com.alecdorrington.scalgebra.normed

Members list

Type members

Classlikes

object Normed extends Ops

The companion object for Normed.

The companion object for Normed.

Attributes

Companion
trait
Supertypes
trait Ops
class Object
trait Matchable
class Any
Self type
Normed.type
trait Normed[X, S] extends Root[X]

For algebraic structures with a norm.

For algebraic structures with a norm.

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Companion
object
Supertypes
trait Root[X]
class Object
trait Matchable
class Any
Known subtypes

A normed version of AdditiveGroup.

A normed version of AdditiveGroup.

Attributes

Companion
object
Supertypes
trait NormedAdditiveInverse[X, S]
trait NormedAdditiveMonoid[X, S]
trait NormedDifference[X, S]
trait Normed[X, S]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
trait NormedPseudoring[X, S]
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
object NormedAdditiveGroup extends Ops

The companion object for NormedAdditiveGroup.

The companion object for NormedAdditiveGroup.

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trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
trait NormedAdditiveIdentity[X, S] extends AdditiveIdentity[X], Normed[X, S]

A normed version of AdditiveIdentity.

A normed version of AdditiveIdentity.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait AdditiveIdentity[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
object NormedAdditiveIdentity extends Ops

The companion object for NormedAdditiveIdentity.

The companion object for NormedAdditiveIdentity.

Attributes

Companion
trait
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trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
object NormedAdditiveInverse extends Ops

The companion object for NormedAdditiveInverse.

The companion object for NormedAdditiveInverse.

Attributes

Companion
trait
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trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
trait NormedAdditiveInverse[X, S] extends AdditiveInverse[X], Normed[X, S]

A normed version of AdditiveInverse.

A normed version of AdditiveInverse.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait AdditiveInverse[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
trait NormedAdditiveGroup[X, S]
trait NormedPseudoring[X, S]
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]

A normed version of AdditiveMonoid.

A normed version of AdditiveMonoid.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
object NormedAdditiveMonoid extends Ops

The companion object for NormedAdditiveMonoid.

The companion object for NormedAdditiveMonoid.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
trait NormedAdditiveSemigroup[X, S] extends AdditiveSemigroup[X], Normed[X, S]

A normed version of AdditiveSemigroup.

A normed version of AdditiveSemigroup.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
object NormedAdditiveSemigroup extends Ops

The companion object for NormedAdditiveSemigroup.

The companion object for NormedAdditiveSemigroup.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
trait NormedDifference[X, S] extends Difference[X], Normed[X, S]

A normed version of Difference.

A normed version of Difference.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
trait NormedAdditiveGroup[X, S]
trait NormedPseudoring[X, S]
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
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object NormedDifference extends Ops

The companion object for NormedDifference.

The companion object for NormedDifference.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of DifferenceMonoid.

A normed version of DifferenceMonoid.

Attributes

Companion
object
Supertypes
trait NormedAdditiveMonoid[X, S]
trait NormedDifference[X, S]
trait Normed[X, S]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedAdditiveGroup[X, S]
trait NormedPseudoring[X, S]
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
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object NormedDifferenceMonoid extends Ops

The companion object for NormedDifferenceMonoid.

The companion object for NormedDifferenceMonoid.

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Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

The companion object for NormedDifferenceSemifield.

The companion object for NormedDifferenceSemifield.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of DifferenceSemifield.

A normed version of DifferenceSemifield.

Attributes

Companion
object
Supertypes
trait NormedSemifield[X, S]
trait NormedEuclideanMonoid[X, S]
trait NormedDifference[X, S]
trait NormedSemiring[X, S]
trait NormedAdditiveMonoid[X, S]
trait Normed[X, S]
trait Semifield[X]
trait EuclideanMonoid[X]
trait Euclidean[X]
trait DifferenceMonoid[X]
trait Difference[X]
trait Semiring[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
trait NormedField[X, S]

A normed version of DifferenceSemigroup.

A normed version of DifferenceSemigroup.

Attributes

Companion
object
Supertypes
trait NormedDifference[X, S]
trait Normed[X, S]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedAdditiveGroup[X, S]
trait NormedPseudoring[X, S]
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
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The companion object for NormedDifferenceSemigroup.

The companion object for NormedDifferenceSemigroup.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
object NormedDifferenceSemiring extends Ops

The companion object for NormedDifferenceSemiring.

The companion object for NormedDifferenceSemiring.

Attributes

Companion
trait
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trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of DifferenceSemiring.

A normed version of DifferenceSemiring.

Attributes

Companion
object
Supertypes
trait NormedDifference[X, S]
trait NormedSemiring[X, S]
trait NormedAdditiveMonoid[X, S]
trait Normed[X, S]
trait DifferenceMonoid[X]
trait Difference[X]
trait Semiring[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
trait NormedField[X, S]
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedEuclidean[X, S] extends Euclidean[X], Normed[X, S]

A normed version of Euclidean.

A normed version of Euclidean.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Euclidean[X]
trait Root[X]
class Object
trait Matchable
class Any
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object NormedEuclidean extends Ops

The companion object for NormedEuclidean.

The companion object for NormedEuclidean.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
object NormedEuclideanMonoid extends Ops

The companion object for NormedEuclideanMonoid.

The companion object for NormedEuclideanMonoid.

Attributes

Companion
trait
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trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of EuclideanMonoid.

A normed version of EuclideanMonoid.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait EuclideanMonoid[X]
trait Euclidean[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
trait NormedSemifield[X, S]
object NormedEuclideanRing extends Ops

The companion object for NormedEuclideanRing.

The companion object for NormedEuclideanRing.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
class Object
trait Matchable
class Any
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Self type
trait NormedEuclideanRing[X, S] extends EuclideanRing[X], NormedRing[X, S], NormedEuclideanMonoid[X, S]

A normed version of EuclideanRing.

A normed version of EuclideanRing.

Attributes

Companion
object
Supertypes
trait NormedEuclideanMonoid[X, S]
trait NormedRing[X, S]
trait NormedSemiring[X, S]
trait NormedPseudoring[X, S]
trait NormedAdditiveGroup[X, S]
trait NormedAdditiveInverse[X, S]
trait NormedAdditiveMonoid[X, S]
trait NormedDifference[X, S]
trait Normed[X, S]
trait EuclideanRing[X]
trait EuclideanMonoid[X]
trait Euclidean[X]
trait Ring[X]
trait Semiring[X]
trait Pseudoring[X]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedField[X, S]

A normed version of EuclideanSemigroup.

A normed version of EuclideanSemigroup.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Euclidean[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedEuclideanMonoid[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
trait NormedSemifield[X, S]
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object NormedEuclideanSemigroup extends Ops

The companion object for NormedEuclideanSemigroup.

The companion object for NormedEuclideanSemigroup.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
object NormedField extends Ops

The companion object for NormedField.

The companion object for NormedField.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
trait NormedField[X, S] extends Field[X], NormedEuclideanRing[X, S], NormedDifferenceSemifield[X, S]

A normed version of Field.

A normed version of Field.

Attributes

Companion
object
Supertypes
trait NormedSemifield[X, S]
trait NormedEuclideanRing[X, S]
trait NormedEuclideanMonoid[X, S]
trait NormedRing[X, S]
trait NormedSemiring[X, S]
trait NormedPseudoring[X, S]
trait NormedAdditiveGroup[X, S]
trait NormedAdditiveInverse[X, S]
trait NormedAdditiveMonoid[X, S]
trait NormedDifference[X, S]
trait Normed[X, S]
trait Field[X]
trait Semifield[X]
trait EuclideanRing[X]
trait EuclideanMonoid[X]
trait Euclidean[X]
trait Ring[X]
trait Semiring[X]
trait Pseudoring[X]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
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The companion object for NormedMultiplicativeGroup.

The companion object for NormedMultiplicativeGroup.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of MultiplicativeGroup.

A normed version of MultiplicativeGroup.

Attributes

Companion
object
Supertypes
trait NormedEuclideanMonoid[X, S]
trait Normed[X, S]
trait EuclideanMonoid[X]
trait Euclidean[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedSemifield[X, S]
trait NormedField[X, S]

The companion object for NormedMultiplicativeIdentity.

The companion object for NormedMultiplicativeIdentity.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of MultiplicativeIdentity.

A normed version of MultiplicativeIdentity.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedEuclideanMonoid[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
trait NormedSemifield[X, S]
trait NormedSemiring[X, S]
trait NormedRing[X, S]
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A normed version of MultiplicativeInverse.

A normed version of MultiplicativeInverse.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedSemifield[X, S]
trait NormedField[X, S]

The companion object for NormedMultiplicativeInverse.

The companion object for NormedMultiplicativeInverse.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

The companion object for NormedMultiplicativeMonoid.

The companion object for NormedMultiplicativeMonoid.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of MultiplicativeMonoid.

A normed version of MultiplicativeMonoid.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedEuclideanMonoid[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
trait NormedSemifield[X, S]
trait NormedSemiring[X, S]
trait NormedRing[X, S]
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The companion object for NormedMultiplicativeSemigroup.

The companion object for NormedMultiplicativeSemigroup.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of MultiplicativeSemigroup.

A normed version of MultiplicativeSemigroup.

Attributes

Companion
object
Supertypes
trait Normed[X, S]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedEuclideanMonoid[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
trait NormedSemifield[X, S]
trait NormedSemiring[X, S]
trait NormedRing[X, S]
trait NormedPseudoring[X, S]
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A normed version of Pseudoring.

A normed version of Pseudoring.

Attributes

Companion
object
Supertypes
trait NormedAdditiveGroup[X, S]
trait NormedAdditiveInverse[X, S]
trait NormedAdditiveMonoid[X, S]
trait NormedDifference[X, S]
trait Normed[X, S]
trait Pseudoring[X]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
object NormedPseudoring extends Ops

The companion object for NormedPseudoring.

The companion object for NormedPseudoring.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
object NormedRing extends Ops

The companion object for NormedRing.

The companion object for NormedRing.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
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class Object
trait Matchable
class Any
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Self type
NormedRing.type
trait NormedRing[X, S] extends Ring[X], NormedPseudoring[X, S], NormedDifferenceSemiring[X, S]

A normed version of Ring.

A normed version of Ring.

Attributes

Companion
object
Supertypes
trait NormedSemiring[X, S]
trait NormedPseudoring[X, S]
trait NormedAdditiveGroup[X, S]
trait NormedAdditiveInverse[X, S]
trait NormedAdditiveMonoid[X, S]
trait NormedDifference[X, S]
trait Normed[X, S]
trait Ring[X]
trait Semiring[X]
trait Pseudoring[X]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Difference[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedEuclideanRing[X, S]
trait NormedField[X, S]
trait NormedSemifield[X, S] extends Semifield[X], NormedSemiring[X, S], NormedMultiplicativeGroup[X, S]

A normed version of Semifield.

A normed version of Semifield.

Attributes

Companion
object
Supertypes
trait NormedEuclideanMonoid[X, S]
trait NormedSemiring[X, S]
trait NormedAdditiveMonoid[X, S]
trait Normed[X, S]
trait Semifield[X]
trait EuclideanMonoid[X]
trait Euclidean[X]
trait Semiring[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Root[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait NormedField[X, S]
object NormedSemifield extends Ops

The companion object for NormedSemifield.

The companion object for NormedSemifield.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
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trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type
object NormedSemiring extends Ops

The companion object for NormedSemiring.

The companion object for NormedSemiring.

Attributes

Companion
trait
Supertypes
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
trait Ops
class Object
trait Matchable
class Any
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Self type

A normed version of Semiring.

A normed version of Semiring.

Attributes

Companion
object
Supertypes
trait NormedAdditiveMonoid[X, S]
trait Normed[X, S]
trait Semiring[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
trait Root[X]
class Object
trait Matchable
class Any
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Known subtypes
trait NormedField[X, S]
trait NormedRing[X, S]
trait NormedEuclideanRing[X, S]
trait NormedSemifield[X, S]
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