axle

# algebra

#### package algebra

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### Type Members

1. #### trait Aggregatable[F, A, B] extends AnyRef

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3. #### trait ArrayFrom[C, A] extends AnyRef

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4. #### trait Bijection[A, B] extends (A) ⇒ B

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6. #### trait DirectedGraph[DG, V, E] extends AnyRef

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8. #### trait Endofunctor[E, T] extends AnyRef

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9. #### trait Finite[C, S] extends AnyRef

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11. #### trait FoldLeft[F[_]] extends AnyRef

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13. #### trait FunctionPair[A, B] extends AnyRef

A FunctionPair is not necessarily a bijection, but it could be.

A FunctionPair is not necessarily a bijection, but it could be.

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14. #### trait Functor[F, A, B, G] extends AnyRef

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17. #### trait Indexed[C, I, A] extends AnyRef

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19. #### trait LengthSpace[V, R, P] extends MetricSpace[V, R]

http://en.wikipedia.org/wiki/Intrinsic_metric

http://en.wikipedia.org/wiki/Intrinsic_metric

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20. #### trait LinearAlgebra[M, R, C, T] extends AnyRef

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21. #### trait MapFrom[C, K, V] extends AnyRef

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22. #### trait MapReducible[M, A, B, K, G] extends AnyRef

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23. #### trait Plottable[T] extends AnyRef

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26. #### trait Reducible[R, A] extends AnyRef

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30. #### trait Scanner[S, A, B, T] extends AnyRef

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31. #### trait SetFrom[C, A] extends AnyRef

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32. #### case class SphericalVector[N](ρ: UnittedQuantity[Distance, N], θ: UnittedQuantity[Angle, N], φ: UnittedQuantity[Angle, N]) extends Product with Serializable

Uses the physics conventions instead of mathematical conventions.

Uses the physics conventions instead of mathematical conventions.

http://en.wikipedia.org/wiki/Spherical_coordinate_system

33. #### trait Talliable[F, A, N] extends AnyRef

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36. #### trait UndirectedGraph[UG, V, E] extends AnyRef

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37. #### trait Vec[V[_]] extends AnyRef

Vec is the Vector typeclass

Vec is the Vector typeclass

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Zero

Zero

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### Value Members

31. #### def generalizedFMean[N, F](f: Bijection[N, N], ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N]): N

Generalized f-Mean

Generalized f-Mean

https://en.wikipedia.org/wiki/Generalized_mean#Generalized_f-mean

https://en.wikipedia.org/wiki/Quasi-arithmetic_mean

TODO f need only be injective

32. #### def generalizedMean[N, F](p: N, ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N], nroot: NRoot[N]): N

Generalized mean

Generalized mean

https://en.wikipedia.org/wiki/Generalized_mean

TODO could be special-cased for p = -∞ or ∞

36. #### def mean[N, F](ns: F)(implicit field: Field[N], aggregatable: Aggregatable[F, N, N], finite: Finite[F, N]): N

arithmetic, geometric, and harmonic means are "Pythagorean"

arithmetic, geometric, and harmonic means are "Pythagorean"

https://en.wikipedia.org/wiki/Pythagorean_means