Scalgebra
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Scalgebra/com.alecdorrington.scalgebra/com.alecdorrington.scalgebra.ordered/OrderedEuclideanRing

OrderedEuclideanRing

com.alecdorrington.scalgebra.ordered.OrderedEuclideanRing
See theOrderedEuclideanRing companion trait
object OrderedEuclideanRing extends Ops

The companion object for OrderedEuclideanRing.

Attributes

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trait Ops
trait Ops
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trait Ops
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trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
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trait Ops
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trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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class Object
trait Matchable
class Any
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Type members

Classlikes

trait Ops extends Ops, Ops, Ops

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Known subtypes
trait Ops
object OrderedField

Value members

Concrete methods

inline def orderedEuclideanRing[X](using orderedEuclideanRing: OrderedEuclideanRing[X]): OrderedEuclideanRing[X]

The OrderedEuclideanRing instance describing the current algebra system.

The OrderedEuclideanRing instance describing the current algebra system.

Attributes

Inherited methods

inline def abs[X](x: X)(using X: OrderedAdditiveGroup[X]): X

Computes the absolute value of a value x, i.e. |x|.

Computes the absolute value of a value x, i.e. |x|.

Attributes

Inherited from:
Ops
inline def add[X](x: X, y: X)(using X: AdditiveSemigroup[X]): X

Computes the sum of two values x and y, i.e. x + y.

Computes the sum of two values x and y, i.e. x + y.

Attributes

Note

All implementations must be associative, i.e. (x + y) + z == x + (y + z).

Inherited from:
Ops
inline def divide[X](x: X, y: X)(using X: Euclidean[X]): X

Computes the quotient between two values x and y, i.e. x / y.

Computes the quotient between two values x and y, i.e. x / y.

Attributes

Inherited from:
Ops
inline def gcd[X](x: X, y: X)(using X: EuclideanRing[X]): X

Computes the greatest common divisor of two values x and y.

Computes the greatest common divisor of two values x and y.

Attributes

Inherited from:
Ops
inline def isNegative[X](x: X)(using X: OrderedAdditiveIdentity[X]): Boolean

Attributes

Returns

true if x is strictly negative, i.e. x < 0.

Inherited from:
Ops
inline def isNonNegative[X](x: X)(using X: OrderedAdditiveIdentity[X]): Boolean

Attributes

Returns

true if x is positive or zero, i.e. x ≥ 0.

Inherited from:
Ops
inline def isNonPositive[X](x: X)(using X: OrderedAdditiveIdentity[X]): Boolean

Attributes

Returns

true if x is negative or zero, i.e. x ≤ 0.

Inherited from:
Ops
inline def isOne[X](x: X)(using X: MultiplicativeIdentity[X]): Boolean

Attributes

Returns

true if x equals one.

Inherited from:
Ops
inline def isPositive[X](x: X)(using X: OrderedAdditiveIdentity[X]): Boolean

Attributes

Returns

true if x is strictly positive, i.e. x > 0.

Inherited from:
Ops
inline def isZero[X](x: X)(using X: AdditiveIdentity[X]): Boolean

Attributes

Returns

true if x equals zero.

Inherited from:
Ops
inline def lcm[X](x: X, y: X)(using X: EuclideanRing[X]): X

Computes the least common multiple of two values x and y.

Computes the least common multiple of two values x and y.

Attributes

Inherited from:
Ops
inline def mod[X](x: X, y: X)(using X: EuclideanRing[X]): X

Computes the signed remainder between two values x and y.

Computes the signed remainder between two values x and y.

Attributes

Inherited from:
Ops
inline def multiply[X](x: X, y: X)(using X: MultiplicativeSemigroup[X]): X

Computes the product of two values x and y, i.e. x × y.

Computes the product of two values x and y, i.e. x × y.

Attributes

Note

All implementations must be associative, i.e. (x × y) × z == x × (y × z).

Inherited from:
Ops
inline def negate[X](x: X)(using X: AdditiveInverse[X]): X

Computes the additive inverse (negative) of a value x, i.e. -x.

Computes the additive inverse (negative) of a value x, i.e. -x.

Attributes

Note

All implementations must be involutions, i.e. negate(negate(x)) == x.

Inherited from:
Ops
inline def negativeOne[X](using X: Ring[X]): X

Attributes

Inherited from:
Ops
inline def one[X](using X: MultiplicativeIdentity[X]): X

The unique representation of the multiplicative identity (1) in this algebra system. Typically corresponds to values such as 1 or 1.0F.

The unique representation of the multiplicative identity (1) in this algebra system. Typically corresponds to values such as 1 or 1.0F.

Attributes

Note

All implementations must obey the identity property, i.e. x × one == one × x == x.

Inherited from:
Ops
inline def pow[X](x: X, n: Int)(using X: MultiplicativeSemigroup[X]): X

Computes x raised to the power n, for any strictly positive n.

Computes x raised to the power n, for any strictly positive n.

Attributes

Throws
IllegalArgumentException

if n ≤ 0.

Inherited from:
Ops
inline def pow[X](x: X, n: Int)(using X: MultiplicativeMonoid[X]): X

Computes x raised to the power n, for any non-negative n.

Computes x raised to the power n, for any non-negative n.

Attributes

Throws
IllegalArgumentException

if n < 0.

Inherited from:
Ops
inline def product[X](x: X, xs: X*)(using X: MultiplicativeSemigroup[X]): X

Computes the product of x and all values in xss, i.e. x × xs₁ × xs₂ × ….

Computes the product of x and all values in xss, i.e. x × xs₁ × xs₂ × ….

Attributes

Inherited from:
Ops
inline def product[X](xs: Iterable[X])(using X: MultiplicativeMonoid[X]): X

Computes the product of all values in xs, i.e. xs₁ × xs₂ × …, or else one if xs is empty.

Computes the product of all values in xs, i.e. xs₁ × xs₂ × …, or else one if xs is empty.

Attributes

Inherited from:
Ops
inline def productOption[X](xs: Iterable[X])(using X: MultiplicativeSemigroup[X]): Option[X]

Computes the product of all values in xs, i.e. xs₁ × xs₂ × …, or else None if xs is empty.

Computes the product of all values in xs, i.e. xs₁ × xs₂ × …, or else None if xs is empty.

Attributes

Inherited from:
Ops
inline def scale[X](x: X, n: Int)(using X: AdditiveSemigroup[X]): X

Computes x multiplied by n, for any strictly positive n.

Computes x multiplied by n, for any strictly positive n.

Attributes

Throws
IllegalArgumentException

if n ≤ 0.

Inherited from:
Ops
inline def scale[X](x: X, n: Int)(using X: AdditiveMonoid[X]): X

Computes x multiplied by n, for any non-negative n.

Computes x multiplied by n, for any non-negative n.

Attributes

Throws
IllegalArgumentException

if n < 0.

Inherited from:
Ops
inline def scale[X](x: X, n: Int)(using X: AdditiveGroup[X]): X

Computes x multiplied by n, for any integer n.

Computes x multiplied by n, for any integer n.

Attributes

Inherited from:
Ops
inline def sign[X](x: X)(using X: OrderedRing[X]): X

Computes the sign of a value x, represented by one for positive, negativeOne for negative, or zero for itself.

Computes the sign of a value x, represented by one for positive, negativeOne for negative, or zero for itself.

Attributes

Inherited from:
Ops
inline def subtract[X](x: X, y: X)(using X: Difference[X]): X

Computes the difference between two values x and y, i.e. x - y.

Computes the difference between two values x and y, i.e. x - y.

Attributes

Inherited from:
Ops
inline def subtract[X](x: X, y: X)(using X: AdditiveGroup[X]): X

Computes the difference between two values x and y, i.e. x - y.

Computes the difference between two values x and y, i.e. x - y.

Attributes

Inherited from:
Ops
inline def sum[X](x: X, xs: X*)(using X: AdditiveSemigroup[X]): X

Computes the sum of x and all values in xs, i.e. x + xs₁ + xs₂ + ….

Computes the sum of x and all values in xs, i.e. x + xs₁ + xs₂ + ….

Attributes

Inherited from:
Ops
inline def sum[X](xs: Iterable[X])(using X: AdditiveMonoid[X]): X

Computes the sum of all values in xs, i.e. xs₁ + xs₂ + …, or else zero if xs is empty.

Computes the sum of all values in xs, i.e. xs₁ + xs₂ + …, or else zero if xs is empty.

Attributes

Inherited from:
Ops
inline def sumOption[X](xs: Iterable[X])(using X: AdditiveSemigroup[X]): Option[X]

Computes the sum of all values in xs, i.e. xs₁ + xs₂ + …, or else None if xs is empty.

Computes the sum of all values in xs, i.e. xs₁ + xs₂ + …, or else None if xs is empty.

Attributes

Inherited from:
Ops
inline def two[X](using X: Semiring[X]): X

Attributes

Inherited from:
Ops
inline def zero[X](using X: AdditiveIdentity[X]): X

The unique representation of the additive identity (0) in this algebra system. Typically corresponds to values such as 0, 0.0F, or Seq.empty.

The unique representation of the additive identity (0) in this algebra system. Typically corresponds to values such as 0, 0.0F, or Seq.empty.

Attributes

Note

All implementations must obey the identity property, i.e. x + zero == zero + x == x.

Inherited from:
Ops

Exports

Defined exports

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