algebra

Type Members

1. trait AbGroup[A] extends Group[A] with CMonoid[A]

   An abelian group is a group whose operation is commutative.

2. trait AdditiveAbGroup[A] extends AdditiveGroup[A] with AdditiveCMonoid[A]

3. trait AdditiveCMonoid[A] extends AdditiveMonoid[A] with AdditiveCSemigroup[A]

4. trait AdditiveCSemigroup[A] extends AdditiveSemigroup[A]

5. trait AdditiveGroup[A] extends AdditiveMonoid[A]

6. trait AdditiveMonoid[A] extends AdditiveSemigroup[A]

7. trait AdditiveSemigroup[A] extends AnyRef

8. trait BooleanAlgebra[A] extends AnyRef

   A boolean algebra is a structure that defines a few basic operations, namely as conjunction (&), disjunction (|), and negation (~).

9. trait CMonoid[A] extends Monoid[A] with CSemigroup[A]

   CMonoid represents a commutative monoid.

10. trait CRig[A] extends Rig[A] with MultiplicativeCMonoid[A]

    CRig is a Rig that is commutative under multiplication.

11. trait CRing[A] extends Ring[A] with MultiplicativeCMonoid[A]

    CRing is a Ring that is commutative under multiplication.

12. trait CSemigroup[A] extends Semigroup[A]

    CSemigroup represents a commutative semigroup.

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

14. trait Eq[A] extends AnyRef

    A type class used to determine equality between 2 instances of the same type.

15. trait EuclideanRing[A] extends CRing[A]

16. trait Field[A] extends EuclideanRing[A] with MultiplicativeAbGroup[A]

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

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

18. trait Group[A] extends Monoid[A]

    A group is a monoid where each element has an inverse.

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

20. trait IsIntegral[A] extends IsReal[A]

21. trait IsReal[A] extends Order[A] with Signed[A]

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

22. trait MetricSpace[V, R] extends AnyRef

    This type class models a metric space V.

23. 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.

24. trait Monoid[A] extends Semigroup[A]

    A monoid is a semigroup with an identity.

25. trait MultiplicativeAbGroup[A] extends MultiplicativeGroup[A] with MultiplicativeCMonoid[A]

26. trait MultiplicativeCMonoid[A] extends MultiplicativeMonoid[A] with MultiplicativeCSemigroup[A]

27. trait MultiplicativeCSemigroup[A] extends MultiplicativeSemigroup[A]

28. trait MultiplicativeGroup[A] extends MultiplicativeMonoid[A]

29. trait MultiplicativeMonoid[A] extends MultiplicativeSemigroup[A]

30. trait MultiplicativeSemigroup[A] extends AnyRef

31. trait NRoot[A] extends AnyRef

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

32. 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.

33. trait NormedVectorSpace0 extends AnyRef

34. trait NormedVectorSpaceFunctions extends AnyRef

35. trait Order[A] extends Eq[A]

    The Order type class is used to define a total ordering on some type A.

36. trait Rig[A] extends Semiring[A] with AdditiveMonoid[A] with MultiplicativeMonoid[A]

    Rig is a ring whose additive structure doesn't have an inverse (ie.

37. trait Ring[A] extends Rig[A] with Rng[A]

    Ring represents a set (A) that is a group over addition (+) and a monoid over multiplication (*).

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

    A RingAlgebra is a module that is also a Rng.

39. trait Rng[A] extends Semiring[A] with AdditiveAbGroup[A]

    Rng is a ring whose multiplicative structure doesn't have an identity (i.

40. trait Semigroup[A] extends AnyRef

    A semigroup is any set A with an associative operation (op).

41. trait Semiring[A] extends AdditiveMonoid[A] with MultiplicativeSemigroup[A]

    Semiring is a ring without identities or an inverse.

42. sealed abstract class Sign extends AnyRef

    A simple ADT representing the Sign of an object.

43. trait Signed[A] extends AnyRef

    A trait for things that have some notion of sign and the ability to ensure something has a positive sign.

44. trait Trig[A] extends AnyRef

45. 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.

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

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

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