spire.algebra

Rig

trait Rig[A] extends Semiring[A] with AdditiveMonoid[A] with MultiplicativeMonoid[A]

Rig is a ring whose additive structure doesn't have an inverse (ie. it is monoid, not a group). Put another way, a Rig is a Ring without a negative.

Linear Supertypes
MultiplicativeMonoid[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Any
Known Subclasses
AlgebraicAlgebra, BigDecimalAlgebra, BigDecimalIsField, BigIntAlgebra, BigIntIsEuclideanRing, BigIntegerAlgebra, BigIntegerIsEuclideanRing, BooleanIsRig, BooleanStructure, ByteAlgebra, ByteIsEuclideanRing, CRig, CRing, ComplexIsNumeric, DistEuclideanRing, DistField, DistRig, DistRing, DoubleAlgebra, DoubleIsField, EuclideanRing, Field, FloatAlgebra, FloatIsField, Fractional, IntAlgebra, IntIsEuclideanRing, Integral, LongAlgebra, LongIsEuclideanRing, NaturalAlgebra, NumberAlgebra, Numeric, PolynomialEuclideanRing, PolynomialRig, PolynomialRing, RationalAlgebra, RealAlgebra, RealIsFractional, Ring, SafeLongAlgebra, ShortAlgebra, ShortIsEuclideanRing, ZAlgebra
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  2. By inheritance
Inherited
  1. Rig
  2. MultiplicativeMonoid
  3. Semiring
  4. MultiplicativeSemigroup
  5. AdditiveMonoid
  6. AdditiveSemigroup
  7. Any
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  1. Public
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Abstract Value Members

  1. abstract def getClass(): Class[_]

    Definition Classes
    Any

  2. abstract def one: A

    Definition Classes
    MultiplicativeMonoid

  3. abstract def plus(x: A, y: A): A

    Definition Classes
    AdditiveSemigroup

  4. abstract def times(x: A, y: A): A

    Definition Classes
    MultiplicativeSemigroup

  5. abstract def zero: A

    Definition Classes
    AdditiveMonoid

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. def additive: Monoid[A]

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  6. def equals(arg0: Any): Boolean

    Definition Classes
    Any

  7. def hashCode(): Int

    Definition Classes
    Any

  8. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    MultiplicativeMonoid

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

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid

  11. def multiplicative: Monoid[A]

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

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

    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    Definition Classes
    Rig → Semiring

  13. def prod(as: TraversableOnce[A]): A

    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes
    MultiplicativeMonoid

  14. def prodOption(as: TraversableOnce[A]): Option[A]

    Given a sequence of as, sum them using the semigroup and return the total.

    Given a sequence of as, sum them using the semigroup and return the total.

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

    Definition Classes
    MultiplicativeSemigroup

  15. def prodn(a: A, n: Int): A

    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  16. def prodnAboveOne(a: A, n: Int): A

    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup

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

    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes
    AdditiveMonoid

  18. def sumOption(as: TraversableOnce[A]): Option[A]

    Given a sequence of as, sum them using the semigroup and return the total.

    Given a sequence of as, sum them using the semigroup and return the total.

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

    Definition Classes
    AdditiveSemigroup

  19. def sumn(a: A, n: Int): A

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

  20. def sumnAboveOne(a: A, n: Int): A

    Attributes
    protected
    Definition Classes
    AdditiveSemigroup

  21. def toString(): String

    Definition Classes
    Any

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Any

Ungrouped