AlgebraicAlgebra

@SerialVersionUID(1L)
class AlgebraicAlgebra extends AlgebraicIsField with AlgebraicIsNRoot with AlgebraicIsReal with Serializable
trait AlgebraicIsReal
trait Order[Algebraic]
trait PartialOrder[Algebraic]
trait Eq[Algebraic]
trait AlgebraicIsNRoot
trait AlgebraicIsField
trait Field[Algebraic]
trait MultiplicativeCommutativeGroup[Algebraic]
trait MultiplicativeGroup[Algebraic]
trait CommutativeRing[Algebraic]
trait CommutativeRng[Algebraic]
trait CommutativeRig[Algebraic]
trait MultiplicativeCommutativeMonoid[Algebraic]
trait CommutativeSemiring[Algebraic]
trait MultiplicativeCommutativeSemigroup[Algebraic]
trait Ring[Algebraic]
trait Rng[Algebraic]
trait AdditiveCommutativeGroup[Algebraic]
trait AdditiveGroup[Algebraic]
trait Rig[Algebraic]
trait MultiplicativeMonoid[Algebraic]
trait Semiring[Algebraic]
trait MultiplicativeSemigroup[Algebraic]
trait AdditiveCommutativeMonoid[Algebraic]
trait AdditiveCommutativeSemigroup[Algebraic]
trait AdditiveMonoid[Algebraic]
trait AdditiveSemigroup[Algebraic]
trait Serializable
class Object
trait Matchable
class Any

Value members

Inherited methods

override
Definition Classes
AlgebraicIsReal -> Signed
Inherited from
AlgebraicIsReal
override
def additive: CommutativeGroup[Algebraic]
Definition Classes
AdditiveCommutativeGroup -> AdditiveCommutativeMonoid -> AdditiveCommutativeSemigroup -> AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
Inherited from
AdditiveCommutativeGroup
Inherited from
AlgebraicIsReal
def compare(x: Algebraic, y: Algebraic): Int
Inherited from
AlgebraicIsReal
def comparison(x: Algebraic, y: Algebraic): Comparison

Like compare, but returns a cats.kernel.Comparison instead of an Int. Has the benefit of being able to pattern match on, but not as performant.

Like compare, but returns a cats.kernel.Comparison instead of an Int. Has the benefit of being able to pattern match on, but not as performant.

Inherited from
Order
Inherited from
AlgebraicIsField
Inherited from
Field
Inherited from
Field
Definition Classes
Inherited from
Field
override
def eqv(x: Algebraic, y: Algebraic): Boolean
Definition Classes
AlgebraicIsReal -> Order -> PartialOrder -> Eq
Inherited from
AlgebraicIsReal
Inherited from
Field
Inherited from
AlgebraicIsReal
Inherited from
AlgebraicIsField
def fromBigInt(n: BigInt): Algebraic

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.

Inherited from
Ring
override
def fromDouble(n: Double): Algebraic
Definition Classes
AlgebraicIsField -> Field
Inherited from
AlgebraicIsField
override
def fromInt(n: Int): Algebraic
Definition Classes
AlgebraicIsField -> Ring
Inherited from
AlgebraicIsField
override
def gcd(a: Algebraic, b: Algebraic)(implicit eqA: Eq[Algebraic]): Algebraic
Definition Classes
Inherited from
WithDefaultGCD
override
def gt(x: Algebraic, y: Algebraic): Boolean

Returns true if x > y, false otherwise.

Returns true if x > y, false otherwise.

Definition Classes
Order -> PartialOrder
Inherited from
Order
override
def gteqv(x: Algebraic, y: Algebraic): Boolean

Returns true if x >= y, false otherwise.

Returns true if x >= y, false otherwise.

Definition Classes
Order -> PartialOrder
Inherited from
Order
def isOne(a: Algebraic)(implicit ev: Eq[Algebraic]): Boolean

Tests if a is one.

Tests if a is one.

Inherited from
MultiplicativeMonoid
def isSignNegative(a: Algebraic): Boolean
Inherited from
Signed
def isSignNonNegative(a: Algebraic): Boolean
Inherited from
Signed
def isSignNonPositive(a: Algebraic): Boolean
Inherited from
Signed
def isSignNonZero(a: Algebraic): Boolean
Inherited from
Signed
def isSignPositive(a: Algebraic): Boolean
Inherited from
Signed
def isSignZero(a: Algebraic): Boolean
Inherited from
Signed
def isWhole(a: Algebraic): Boolean
Inherited from
AlgebraicIsReal
def isZero(a: Algebraic)(implicit ev: Eq[Algebraic]): Boolean

Tests if a is zero.

Tests if a is zero.

Inherited from
AdditiveMonoid
override
def lcm(a: Algebraic, b: Algebraic)(implicit eqA: Eq[Algebraic]): Algebraic
Definition Classes
Inherited from
WithDefaultGCD
override
def lt(x: Algebraic, y: Algebraic): Boolean

Returns true if x < y, false otherwise.

Returns true if x < y, false otherwise.

Definition Classes
Order -> PartialOrder
Inherited from
Order
override
def lteqv(x: Algebraic, y: Algebraic): Boolean

Returns true if x <= y, false otherwise.

Returns true if x <= y, false otherwise.

Definition Classes
Order -> PartialOrder
Inherited from
Order

If x > y, return x, else return y.

If x > y, return x, else return y.

Inherited from
Order

If x < y, return x, else return y.

If x < y, return x, else return y.

Inherited from
Order
override
Definition Classes
AlgebraicIsField -> AdditiveGroup
Inherited from
AlgebraicIsField
override
def multiplicative: CommutativeGroup[Algebraic]
Definition Classes
MultiplicativeCommutativeGroup -> MultiplicativeCommutativeMonoid -> MultiplicativeCommutativeSemigroup -> MultiplicativeGroup -> MultiplicativeMonoid -> MultiplicativeSemigroup
Inherited from
MultiplicativeCommutativeGroup
Inherited from
AlgebraicIsField
override
def neqv(x: Algebraic, y: Algebraic): Boolean
Definition Classes
AlgebraicIsReal -> Order -> Eq
Inherited from
AlgebraicIsReal
def nroot(a: Algebraic, k: Int): Algebraic
Inherited from
AlgebraicIsField
Inherited from
AlgebraicIsField
def partialCompare(x: Algebraic, y: Algebraic): Double
Inherited from
Order
def partialComparison(x: Algebraic, y: Algebraic): Option[Comparison]

Like partialCompare, but returns a cats.kernel.Comparison instead of an Double. Has the benefit of being able to pattern match on, but not as performant.

Like partialCompare, but returns a cats.kernel.Comparison instead of an Double. Has the benefit of being able to pattern match on, but not as performant.

Inherited from
PartialOrder
Inherited from
AlgebraicIsField
def pmax(x: Algebraic, y: Algebraic): Option[Algebraic]

Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.

Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.

Inherited from
PartialOrder
def pmin(x: Algebraic, y: Algebraic): Option[Algebraic]

Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.

Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.

Inherited from
PartialOrder
override
def pow(a: Algebraic, b: Int): Algebraic
Definition Classes
AlgebraicIsField -> MultiplicativeGroup -> MultiplicativeMonoid -> MultiplicativeSemigroup
Inherited from
AlgebraicIsField
def product(as: IterableOnce[Algebraic]): Algebraic

Given a sequence of as, compute the product.

Given a sequence of as, compute the product.

Inherited from
MultiplicativeMonoid
Inherited from
MultiplicativeGroup
Inherited from
AlgebraicIsReal
override
Definition Classes
AlgebraicIsReal -> Signed
Inherited from
AlgebraicIsReal
override
def signum(a: Algebraic): Int
Definition Classes
AlgebraicIsReal -> Signed
Inherited from
AlgebraicIsReal
Inherited from
NRoot
def sum(as: IterableOnce[Algebraic]): Algebraic

Given a sequence of as, compute the sum.

Given a sequence of as, compute the sum.

Inherited from
AdditiveMonoid
override
def sumN(a: Algebraic, n: Int): Algebraic
Definition Classes
AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
Inherited from
AdditiveGroup
override
Definition Classes
AlgebraicIsField -> MultiplicativeSemigroup
Inherited from
AlgebraicIsField
Inherited from
AlgebraicIsReal
Inherited from
AlgebraicIsReal
def toBigIntOpt(a: Algebraic): Opt[BigInt]
Inherited from
AlgebraicIsReal
def toDouble(x: Algebraic): Double
Inherited from
AlgebraicIsReal
def toOrdering: Ordering[Algebraic]

Convert a Order[A] to a scala.math.Ordering[A] instance.

Convert a Order[A] to a scala.math.Ordering[A] instance.

Inherited from
Order
Inherited from
IsAlgebraic
Inherited from
AlgebraicIsReal
def tryCompare(x: Algebraic, y: Algebraic): Option[Int]

Result of comparing x with y. Returns None if operands are not comparable. If operands are comparable, returns Some[Int] where the Int sign is:

Result of comparing x with y. Returns None if operands are not comparable. If operands are comparable, returns Some[Int] where the Int sign is:

  • negative iff x < y
  • zero iff x = y
  • positive iff x > y
Inherited from
PartialOrder
override
def tryProduct(as: IterableOnce[Algebraic]): Option[Algebraic]
Definition Classes
MultiplicativeMonoid -> MultiplicativeSemigroup
Inherited from
MultiplicativeMonoid
override
def trySum(as: IterableOnce[Algebraic]): Option[Algebraic]
Definition Classes
AdditiveMonoid -> AdditiveSemigroup
Inherited from
AdditiveMonoid
Inherited from
AlgebraicIsField