Interface GroupElement<E extends GroupElement<E>>

public interface GroupElement<E extends GroupElement<E>>

Marker interface for elements of a group structure.

A group element supports a binary operation and inverse.

Group Axioms

• Closure: a ∘ b is in G
• Associativity: (a ∘ b) ∘ c = a ∘ (b ∘ c)
• Identity: e ∘ a = a ∘ e = a
• Inverse: a ∘ a⁻¹ = a⁻¹ ∘ a = e

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Method Summary

Modifier and Type	Method	Description
E	identity()	Returns the identity element of this group.
E	inverse()	Returns the inverse of this element.
E	operate(E other)	Applies the group operation with another element.

Method Details

operate

E operate(E other)

Applies the group operation with another element.

Parameters:

other - the other element

Returns:

this ∘ other

inverse

E inverse()

Returns the inverse of this element.

Returns:

this⁻¹

identity

E identity()

Returns the identity element of this group.

Returns:

the identity element e