# Package com.numericalmethod.suanshu.algebra.structure

• Interface Summary
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> & 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> & 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 Summary
Exception Description
Field.InverseNonExistent
This is the exception thrown when the inverse of a field element does not exist.