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TejIsField

io.github.quafadas.spireAD.TejIsField
trait TejIsField[T] extends TejIsEuclideanRing[T], Field[Tej[T]]

Attributes

Graph
Supertypes
trait Field[Tej[T]]
trait CommutativeSemifield[Tej[T]]
trait MultiplicativeCommutativeGroup[Tej[T]]
trait DivisionRing[Tej[T]]
trait Semifield[Tej[T]]
trait MultiplicativeGroup[Tej[T]]
trait EuclideanRing[Tej[T]]
trait TejIsGCDRing[T]
trait GCDRing[Tej[T]]
trait CommutativeRing[Tej[T]]
trait CommutativeRng[Tej[T]]
trait CommutativeRig[Tej[T]]
trait MultiplicativeCommutativeMonoid[Tej[T]]
trait CommutativeSemiring[Tej[T]]
trait MultiplicativeCommutativeSemigroup[Tej[T]]
trait TejIsRing[T]
trait Ring[Tej[T]]
trait Rng[Tej[T]]
trait AdditiveCommutativeGroup[Tej[T]]
trait AdditiveGroup[Tej[T]]
trait Rig[Tej[T]]
trait MultiplicativeMonoid[Tej[T]]
trait Semiring[Tej[T]]
trait MultiplicativeSemigroup[Tej[T]]
trait AdditiveCommutativeMonoid[Tej[T]]
trait AdditiveCommutativeSemigroup[Tej[T]]
trait AdditiveMonoid[Tej[T]]
trait AdditiveSemigroup[Tej[T]]
trait Serializable
class Object
trait Matchable
class Any
Show all
Known subtypes
class TejAlgebra[T]

Members list

Value members

Concrete methods

def div(a: Tej[T], b: Tej[T]): Tej[T]
override def fromDouble(n: Double): Tej[T]

This is implemented in terms of basic Ring 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 implemented in terms of basic Ring 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.

Attributes

Definition Classes
Field -> DivisionRing

Inherited methods

override def additive: CommutativeGroup[Tej[T]]

Attributes

Definition Classes
AdditiveCommutativeGroup -> AdditiveCommutativeMonoid -> AdditiveCommutativeSemigroup -> AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
Inherited from:
AdditiveCommutativeGroup
def emod(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Inherited from:
Field
def equot(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Inherited from:
Field
override def equotmod(a: Tej[T], b: Tej[T]): (Tej[T], Tej[T])

Attributes

Definition Classes
Field -> EuclideanRing
Inherited from:
Field
def euclideanFunction(a: Tej[T]): BigInt

Attributes

Inherited from:
Field
def fromBigInt(n: BigInt): Tej[T]

Convert the given BigInt to an instance of A.

Convert the given BigInt to an instance of A.

This is equivalent to n repeated summations of this ring's one, or -n summations of -one if n is negative.

Most type class instances should consider overriding this method for performance reasons.

Attributes

Inherited from:
Ring
override def fromInt(n: Int): Tej[T]

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, n repeated summations of this ring's one, or -n summations of -one if n is negative.

Most type class instances should consider overriding this method for performance reasons.

Attributes

Definition Classes
TejIsRing -> Ring
Inherited from:
TejIsRing
override def gcd(a: Tej[T], b: Tej[T])(implicit eqA: Eq[Tej[T]]): Tej[T]

Attributes

Definition Classes
Field -> EuclideanRing -> GCDRing
Inherited from:
Field
def isOne(a: Tej[T])(implicit ev: Eq[Tej[T]]): Boolean

Tests if a is one.

Tests if a is one.

Attributes

Inherited from:
MultiplicativeMonoid
def isZero(a: Tej[T])(implicit ev: Eq[Tej[T]]): Boolean

Tests if a is zero.

Tests if a is zero.

Attributes

Inherited from:
AdditiveMonoid
override def lcm(a: Tej[T], b: Tej[T])(implicit eqA: Eq[Tej[T]]): Tej[T]

Attributes

Definition Classes
Field -> EuclideanRing -> GCDRing
Inherited from:
Field
override def minus(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Definition Classes
TejIsRing -> AdditiveGroup
Inherited from:
TejIsRing
override def multiplicative: CommutativeGroup[Tej[T]]

Attributes

Definition Classes
MultiplicativeCommutativeGroup -> MultiplicativeCommutativeMonoid -> MultiplicativeCommutativeSemigroup -> MultiplicativeGroup -> MultiplicativeMonoid -> MultiplicativeSemigroup
Inherited from:
MultiplicativeCommutativeGroup
def negate(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsRing
def one: Tej[T]

Attributes

Inherited from:
TejIsRing
def plus(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsRing
override def pow(a: Tej[T], n: Int): Tej[T]

Attributes

Definition Classes
MultiplicativeGroup -> MultiplicativeMonoid -> MultiplicativeSemigroup
Inherited from:
MultiplicativeGroup
def product(as: IterableOnce[Tej[T]]): Tej[T]

Given a sequence of as, compute the product.

Given a sequence of as, compute the product.

Attributes

Inherited from:
MultiplicativeMonoid
def reciprocal(x: Tej[T]): Tej[T]

Attributes

Inherited from:
MultiplicativeGroup
def sum(as: IterableOnce[Tej[T]]): Tej[T]

Given a sequence of as, compute the sum.

Given a sequence of as, compute the sum.

Attributes

Inherited from:
AdditiveMonoid
override def sumN(a: Tej[T], n: Int): Tej[T]

Attributes

Definition Classes
AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
Inherited from:
AdditiveGroup
override def times(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Definition Classes
TejIsRing -> MultiplicativeSemigroup
Inherited from:
TejIsRing
override def tryProduct(as: IterableOnce[Tej[T]]): Option[Tej[T]]

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).

Attributes

Definition Classes
MultiplicativeMonoid -> MultiplicativeSemigroup
Inherited from:
MultiplicativeMonoid
override def trySum(as: IterableOnce[Tej[T]]): Option[Tej[T]]

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).

Attributes

Definition Classes
AdditiveMonoid -> AdditiveSemigroup
Inherited from:
AdditiveMonoid
def zero: Tej[T]

Attributes

Inherited from:
TejIsRing

Implicits

Inherited and Abstract implicits

implicit def c: ClassTag[T]

Attributes

Inherited from:
TejIsRing
implicit def d: TejDim[T]

Attributes

Inherited from:
TejIsRing
implicit def eq: Eq[T]

Attributes

Inherited from:
TejIsRing
implicit def f: Field[T]

Attributes

Inherited from:
TejIsRing
implicit def n: NRoot[T]

Attributes

Inherited from:
TejIsRing
implicit def s: Signed[T]

Attributes

Inherited from:
TejIsRing
implicit def t: Trig[T]

Attributes

Inherited from:
TejIsRing
implicit def v: VectorSpace[Array[T], T]

Attributes

Inherited from:
TejIsRing
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