Trac #21254: Implement cluster algebras using the Parent-Element fram…

…ework

This module uses structural results from "Cluster algebras IV" to
implement cluster algebras as a subobject of
`LaurentPolynomialRing_generic`.

It provides a new class `ClusterAlgebra`, and two new auxiliary classes
`ClusterAlgebraSeed` and `ClusterAlgebraElement`.

URL: https://trac.sagemath.org/21254
Reported by: etn40ff
Ticket author(s): Dylan Rupel, Salvatore Stella
Reviewer(s): Frédéric Chapoton

src/doc/en/reference/algebras/index.rst

@@ -42,6 +42,7 @@ Named associative algebras
    sage/algebras/affine_nil_temperley_lieb
    sage/combinat/diagram_algebras
    sage/algebras/clifford_algebra
+   sage/algebras/cluster_algebra
    sage/combinat/descent_algebra
    sage/algebras/hall_algebra
    sage/algebras/iwahori_hecke_algebra

src/sage/algebras/all.py

@@ -56,3 +56,4 @@
 
 lazy_import('sage.algebras.q_system', 'QSystem')
 
+lazy_import('sage.algebras.cluster_algebra', 'ClusterAlgebra')

src/sage/algebras/catalog.py

@@ -11,6 +11,7 @@
 
 - :class:`algebras.Brauer <sage.combinat.diagram_algebras.BrauerAlgebra>`
 - :class:`algebras.Clifford <sage.algebras.clifford_algebra.CliffordAlgebra>`
+- :class:`algebras.ClusterAlgebra <sage.algebras.cluster_algebra.ClusterAlgebra>`
 - :class:`algebras.Descent <sage.combinat.descent_algebra.DescentAlgebra>`
 - :class:`algebras.DifferentialWeyl
   <sage.algebras.weyl_algebra.DifferentialWeylAlgebra>`