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.
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- Rig
- MultiplicativeMonoid
- Semiring
- MultiplicativeSemigroup
- AdditiveMonoid
- AdditiveSemigroup
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Abstract Value Members
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abstract
def
getClass(): Class[_]
- Definition Classes
- Any
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abstract
def
one: A
- Definition Classes
- MultiplicativeMonoid
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abstract
def
plus(x: A, y: A): A
- Definition Classes
- AdditiveSemigroup
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abstract
def
times(x: A, y: A): A
- Definition Classes
- MultiplicativeSemigroup
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abstract
def
zero: A
- Definition Classes
- AdditiveMonoid
Concrete Value Members
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final
def
!=(arg0: Any): Boolean
- Definition Classes
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final
def
##(): Int
- Definition Classes
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final
def
==(arg0: Any): Boolean
- Definition Classes
- Any
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def
additive: Monoid[A]
- Definition Classes
- AdditiveMonoid → AdditiveSemigroup
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final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
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def
equals(arg0: Any): Boolean
- Definition Classes
- Any
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def
hashCode(): Int
- Definition Classes
- Any
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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def
isOne(a: A)(implicit ev: Eq[A]): Boolean
- Definition Classes
- MultiplicativeMonoid
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def
isZero(a: A)(implicit ev: Eq[A]): Boolean
Tests if
ais zero.Tests if
ais zero.- Definition Classes
- AdditiveMonoid
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def
multiplicative: Monoid[A]
- Definition Classes
- MultiplicativeMonoid → MultiplicativeSemigroup
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def
pow(a: A, n: Int): A
This is similar to
Semigroup#pow, except thata pow 0is defined to be the multiplicative identity. -
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
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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
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def
prodn(a: A, n: Int): A
Return
amultiplied with itselfntimes.Return
amultiplied with itselfntimes.- Definition Classes
- MultiplicativeMonoid → MultiplicativeSemigroup
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def
prodnAboveOne(a: A, n: Int): A
- Attributes
- protected
- Definition Classes
- MultiplicativeSemigroup
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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
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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
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def
sumn(a: A, n: Int): A
Return
aadded with itselfntimes.Return
aadded with itselfntimes.- Definition Classes
- AdditiveMonoid → AdditiveSemigroup
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def
sumnAboveOne(a: A, n: Int): A
- Attributes
- protected
- Definition Classes
- AdditiveSemigroup
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def
toString(): String
- Definition Classes
- Any