CModule

trait CModule[V, @specialized(Int, Long, Float, Double) R] extends LeftModule[V, R] with RightModule[V, R]

A module over a commutative ring has by definition equivalent left and right modules.

In addition to the laws above 1-5 left and 1-5 right, we have:

6. (r *: x) :* s = r *: (x :* s)
Type Params
R

Scalar type

V

Abelian group type

Companion
object
trait RightModule[V, R]
trait LeftModule[V, R]
trait AdditiveCommutativeGroup[V]
trait AdditiveCommutativeMonoid[V]
trait AdditiveCommutativeSemigroup[V]
trait AdditiveGroup[V]
trait AdditiveMonoid[V]
trait AdditiveSemigroup[V]
trait Serializable
class Any
trait ZAlgebra[V]
trait VectorSpace[V, F]
trait InnerProductSpace[V, F]
trait CoordinateSpace[V, F]
class SeqCoordinateSpace[A, SA]
trait NormedVectorSpace[V, F]
trait DistVectorSpace[V, K]
class MapVectorSpace[K, V]
class SeqVectorSpace[A, SA]
trait DistCModule[V, K]
class MapCRng[K, V]
class SeqCModule[A, SA]

Value members

Concrete methods

override
def timesr(v: V, r: R): V
Definition Classes

Inherited methods

override
def additive: CommutativeGroup[V]
Definition Classes
AdditiveCommutativeGroup -> AdditiveCommutativeMonoid -> AdditiveCommutativeSemigroup -> AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
Inherited from
AdditiveCommutativeGroup
def isZero(a: V)(implicit ev: Eq[V]): Boolean

Tests if a is zero.

Tests if a is zero.

Inherited from
AdditiveMonoid
def minus(x: V, y: V): V
Inherited from
AdditiveGroup
def negate(x: V): V
Inherited from
AdditiveGroup
def plus(x: V, y: V): V
Inherited from
AdditiveSemigroup
def sum(as: IterableOnce[V]): V

Given a sequence of as, compute the sum.

Given a sequence of as, compute the sum.

Inherited from
AdditiveMonoid
override
def sumN(a: V, n: Int): V
Definition Classes
AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
Inherited from
AdditiveGroup
def timesl(r: R, v: V): V
Inherited from
LeftModule
override
def trySum(as: IterableOnce[V]): Option[V]
Definition Classes
AdditiveMonoid -> AdditiveSemigroup
Inherited from
AdditiveMonoid
def zero: V
Inherited from
AdditiveMonoid

Implicits

Implicits

implicit
def scalar: CommutativeRing[R]