GCDRing

GCDRing implements a GCD ring.

For two elements x and y in a GCD ring, we can choose two elements d and m such that:

d = gcd(x, y) m = lcm(x, y)

d * m = x * y

Additionally, we require:

gcd(0, 0) = 0 lcm(x, 0) = lcm(0, x) = 0

and commutativity:

gcd(x, y) = gcd(y, x) lcm(x, y) = lcm(y, x)

Linear Supertypes

CommutativeRing[A], CommutativeRng[A], CommutativeRig[A], MultiplicativeCommutativeMonoid[A], CommutativeSemiring[A], MultiplicativeCommutativeSemigroup[A], algebra.ring.Ring[A], algebra.ring.Rng[A], AdditiveCommutativeGroup[A], algebra.ring.AdditiveGroup[A], algebra.ring.Rig[A], algebra.ring.MultiplicativeMonoid[A], algebra.ring.Semiring[A], algebra.ring.MultiplicativeSemigroup[A], AdditiveCommutativeMonoid[A], AdditiveCommutativeSemigroup[A], algebra.ring.AdditiveMonoid[A], algebra.ring.AdditiveSemigroup[A], Serializable, Serializable, Any

Abstract Value Members

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

Definition Classes
Any
abstract def lcm(a: A, b: A)(implicit ev: Eq[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 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: CommutativeGroup[A]

Definition Classes
AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
final def asInstanceOf[T0]: T0

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

Definition Classes
Any
def fromBigInt(n: BigInt): A

Definition Classes
Ring
def fromInt(n: Int): A

Definition Classes
Ring
def hashCode(): Int

Definition Classes
Any
final def isInstanceOf[T0]: Boolean

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

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

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

Definition Classes
AdditiveGroup
def multiplicative: CommutativeMonoid[A]

Definition Classes
MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup
def positivePow(a: A, n: Int): A

Attributes
protected[this]
Definition Classes
MultiplicativeSemigroup
def positiveSumN(a: A, n: Int): A

Attributes
protected[this]
Definition Classes
AdditiveSemigroup
def pow(a: A, n: Int): A

Definition Classes
MultiplicativeMonoid → MultiplicativeSemigroup
def product(as: TraversableOnce[A]): A

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

Definition Classes
AdditiveMonoid
def sumN(a: A, n: Int): A

Definition Classes
AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
def toString(): String

Definition Classes
Any
def tryProduct(as: TraversableOnce[A]): Option[A]

Definition Classes
MultiplicativeMonoid → MultiplicativeSemigroup
def trySum(as: TraversableOnce[A]): Option[A]

Definition Classes
AdditiveMonoid → AdditiveSemigroup

Inherited from CommutativeRing[A]

Inherited from CommutativeRng[A]

Inherited from CommutativeRig[A]

Related Docs: object GCDRing | package algebra

trait GCDRing[A] extends CRing[A]

Abstract Value Members

abstract def gcd(a: A, b: A)(implicit ev: Eq[A]): A

abstract def getClass(): Class[_]

abstract def lcm(a: A, b: A)(implicit ev: Eq[A]): A

abstract def negate(x: A): A

abstract def one: A

abstract def plus(x: A, y: 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: CommutativeGroup[A]

final def asInstanceOf[T0]: T0

def equals(arg0: Any): Boolean

def fromBigInt(n: BigInt): A

def fromInt(n: Int): A

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

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

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

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

def multiplicative: CommutativeMonoid[A]

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

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

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

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

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

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

def toString(): String

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

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

Inherited from CommutativeRing[A]

Inherited from CommutativeRng[A]

Inherited from CommutativeRig[A]

Inherited from MultiplicativeCommutativeMonoid[A]

Inherited from CommutativeSemiring[A]

Inherited from MultiplicativeCommutativeSemigroup[A]

Inherited from algebra.ring.Ring[A]

Inherited from algebra.ring.Rng[A]

Inherited from AdditiveCommutativeGroup[A]

Inherited from algebra.ring.AdditiveGroup[A]

Inherited from algebra.ring.Rig[A]

Inherited from algebra.ring.MultiplicativeMonoid[A]

Inherited from algebra.ring.Semiring[A]

Inherited from algebra.ring.MultiplicativeSemigroup[A]

Inherited from AdditiveCommutativeMonoid[A]

Inherited from AdditiveCommutativeSemigroup[A]

Inherited from algebra.ring.AdditiveMonoid[A]

Inherited from algebra.ring.AdditiveSemigroup[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped