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spireAD/io.github.quafadas.spireAD/TejAlgebra

TejAlgebra

io.github.quafadas.spireAD.TejAlgebra
class TejAlgebra[T](implicit val c: ClassTag[T], val d: TejDim[T], val eq: Eq[T], val f: Field[T], val n: NRoot[T], val o: Order[T], val t: Trig[T], val s: Signed[T], val v: VectorSpace[Array[T], T]) extends TejIsField[T], TejIsTrig[T], TejIsNRoot[T], VectorSpace[Tej[T], T], FieldAssociativeAlgebra[Tej[T], T], Serializable

Attributes

Graph
Supertypes
trait FieldAssociativeAlgebra[Tej[T], T]
trait RingAssociativeAlgebra[Tej[T], T]
trait VectorSpace[Tej[T], T]
trait CModule[Tej[T], T]
trait RightModule[Tej[T], T]
trait LeftModule[Tej[T], T]
trait TejIsNRoot[T]
trait NRoot[Tej[T]]
trait TejIsTrig[T]
trait Trig[Tej[T]]
trait TejIsField[T]
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

Members list

Value members

Concrete methods

def dot(x: Tej[T], y: Tej[T]): T
inline def nroot: NRoot[T]
inline def scalar: Field[T]
def timesl(a: T, w: Tej[T]): Tej[T]

Inherited methods

def acos(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
override def additive: CommutativeGroup[Tej[T]]

Attributes

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

Attributes

Inherited from:
TejIsTrig
def atan(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def atan2(y: Tej[T], x: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def cos(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def cosh(x: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def div(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsField
def divr(v: Tej[T], f: T): Tej[T]

Attributes

Inherited from:
VectorSpace
def e: Tej[T]

Attributes

Inherited from:
TejIsTrig
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 exp(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def expm1(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def fpow(a: T, b: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsNRoot
def fpow(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsNRoot
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 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
TejIsField -> Field -> DivisionRing
Inherited from:
TejIsField
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
def log(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def log1p(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
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 nroot(a: Tej[T], k: Int): Tej[T]

Attributes

Inherited from:
TejIsNRoot
def one: Tej[T]

Attributes

Inherited from:
TejIsRing
def pi: Tej[T]

Attributes

Inherited from:
TejIsTrig
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 sin(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def sinh(x: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
override def sqrt(a: Tej[T]): Tej[T]

Attributes

Definition Classes
TejIsNRoot -> NRoot
Inherited from:
TejIsNRoot
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
def tan(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def tanh(x: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
override def times(a: Tej[T], b: Tej[T]): Tej[T]

Attributes

Definition Classes
TejIsRing -> MultiplicativeSemigroup
Inherited from:
TejIsRing
override def timesr(v: Tej[T], r: T): Tej[T]

Attributes

Definition Classes
CModule -> RightModule
Inherited from:
CModule
def toDegrees(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
def toRadians(a: Tej[T]): Tej[T]

Attributes

Inherited from:
TejIsTrig
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

Implicits

implicit val c: ClassTag[T]
implicit val d: TejDim[T]
implicit val eq: Eq[T]
implicit val f: Field[T]
implicit val n: NRoot[T]
implicit val o: Order[T]
implicit val s: Signed[T]
implicit val t: Trig[T]
implicit val v: VectorSpace[Array[T], T]
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