algebra

Type Members

1. type AbGroup[A] = CommutativeGroup[A]

2. trait Action[P, G] extends LeftAction[P, G] with RightAction[P, G]

   A semigroup/monoid/group action of G on P is the combination of compatible left and right actions, providing:

3. type AdditiveAbGroup[A] = AdditiveCommutativeGroup[A]

4. trait AdditiveAction[P, G] extends Any

5. type AdditiveCMonoid[A] = AdditiveCommutativeMonoid[A]

6. type AdditiveCSemigroup[A] = AdditiveCommutativeSemigroup[A]

7. type AdditiveGroup[A] = algebra.ring.AdditiveGroup[A]

8. type AdditiveMonoid[A] = algebra.ring.AdditiveMonoid[A]

9. type AdditiveSemigroup[A] = algebra.ring.AdditiveSemigroup[A]

10. trait AdditiveTorsor[V, R] extends AdditiveAction[V, R]

11. type AlgebraField[A] = algebra.ring.Field[A]

12. type Bool[A] = algebra.lattice.Bool[A]

13. type CMonoid[A] = CommutativeMonoid[A]

14. type CRig[A] = CommutativeRig[A]

15. type CRing[A] = CommutativeRing[A]

16. type CRng[A] = CommutativeRng[A]

17. type CSemigroup[A] = CommutativeSemigroup[A]

18. type CSemiring[A] = CommutativeSemiring[A]

19. trait CoordinateSpace[V, F] extends InnerProductSpace[V, F]

20. trait DivisionRing[A] extends Ring[A] with MultiplicativeGroup[A]

21. type Eq[A] = cats.kernel.Eq[A]

22. trait EuclideanRing[A] extends GCDRing[A]

    EuclideanRing implements a Euclidean domain.

23. trait EuclideanRingFunctions[R[T] <: EuclideanRing[T]] extends GCDRingFunctions[R]

24. trait Field[A] extends AlgebraField[A] with EuclideanRing[A]

25. trait FieldAlgebra[V, F] extends RingAlgebra[V, F] with VectorSpace[V, F]

    A FieldAlgebra is a vector space that is also a Ring.

26. trait GCDRing[A] extends CRing[A]

    GCDRing implements a GCD ring.

27. trait GCDRingFunctions[R[T] <: GCDRing[T]] extends RingFunctions[R]

28. type Group[A] = cats.kernel.Group[A]

29. trait InnerProductSpace[V, F] extends VectorSpace[V, F]

30. trait IsAlgebraic[A] extends IsReal[A]

31. trait IsIntegral[A] extends IsRational[A]

32. trait IsRational[A] extends IsAlgebraic[A]

33. trait IsReal[A] extends Signed[A]

    A simple type class for numeric types that are a subset of the reals.

34. trait LeftAction[P, G] extends Any

    A (left) semigroup/monoid/group action of G on P is simply the implementation of a method actl(g, p), or g |+|> p, such that:

35. trait MetricSpace[V, R] extends Any

    This type class models a metric space V.

36. trait Module[V, R] extends AdditiveAbGroup[V]

    A module generalizes a vector space by requiring its scalar need only form a ring, rather than a field.

37. type Monoid[A] = cats.kernel.Monoid[A]

38. type MultiplicativeAbGroup[A] = MultiplicativeCommutativeGroup[A]

39. trait MultiplicativeAction[P, G] extends Any

40. type MultiplicativeCMonoid[A] = MultiplicativeCommutativeMonoid[A]

41. type MultiplicativeCSemigroup[A] = MultiplicativeCommutativeSemigroup[A]

42. type MultiplicativeGroup[A] = algebra.ring.MultiplicativeGroup[A]

43. type MultiplicativeMonoid[A] = algebra.ring.MultiplicativeMonoid[A]

44. type MultiplicativeSemigroup[A] = algebra.ring.MultiplicativeSemigroup[A]

45. trait MultiplicativeTorsor[V, R] extends MultiplicativeAction[V, R]

46. trait NRoot[A] extends Any

    This is a type class for types with n-roots.

47. trait NormedVectorSpace[V, F] extends VectorSpace[V, F] with MetricSpace[V, F]

    A normed vector space is a vector space equipped with a function norm: V => F.

48. type Order[A] = cats.kernel.Order[A]

49. type PartialOrder[A] = cats.kernel.PartialOrder[A]

50. type Rig[A] = algebra.ring.Rig[A]

51. trait RightAction[P, G] extends Any

    A (right) semigroup/monoid/group action of G on P is simply the implementation of a method actr(p, g), or p <|+| g, such that:

52. type Ring[A] = algebra.ring.Ring[A]

53. trait RingAlgebra[V, R] extends Module[V, R] with Rng[V]

    A RingAlgebra is a module that is also a Rng.

54. type Rng[A] = algebra.ring.Rng[A]

55. type Semigroup[A] = cats.kernel.Semigroup[A]

56. type Semiring[A] = algebra.ring.Semiring[A]

57. sealed abstract class Sign extends AnyRef

    A simple ADT representing the Sign of an object.

58. trait Signed[A] extends Order[A]

    A trait for linearly ordered additive commutative monoid.

59. trait SignedAdditiveAbGroup[A] extends SignedAdditiveCMonoid[A] with AdditiveAbGroup[A]

60. trait SignedAdditiveCMonoid[A] extends Signed[A] with AdditiveCMonoid[A]

61. trait Torsor[V, R] extends Action[V, R]

    A Torsor[V, R] requires an AbGroup[R] and provides Action[V, R], plus a diff operator, <-> in additive notation, such that:

62. trait Trig[A] extends Any

63. trait VectorSpace[V, F] extends Module[V, F]

    A vector space is a group V that can be multiplied by scalars in F that lie in a field.

64. trait ZAlgebra[V] extends RingAlgebra[V, Int] with Ring[V]

    Given any Ring[A] we can construct a RingAlgebra[A, Int].

65. final case class ZModule[V](vector: Group[V]) extends Module[V, Int] with Product with Serializable