For algebraic structures with addition, multiplication, and reciprocation.
Attributes
- Companion
- object
- Graph
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- Supertypes
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trait MultiplicativeGroup[X]trait MultiplicativeInverse[X]trait EuclideanMonoid[X]trait EuclideanSemigroup[X]trait Euclidean[X]trait Semiring[X]trait MultiplicativeMonoid[X]trait MultiplicativeIdentity[X]trait MultiplicativeSemigroup[X]trait AdditiveMonoid[X]trait AdditiveIdentity[X]trait AdditiveSemigroup[X]trait Root[X]class Objecttrait Matchableclass AnyShow all
- Known subtypes
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trait OrderedSemifield[X]trait OrderedDifferenceSemifield[X]trait OrderedField[X]trait DifferenceSemifield[X]trait Field[X]Show all
Members list
Value members
Inherited methods
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
- Definition Classes
- Inherited from:
- MultiplicativeGroup
Attributes
- Returns
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trueif x equals one. - Inherited from:
- MultiplicativeIdentity
Attributes
- Returns
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trueif x equals zero. - Inherited from:
- AdditiveIdentity
Computes x raised to the power n, for any integer n.
Computes x raised to the power n, for any integer n.
Attributes
- Definition Classes
- Inherited from:
- MultiplicativeGroup
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:
- MultiplicativeMonoid
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:
- MultiplicativeSemigroup
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:
- MultiplicativeSemigroup
Computes x multiplied by n, for any non-negative n.
Computes x multiplied by n, for any non-negative n.
Attributes
- Throws
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IllegalArgumentException
if
n < 0. - Definition Classes
- Inherited from:
- AdditiveMonoid
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:
- AdditiveMonoid
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:
- AdditiveSemigroup
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:
- AdditiveSemigroup
Inherited and Abstract methods
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
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All implementations must be associative, i.e.
(x + y) + z == x + (y + z). - Inherited from:
- AdditiveSemigroup
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
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All implementations must be associative, i.e.
(x × y) × z == x × (y × z). - Inherited from:
- MultiplicativeSemigroup
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
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All implementations must obey the identity property, i.e.
x × one == one × x == x. - Inherited from:
- MultiplicativeIdentity
Computes the multiplicative inverse (reciprocal) of a value x, i.e. 1 / x.
Computes the multiplicative inverse (reciprocal) of a value x, i.e. 1 / x.
Attributes
- Note
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All implementations must be involutions, i.e.
reciprocate(reciprocate(x)) == x. - Inherited from:
- MultiplicativeInverse
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
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All implementations must obey the identity property, i.e.
x + zero == zero + x == x. - Inherited from:
- AdditiveIdentity
Extensions
Inherited extensions
Computes the multiplicative inverse (reciprocal) of this value.
Computes the multiplicative inverse (reciprocal) of this value.
Attributes
- Inherited from:
- MultiplicativeInverse
Attributes
- Returns
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trueif x equals one. - Inherited from:
- MultiplicativeIdentity
Attributes
- Returns
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trueif x equals zero. - Inherited from:
- AdditiveIdentity
Alias of scale, with the factor on the left.
Computes the sum of two values x and y, i.e. x + y.
Alias of scale, with the factor on the right.
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
- Inherited from:
- MultiplicativeSemigroup
Alias of pow, with the exponent on the right.