Interface GradedAlgebra<E,F>

All Superinterfaces:
AbelianGroup<E>, AbelianMonoid<E>, Algebra<E,F>, Group<E>, Magma<E>, Module<E,F>, Monoid<E>, Ring<E>, Semiring<E>, Set<E>
public interface GradedAlgebra<E,F> extends Algebra<E,F>
Represents a graded algebra - an algebra that can be decomposed into a direct sum of subspaces indexed by a grading group (typically integers).

A graded algebra A = ⊕ᵢ Aᵢ where the multiplication respects the grading: Aᵢ · Aⱼ ⊆ Aᵢ₊ⱼ

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Details

    • grade

      int grade(E element)
      Returns the grade (degree) of the given element.

    • projectToGrade

      E projectToGrade(E element, int grade)
      Projects an element onto the homogeneous component of the specified grade.

    • isHomogeneous

      boolean isHomogeneous(E element)
      Returns true if the element is homogeneous (has a single grade).

    • maxGrade

      int maxGrade()
      Returns the maximum grade present in this algebra, or -1 if infinite.

    • minGrade

      default int minGrade()
      Returns the minimum grade present in this algebra.