Field

Type Members

trait FieldOfFractionsGCD[A, R] extends Field[A]

Field defined as a field of fractions with a default implementation of GCD/LCM such that - gcd(a/b, c/d) = gcd(a, c) / lcm(b, d) - lcm(a/b, c/d) = lcm(a, c) / gcd(b, d) which corresponds to the convention of the GCD domains of SageMath; on rational numbers, it "yields the unique extension of gcd from integers to rationals presuming the natural extension of the divisibility relation from integers to rationals", see http://math.stackexchange.com/a/151431
trait WithDefaultGCD[A] extends Field[A]

Field with simple default GCD/LCM implementations: gcd(a, b) = 1 (except gcd(0, 0) = 0) while lcm(a, b) = a * b.

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 apply[A](implicit ev: Field[A]): Field[A]

Annotations
@inline()
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
final def defaultFromBigInt[A](n: BigInt)(implicit ev: Field[A]): A

Definition Classes
RingFunctions
final def defaultFromDouble[A](a: Double)(implicit ringA: algebra.ring.Ring[A], mgA: algebra.ring.MultiplicativeGroup[A]): A

Definition Classes
RingFunctions
def div[A](x: A, y: A)(implicit ev: Field[A]): A

Definition Classes
MultiplicativeGroupFunctions
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def euclideanFunction[A](a: A)(implicit ev: Field[A]): BigInt

Definition Classes
EuclideanRingFunctions
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
def fromBigInt[A](n: BigInt)(implicit ev: Field[A]): A

Definition Classes
RingFunctions
def fromDouble[A](n: Double)(implicit ev: Field[A]): A

Definition Classes
FieldFunctions
def fromInt[A](n: Int)(implicit ev: Field[A]): A

Definition Classes
RingFunctions
def gcd[A](a: A, b: A)(implicit ev: Field[A], eqA: Eq[A]): A

Definition Classes
GCDRingFunctions
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → Any
def isAdditiveCommutative[A](implicit ev: Field[A]): Boolean

Definition Classes
AdditiveSemigroupFunctions
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isMultiplicativeCommutative[A](implicit ev: Field[A]): Boolean

Definition Classes
MultiplicativeSemigroupFunctions
def isOne[A](a: A)(implicit ev0: Field[A], ev1: algebra.Eq[A]): Boolean

Definition Classes
MultiplicativeMonoidFunctions
def isZero[A](a: A)(implicit ev0: Field[A], ev1: algebra.Eq[A]): Boolean

Definition Classes
AdditiveMonoidFunctions
def lcm[A](a: A, b: A)(implicit ev: Field[A], eqA: Eq[A]): A

Definition Classes
GCDRingFunctions
def minus[A](x: A, y: A)(implicit ev: Field[A]): A

Definition Classes
AdditiveGroupFunctions
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def negate[A](x: A)(implicit ev: Field[A]): A

Definition Classes
AdditiveGroupFunctions
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def one[A](implicit ev: Field[A]): A

Definition Classes
MultiplicativeMonoidFunctions
def plus[A](x: A, y: A)(implicit ev: Field[A]): A

Definition Classes
AdditiveSemigroupFunctions
def pow[A](a: A, n: Int)(implicit ev: Field[A]): A

Definition Classes
MultiplicativeSemigroupFunctions
def product[A](as: TraversableOnce[A])(implicit ev: Field[A]): A

Definition Classes
MultiplicativeMonoidFunctions
def quot[A](a: A, b: A)(implicit ev: Field[A]): A

Definition Classes
EuclideanRingFunctions
def reciprocal[A](x: A)(implicit ev: Field[A]): A

Definition Classes
MultiplicativeGroupFunctions
def sum[A](as: TraversableOnce[A])(implicit ev: Field[A]): A

Definition Classes
AdditiveMonoidFunctions
def sumN[A](a: A, n: Int)(implicit ev: Field[A]): A

Definition Classes
AdditiveSemigroupFunctions
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def times[A](x: A, y: A)(implicit ev: Field[A]): A

Definition Classes
MultiplicativeSemigroupFunctions
def toString(): String

Definition Classes
AnyRef → Any
def tryProduct[A](as: TraversableOnce[A])(implicit ev: Field[A]): Option[A]

Definition Classes
MultiplicativeSemigroupFunctions
def trySum[A](as: TraversableOnce[A])(implicit ev: Field[A]): Option[A]

Definition Classes
AdditiveSemigroupFunctions
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( ... )
def zero[A](implicit ev: Field[A]): A

Definition Classes
AdditiveMonoidFunctions

Related Docs: trait Field | package algebra

object Field extends FieldFunctions[Field] with EuclideanRingFunctions[Field] with Serializable

Type Members

trait FieldOfFractionsGCD[A, R] extends Field[A]

trait WithDefaultGCD[A] extends Field[A]

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

def apply[A](implicit ev: Field[A]): Field[A]

final def asInstanceOf[T0]: T0

def clone(): AnyRef

final def defaultFromBigInt[A](n: BigInt)(implicit ev: Field[A]): A

final def defaultFromDouble[A](a: Double)(implicit ringA: algebra.ring.Ring[A], mgA: algebra.ring.MultiplicativeGroup[A]): A

def div[A](x: A, y: A)(implicit ev: Field[A]): A

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def euclideanFunction[A](a: A)(implicit ev: Field[A]): BigInt

def finalize(): Unit

def fromBigInt[A](n: BigInt)(implicit ev: Field[A]): A

def fromDouble[A](n: Double)(implicit ev: Field[A]): A

def fromInt[A](n: Int)(implicit ev: Field[A]): A

def gcd[A](a: A, b: A)(implicit ev: Field[A], eqA: Eq[A]): A

final def getClass(): Class[_]

def hashCode(): Int

def isAdditiveCommutative[A](implicit ev: Field[A]): Boolean

final def isInstanceOf[T0]: Boolean

def isMultiplicativeCommutative[A](implicit ev: Field[A]): Boolean

def isOne[A](a: A)(implicit ev0: Field[A], ev1: algebra.Eq[A]): Boolean

def isZero[A](a: A)(implicit ev0: Field[A], ev1: algebra.Eq[A]): Boolean

def lcm[A](a: A, b: A)(implicit ev: Field[A], eqA: Eq[A]): A

def minus[A](x: A, y: A)(implicit ev: Field[A]): A

final def ne(arg0: AnyRef): Boolean

def negate[A](x: A)(implicit ev: Field[A]): A

final def notify(): Unit

final def notifyAll(): Unit

def one[A](implicit ev: Field[A]): A

def plus[A](x: A, y: A)(implicit ev: Field[A]): A

def pow[A](a: A, n: Int)(implicit ev: Field[A]): A

def product[A](as: TraversableOnce[A])(implicit ev: Field[A]): A

def quot[A](a: A, b: A)(implicit ev: Field[A]): A

def reciprocal[A](x: A)(implicit ev: Field[A]): A

def sum[A](as: TraversableOnce[A])(implicit ev: Field[A]): A

def sumN[A](a: A, n: Int)(implicit ev: Field[A]): A

final def synchronized[T0](arg0: ⇒ T0): T0

def times[A](x: A, y: A)(implicit ev: Field[A]): A

def toString(): String

def tryProduct[A](as: TraversableOnce[A])(implicit ev: Field[A]): Option[A]

def trySum[A](as: TraversableOnce[A])(implicit ev: Field[A]): Option[A]

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

def zero[A](implicit ev: Field[A]): A

Inherited from Serializable

Inherited from Serializable

Inherited from EuclideanRingFunctions[Field]

Inherited from GCDRingFunctions[Field]

Inherited from FieldFunctions[Field]

Inherited from MultiplicativeGroupFunctions[Field]

Inherited from RingFunctions[Field]

Inherited from MultiplicativeMonoidFunctions[Field]

Inherited from MultiplicativeSemigroupFunctions[Field]

Inherited from AdditiveGroupFunctions[Field]

Inherited from AdditiveMonoidFunctions[Field]

Inherited from AdditiveSemigroupFunctions[Field]

Inherited from AnyRef

Inherited from Any

Ungrouped