trait Field[A] extends CommutativeRing[A] with MultiplicativeCommutativeGroup[A]
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- Field
- MultiplicativeCommutativeGroup
- MultiplicativeGroup
- CommutativeRing
- CommutativeRng
- CommutativeRig
- MultiplicativeCommutativeMonoid
- CommutativeSemiring
- MultiplicativeCommutativeSemigroup
- Ring
- Rng
- AdditiveCommutativeGroup
- AdditiveGroup
- Rig
- MultiplicativeMonoid
- Semiring
- MultiplicativeSemigroup
- AdditiveCommutativeMonoid
- AdditiveCommutativeSemigroup
- AdditiveMonoid
- AdditiveSemigroup
- Serializable
- Serializable
- Any
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Abstract Value Members
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abstract
def
div(x: A, y: A): A
- Definition Classes
- MultiplicativeGroup
-
abstract
def
getClass(): Class[_]
- Definition Classes
- Any
-
abstract
def
negate(x: A): A
- Definition Classes
- AdditiveGroup
-
abstract
def
one: A
- Definition Classes
- MultiplicativeMonoid
-
abstract
def
plus(x: A, y: A): A
- Definition Classes
- AdditiveSemigroup
-
abstract
def
times(x: A, y: A): A
- Definition Classes
- MultiplicativeSemigroup
-
abstract
def
zero: A
- Definition Classes
- AdditiveMonoid
Concrete Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- Any
-
final
def
##(): Int
- Definition Classes
- Any
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- Any
-
def
additive: CommutativeGroup[A]
- Definition Classes
- AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
equals(arg0: Any): Boolean
- Definition Classes
- Any
-
def
fromBigInt(n: BigInt): A
Convert the given BigInt to an instance of A.
Convert the given BigInt to an instance of A.
This is equivalent to
nrepeated summations of this ring'sone, or-nsummations of-oneifnis negative.Most type class instances should consider overriding this method for performance reasons.
- Definition Classes
- Ring
-
def
fromDouble(a: Double): A
This is implemented in terms of basic Field ops.
This is implemented in terms of basic Field ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method be overriden.
This is possible because a Double is a rational number.
-
def
fromInt(n: Int): A
Convert the given integer to an instance of A.
Convert the given integer to an instance of A.
Defined to be equivalent to
sumN(one, n).That is,
nrepeated summations of this ring'sone, or-nsummations of-oneifnis negative.Most type class instances should consider overriding this method for performance reasons.
- Definition Classes
- Ring
-
def
hashCode(): Int
- Definition Classes
- Any
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
isOne(a: A)(implicit ev: Eq[A]): Boolean
Tests if
ais one.Tests if
ais one.- Definition Classes
- MultiplicativeMonoid
-
def
isZero(a: A)(implicit ev: Eq[A]): Boolean
Tests if
ais zero.Tests if
ais zero.- Definition Classes
- AdditiveMonoid
-
def
minus(x: A, y: A): A
- Definition Classes
- AdditiveGroup
- def multiplicative: CommutativeGroup[A]
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def
positivePow(a: A, n: Int): A
- Attributes
- protected[this]
- Definition Classes
- MultiplicativeSemigroup
-
def
positiveSumN(a: A, n: Int): A
- Attributes
- protected[this]
- Definition Classes
- AdditiveSemigroup
-
def
pow(a: A, n: Int): A
- Definition Classes
- MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup
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def
product(as: TraversableOnce[A]): A
Given a sequence of
as, compute the product.Given a sequence of
as, compute the product.- Definition Classes
- MultiplicativeMonoid
-
def
reciprocal(x: A): A
- Definition Classes
- MultiplicativeGroup
-
def
sum(as: TraversableOnce[A]): A
Given a sequence of
as, compute the sum.Given a sequence of
as, compute the sum.- Definition Classes
- AdditiveMonoid
-
def
sumN(a: A, n: Int): A
- Definition Classes
- AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
-
def
toString(): String
- Definition Classes
- Any
-
def
tryProduct(as: TraversableOnce[A]): Option[A]
Given a sequence of
as, combine them and return the total.Given a sequence of
as, combine them and return the total.If the sequence is empty, returns None. Otherwise, returns Some(total).
- Definition Classes
- MultiplicativeMonoid → MultiplicativeSemigroup
-
def
trySum(as: TraversableOnce[A]): Option[A]
Given a sequence of
as, combine them and return the total.Given a sequence of
as, combine them and return the total.If the sequence is empty, returns None. Otherwise, returns Some(total).
- Definition Classes
- AdditiveMonoid → AdditiveSemigroup