trait Field[X] extends CRing[X] with MultiplicativeCGroup[X]
Represents a field.
- Since
0.1.0
- Alphabetic
- By Inheritance
- Field
- MultiplicativeCGroup
- MultiplicativeGroup
- CRing
- CSemiring
- MultiplicativeCMonoid
- MultiplicativeCSemigroup
- Ring
- AdditiveCGroup
- AdditiveGroup
- Semiring
- MultiplicativeMonoid
- HasOne
- MultiplicativeSemigroup
- AdditiveCMonoid
- AdditiveCSemigroup
- AdditiveMonoid
- HasZero
- AdditiveSemigroup
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- Any
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Abstract Value Members
-
abstract
def
add(x: X, y: X): X
The
+operation of this semigroup.The
+operation of this semigroup.- Definition Classes
- AdditiveSemigroup
-
abstract
def
inv(x: X): X
- Definition Classes
- MultiplicativeGroup
-
abstract
def
mul(x: X, y: X): X
Returns the product of two elements.
Returns the product of two elements.
- Definition Classes
- MultiplicativeSemigroup
-
abstract
def
neg(x: X): X
Returns the negation (additive inverse) of an element.
Returns the negation (additive inverse) of an element.
- Definition Classes
- AdditiveGroup
-
abstract
def
one: X
The
1element (multiplicative identity) of this type.The
1element (multiplicative identity) of this type.- Definition Classes
- HasOne
-
abstract
def
zero: X
The
0element (additive identity) of this type.The
0element (additive identity) of this type.- Definition Classes
- HasZero
Concrete Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
asGroupWithAdd: CGroup[X]
Casts this object to a symbol-agnostic group with the group operation
+.Casts this object to a symbol-agnostic group with the group operation
+.- Definition Classes
- AdditiveCGroup → AdditiveGroup
-
def
asGroupWithMul: CGroup[X]
- Definition Classes
- MultiplicativeCGroup → MultiplicativeGroup
-
def
asIdentityWithOne: HasIdentity[X]
Casts this object to a
HasIdentitywith identity1.Casts this object to a
HasIdentitywith identity1.- Definition Classes
- HasOne
-
def
asIdentityWithZero: HasIdentity[X]
Casts this object to a
HasIdentitywith identity0.Casts this object to a
HasIdentitywith identity0.- Definition Classes
- HasZero
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
asMonoidWithAdd: CMonoid[X]
Casts this object as a symbol-agnostic monoid with the operation
+.Casts this object as a symbol-agnostic monoid with the operation
+.- Definition Classes
- AdditiveCMonoid → AdditiveMonoid
-
def
asMonoidWithMul: CMonoid[X]
- Definition Classes
- MultiplicativeCMonoid → MultiplicativeMonoid
-
def
asSemigroupWithAdd: CSemigroup[X]
Casts this structure as a symbol-agnostic semigroup.
Casts this structure as a symbol-agnostic semigroup.
- Definition Classes
- AdditiveCSemigroup → AdditiveSemigroup
-
def
asSemigroupWithMul: CSemigroup[X]
Casts this structure as a symbol-agnostic semigroup.
Casts this structure as a symbol-agnostic semigroup.
- Definition Classes
- MultiplicativeCSemigroup → MultiplicativeSemigroup
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
def
div(x: X, y: X): X
- Definition Classes
- MultiplicativeGroup
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
-
def
half: X
Returns the 1/2 element in this field.
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
-
def
ipow(x: X, n: Int): X
Computes the product x * x * ··· * x with x repeated for n times.
Computes the product x * x * ··· * x with x repeated for n times.
- Definition Classes
- MultiplicativeMonoid → MultiplicativeSemigroup
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
negOne: X
Returns the -1 element in this ring.
Returns the -1 element in this ring.
- Definition Classes
- Ring
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
-
def
product[Y](that: Semiring[Y]): Semiring[(X, Y)]
- Definition Classes
- Semiring
-
def
sub(x: X, y: X): X
Returns the difference of two elements.
Returns the difference of two elements.
- Definition Classes
- AdditiveGroup
-
def
sumN(x: X, n: Int): X
Computes the sum x + x + ··· + x with x repeated for n times.
Computes the sum x + x + ··· + x with x repeated for n times.
- Definition Classes
- AdditiveMonoid → AdditiveSemigroup
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
toString(): String
- Definition Classes
- AnyRef → Any
-
def
two: X
Returns the 2 element in this semiring.
Returns the 2 element in this semiring.
- Definition Classes
- Semiring
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )