this Ring.

Sources

common source