0.0.0-experiment

kone.algebraic/dev.lounres.kone.algebraic/EuclideanSemiring

EuclideanSemiring

interface EuclideanSemiring<Number> : Semiring<Number> (source)

Describes a context that represents Euclidean semiring (i.e. Euclidean ring (a.k.a. Euclidean domain) but without subtraction). It means that it extends Semiring interface, and besides ring's operations also provides Euclidean division (a.k.a. division with remainder) that takes dividend and divisor and returns quotient and remainder, where either remainder is zero or has less Euclidean norm.

Note! Euclidean norm is not provided by the interface. It means that only the Euclidean division operations are provided mentioning that there is some Euclidean norm, so that the operations satisfy conditions on it, but no actual programming representation of the norm is not provided.

Inheritors

Types

class Key<Number>(elementType: SuppliedType<Number>) : RegistryKey<EuclideanSemiring<Number>>

Registry key for EuclideanSemiring interface in KoneContextRegistry.

Properties

abstract val one: Number

Represents a unit element (a.k.a. neutral multiplicative element).

open val UInt.value: Number

Converts instance of UInt to an element of the Semiring it is equal to.

open val ULong.value: Number

Converts instance of Long to an element of the Semiring it is equal to.

abstract val zero: Number

Represents a zero element (a.k.a. neutral additive element).

Functions

open operator fun Number.div(other: Number): Number

Returns quotient of Euclidean division (a.k.a. a division with remainder).

abstract infix fun Number.divrem(other: Number): EuclideanDivisionResult<Number>

Returns result of Euclidean division (a.k.a. a division with remainder), both quotient and remainder.

open infix fun Number.equalsTo(other: Number): Boolean

open fun Number.isNotOne(): Boolean

Checks that this number is not a one in the context of the Semiring.

open fun Number.isNotZero(): Boolean

Checks that this number is not a zero in the context of the Semiring.

open fun Number.isOne(): Boolean

Checks that this number is a one in the context of the Semiring.

open fun Number.isZero(): Boolean

Checks that this number is a zero in the context of the Semiring.

abstract operator fun Number.plus(other: Number): Number

Sums this and the other numbers in terms of the Semiring.

open operator fun Number.plus(other: UInt): Number

open operator fun Number.plus(other: ULong): Number

Sums this number and the other integer as elements of the Semiring.

open operator fun UInt.plus(other: Number): Number

open operator fun ULong.plus(other: Number): Number

Sums this integer and the other number as elements of the Semiring.

open infix fun Number.pow(exponent: UInt): Number

open infix fun Number.pow(exponent: ULong): Number

Raises this number in the power of exponent.

open fun power(base: Number, exponent: UInt): Number

open fun power(base: Number, exponent: ULong): Number

Raises base number in the power of exponent.

open operator fun Number.rem(other: Number): Number

Returns remainder of Euclidean division (a.k.a. a division with remainder).

abstract operator fun Number.times(other: Number): Number

Multiplies this and the other numbers in terms of the Semiring.

open operator fun Number.times(other: UInt): Number

open operator fun Number.times(other: ULong): Number

Multiplies this number and the other integer as elements of the Semiring.

open operator fun UInt.times(other: Number): Number

open operator fun ULong.times(other: Number): Number

Sums this integer and the other number as elements of the Semiring.

open fun valueOf(arg: UInt): Number

Converts instance of UInt to an element of the Semiring it is equal to.

open fun valueOf(arg: ULong): Number

Converts instance of ULong to an element of the Semiring it is equal to.