trait Signed[A] extends Any

A trait that expresses the existence of signs and absolute values on linearly ordered additive commutative monoids (i.e. types with addition and a zero).

The following laws holds:

(1) if a <= b then a + c <= b + c (linear order), (2) signum(x) = -1 if x < 0, signum(x) = 1 if x > 0, signum(x) = 0 otherwise,

Negative elements only appear when the scalar is taken from a additive abelian group. Then:

(3) abs(x) = -x if x < 0, or x otherwise,

Laws (1) and (2) lead to the triange inequality:

(4) abs(a + b) <= abs(a) + abs(b)

Signed should never be extended in implementations, rather the Signed.forAdditiveCommutativeMonoid and subtraits.

It's better to have the Signed hierarchy separate from the Ring/Order hierarchy, so that we do not end up with duplicate implicits.

Source
Signed.scala
Linear Supertypes
Any
Known Subclasses
BigIntTruncatedDivison, forAdditiveCommutativeGroup, forAdditiveCommutativeMonoid, TruncatedDivision, forCommutativeRing
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Inherited
  1. Signed
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Visibility
  1. Public
  2. Protected

Abstract Value Members

  1. abstract def abs(a: A): A

    An idempotent function that ensures an object has a non-negative sign.

  2. abstract def additiveCommutativeMonoid: AdditiveCommutativeMonoid[A]
  3. abstract def getClass(): Class[_ <: AnyRef]
    Definition Classes
    Any
  4. abstract def order: Order[A]
  5. abstract def signum(a: A): Int

    Returns 0 if a is 0, 1 if a is positive, and -1 is a is negative.

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    Any
  2. final def ##: Int
    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def equals(arg0: Any): Boolean
    Definition Classes
    Any
  6. def hashCode(): Int
    Definition Classes
    Any
  7. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  8. def isSignNegative(a: A): Boolean
  9. def isSignNonNegative(a: A): Boolean
  10. def isSignNonPositive(a: A): Boolean
  11. def isSignNonZero(a: A): Boolean
  12. def isSignPositive(a: A): Boolean
  13. def isSignZero(a: A): Boolean
  14. def sign(a: A): Sign

    Returns Zero if a is 0, Positive if a is positive, and Negative is a is negative.

  15. def toString(): String
    Definition Classes
    Any

Inherited from Any

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