CommutativeGroup

trait CommutativeGroup[a: Type] with Group[a], CommutativeMonoid[a]Source

A trait for types that form a commutative group (abelian group) i.e. groups where the combine function is commutative.

The default instances for number define the additive inverse in the real numbers.

Instances

instance CommutativeGroup[Unit]Source

instance CommutativeGroup[Int8]Source

instance CommutativeGroup[Int16]Source

instance CommutativeGroup[Int32]Source

instance CommutativeGroup[Int64]Source

instance CommutativeGroup[BigInt]Source

instance CommutativeGroup[Float32]Source

instance CommutativeGroup[Float64]Source

instance CommutativeGroup[BigDecimal]Source

instance CommutativeGroup[(a1, a2)] with CommutativeGroup[a1], CommutativeGroup[a2]Source

instance CommutativeGroup[(a1, a2, a3)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3]Source

instance CommutativeGroup[(a1, a2, a3, a4)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3], CommutativeGroup[a4]

Source

instance CommutativeGroup[(a1, a2, a3, a4, a5)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3], CommutativeGroup[a4], CommutativeGroup[a5]

Source

instance CommutativeGroup[(a1, a2, a3, a4, a5, a6)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3], CommutativeGroup[a4], CommutativeGroup[a5], CommutativeGroup[a6]

Source

instance CommutativeGroup[(a1, a2, a3, a4, a5, a6, a7)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3], CommutativeGroup[a4], CommutativeGroup[a5], CommutativeGroup[a6], CommutativeGroup[a7]

Source

instance CommutativeGroup[(a1, a2, a3, a4, a5, a6, a7, a8)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3], CommutativeGroup[a4], CommutativeGroup[a5], CommutativeGroup[a6], CommutativeGroup[a7], CommutativeGroup[a8]

Source

instance CommutativeGroup[(a1, a2, a3, a4, a5, a6, a7, a8, a9)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3], CommutativeGroup[a4], CommutativeGroup[a5], CommutativeGroup[a6], CommutativeGroup[a7], CommutativeGroup[a8], CommutativeGroup[a9]

Source

instance CommutativeGroup[(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10)] with CommutativeGroup[a1], CommutativeGroup[a2], CommutativeGroup[a3], CommutativeGroup[a4], CommutativeGroup[a5], CommutativeGroup[a6], CommutativeGroup[a7], CommutativeGroup[a8], CommutativeGroup[a9], CommutativeGroup[a10]

Source