GCDRing

algebra.ring.GCDRing
See theGCDRing companion object
trait GCDRing[A] extends CommutativeRing[A]

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)

Attributes

Companion:
object
Source:
GCDRing.scala
Graph
Supertypes
Known subtypes

Members list

Concise view

Value members

Abstract methods

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

Attributes

Source:
GCDRing.scala
def lcm(a: A, b: A)(implicit ev: Eq[A]): A

Attributes

Source:
GCDRing.scala

Inherited methods

def fromBigInt(n: BigInt): A

Convert the given BigInt to an instance of A.

Convert the given BigInt to an instance of A.

This is equivalent to n repeated summations of this ring's one, or -n summations of -one if n is negative.

Most type class instances should consider overriding this method for performance reasons.

Attributes

Inherited from:
Ring
Source:
Ring.scala
def fromInt(n: Int): A

Convert the given integer to an instance of A.

Convert the given integer to an instance of A.

Defined to be equivalent to sumN(one, n).

That is, n repeated summations of this ring's one, or -n summations of -one if n is negative.

Most type class instances should consider overriding this method for performance reasons.

Attributes

Inherited from:
Ring
Source:
Ring.scala
def isOne(a: A)(implicit ev: Eq[A]): Boolean

Tests if a is one.

Tests if a is one.

Attributes

Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
def isZero(a: A)(implicit ev: Eq[A]): Boolean

Tests if a is zero.

Tests if a is zero.

Attributes

Inherited from:
AdditiveMonoid
Source:
Additive.scala
def minus(x: A, y: A): A

Attributes

Inherited from:
AdditiveGroup
Source:
Additive.scala
def negate(x: A): A

Attributes

Inherited from:
AdditiveGroup
Source:
Additive.scala
def one: A

Attributes

Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
def plus(x: A, y: A): A

Attributes

Inherited from:
AdditiveSemigroup
Source:
Additive.scala
override def pow(a: A, n: Int): A
def product(as: IterableOnce[A]): A

Given a sequence of as, compute the product.

Given a sequence of as, compute the product.

Attributes

Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
def sum(as: IterableOnce[A]): A

Given a sequence of as, compute the sum.

Given a sequence of as, compute the sum.

Attributes

Inherited from:
AdditiveMonoid
Source:
Additive.scala
override def sumN(a: A, n: Int): A

Attributes

Definition Classes
Inherited from:
AdditiveGroup
Source:
Additive.scala
def times(x: A, y: A): A

Attributes

Inherited from:
MultiplicativeSemigroup
Source:
Multiplicative.scala
override def tryProduct(as: IterableOnce[A]): Option[A]

Given a sequence of as, combine them and return the total.

Given a sequence of as, combine them and return the total.

If the sequence is empty, returns None. Otherwise, returns Some(total).

Attributes

Definition Classes
Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
override def trySum(as: IterableOnce[A]): Option[A]

Given a sequence of as, combine them and return the total.

Given a sequence of as, combine them and return the total.

If the sequence is empty, returns None. Otherwise, returns Some(total).

Attributes

Definition Classes
Inherited from:
AdditiveMonoid
Source:
Additive.scala
def zero: A

Attributes

Inherited from:
AdditiveMonoid
Source:
Additive.scala