0.0.0-experiment

kone.algebraic/dev.lounres.kone.algebraic/ExtendedSemiring

ExtendedSemiring

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

Describes a context that represents "extended" mathematical commutative semiring. It means that it provides operations like +, *, power, and some other that satisfy axioms of semiring like a + b == b + a or a * (b * c) == (a * b) * c.

Warning! Aside from Semiring's operations it also provides partially defined binary - operation. That's why it is "extended" Semiring. This interface is made only to remove duplication of bridge contextual functions for contexts like UIntContext and ULongContext. For the same reason Ring does not inherit this interface. Thus, it should not be used in algorithms.

Usual structures like integers or real numbers satisfy the axioms (one says that they form commutative rings), so you don't need to worry about fully understanding the concept of commutative ring. It won't be true only the moment you introduce such structures as a semiring of matrices 2⨯2 with usual operations you learn on any course of linear algebra.

Obviously, the Semiring interface extends the Equality interface because otherwise there is no understanding of the mathematical operations.

Inheritors

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 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.minus(other: Number): Number

Subtracts this and the other numbers in terms of the Ring.

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

Subtracts this number and the other integer as elements of the ExtendedSemiring.

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

Subtracts this number and the other integer as elements of the Ring.

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

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

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

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.

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.