| Interface | Description |
|---|---|
| AbelianGroup<G> |
An Abelian group is a group with a binary additive operation (+), satisfying the group axioms:
closure
associativity
existence of additive identity
existence of additive opposite
commutativity of addition
|
| BanachSpace<B,F extends Field<F> & java.lang.Comparable<F>> |
A Banach space, B, is a complete normed vector space such that
every Cauchy sequence (with respect to the metric d(x, y) = |x − y|) in B has a limit in B.
|
| Field<F> |
As an algebraic structure, every field is a ring, but not every ring is a field.
|
| HilbertSpace<H,F extends Field<F> & java.lang.Comparable<F>> |
A Hilbert space is an inner product space, an abstract vector space in which distances and angles can be measured.
|
| Monoid<G> |
A monoid is a group with a binary operation (×), satisfying the group axioms:
closure
associativity
existence of multiplicative identity
|
| Ring<R> |
A ring is a set R equipped with two binary operations called addition and multiplication:
+ : R × R → R and
· : R × R → R
To qualify as a ring, the set and two operations, (R, +, ⋅), must satisfy the requirements known as the ring axioms. |
| VectorSpace<V,F extends Field<F>> |
A vector space is a set V together with two binary operations that combine two entities to yield a third,
called vector addition and scalar multiplication.
|
| Exception | Description |
|---|---|
| Field.InverseNonExistent |
This is the exception thrown when the inverse of a field element does not exist.
|