EuclideanRing

Abstract Value Members

abstract def gcd(a: A, b: A): A
abstract def getClass(): Class[_]

Definition Classes
Any
abstract def mod(a: A, b: A): A
abstract def negate(x: A): A

Definition Classes
AdditiveGroup
abstract def one: A

Definition Classes
MultiplicativeMonoid
abstract def plus(x: A, y: A): A

Definition Classes
AdditiveSemigroup
abstract def quot(a: A, b: A): A
abstract def times(x: A, y: A): A

Definition Classes
MultiplicativeSemigroup
abstract def zero: A

Definition Classes
AdditiveMonoid

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
Any
final def ##(): Int

Definition Classes
Any
final def ==(arg0: Any): Boolean

Definition Classes
Any
def additive: AbGroup[A]

Definition Classes
AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
final def asInstanceOf[T0]: T0

Definition Classes
Any
def equals(arg0: Any): Boolean

Definition Classes
Any
final def euclid(a: A, b: A)(implicit eq: Eq[A]): A

Attributes
protected[this]
Annotations
@tailrec()
def fromInt(n: Int): A

Defined to be equivalent to additive.sumn(one, n).
Defined to be equivalent to additive.sumn(one, n). That is, n repeated summations of this ring's one, or -one if n is negative.

Definition Classes
Ring
def hashCode(): Int

Definition Classes
Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isOne(a: A)(implicit ev: Eq[A]): Boolean

Definition Classes
MultiplicativeMonoid
def isZero(a: A)(implicit ev: Eq[A]): Boolean

Tests if a is zero.
Tests if a is zero.

Definition Classes
AdditiveMonoid
def lcm(a: A, b: A): A
def minus(x: A, y: A): A

Definition Classes
AdditiveGroup
def multiplicative: CMonoid[A]

Definition Classes
MultiplicativeCMonoid → MultiplicativeCSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup
def pow(a: A, n: Int): A

This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.
This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

Definition Classes
Rig → Semiring
def prod(as: TraversableOnce[A]): A

Given a sequence of as, sum them using the monoid and return the total.
Given a sequence of as, sum them using the monoid and return the total.

Definition Classes
MultiplicativeMonoid
def prodOption(as: TraversableOnce[A]): Option[A]

Given a sequence of as, sum them using the semigroup and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
If the sequence is empty, returns None. Otherwise, returns Some(total).

Definition Classes
MultiplicativeSemigroup
def prodn(a: A, n: Int): A

Return a multiplied with itself n times.
Return a multiplied with itself n times.

Definition Classes
MultiplicativeMonoid → MultiplicativeSemigroup
def prodnAboveOne(a: A, n: Int): A

Attributes
protected
Definition Classes
MultiplicativeSemigroup
def quotmod(a: A, b: A): (A, A)
def sum(as: TraversableOnce[A]): A

Given a sequence of as, sum them using the monoid and return the total.
Given a sequence of as, sum them using the monoid and return the total.

Definition Classes
AdditiveMonoid
def sumOption(as: TraversableOnce[A]): Option[A]

Given a sequence of as, sum them using the semigroup and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
If the sequence is empty, returns None. Otherwise, returns Some(total).

Definition Classes
AdditiveSemigroup
def sumn(a: A, n: Int): A

Return a added with itself n times.
Return a added with itself n times.

Definition Classes
AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
def sumnAboveOne(a: A, n: Int): A

Attributes
protected
Definition Classes
AdditiveSemigroup
def toString(): String

Definition Classes
Any

Related Docs: object EuclideanRing | package algebra

trait EuclideanRing[A] extends CRing[A]

Abstract Value Members

abstract def gcd(a: A, b: A): A

abstract def getClass(): Class[_]

abstract def mod(a: A, b: A): A

abstract def negate(x: A): A

abstract def one: A

abstract def plus(x: A, y: A): A

abstract def quot(a: A, b: A): A

abstract def times(x: A, y: A): A

abstract def zero: A

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

def additive: AbGroup[A]

final def asInstanceOf[T0]: T0

def equals(arg0: Any): Boolean

final def euclid(a: A, b: A)(implicit eq: Eq[A]): A

def fromInt(n: Int): A

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def isOne(a: A)(implicit ev: Eq[A]): Boolean

def isZero(a: A)(implicit ev: Eq[A]): Boolean

def lcm(a: A, b: A): A

def minus(x: A, y: A): A

def multiplicative: CMonoid[A]

def pow(a: A, n: Int): A

def prod(as: TraversableOnce[A]): A

def prodOption(as: TraversableOnce[A]): Option[A]

def prodn(a: A, n: Int): A

def prodnAboveOne(a: A, n: Int): A

def quotmod(a: A, b: A): (A, A)

def sum(as: TraversableOnce[A]): A

def sumOption(as: TraversableOnce[A]): Option[A]

def sumn(a: A, n: Int): A

def sumnAboveOne(a: A, n: Int): A

def toString(): String

Inherited from CRing[A]

Inherited from MultiplicativeCMonoid[A]

Inherited from MultiplicativeCSemigroup[A]

Inherited from Ring[A]

Inherited from Rng[A]

Inherited from AdditiveAbGroup[A]

Inherited from AdditiveCMonoid[A]

Inherited from AdditiveCSemigroup[A]

Inherited from AdditiveGroup[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Any

Ungrouped