Opened 3 years ago

Fix few bugs in ClusterAlgebra discovered while working on #26771 — at Initial Version

Reported by: Owned by: etn40ff major sage-8.9 algebra ClusterAlgebras tscrim, gmoose05, stumpc5, gh-EBanaian, drupel, gh-kelleye Salvatore Stella N/A

Description

As pointed out by the people at #26771, ClusterAlgebra has few bugs.

• Default arguments do not play nicely with UniqueRepresentation

sage: A1 = ClusterAlgebra(['A',2])
sage: A2 = ClusterAlgebra(['A',2], cluster_variable_prefix='x')
sage: A1 is A2
False
• mutate_initial keeps the same variable names; In theory this is not a problem but may create confusion. For example suppose we are looking at the Grassmannian of planes in a 4 dimensional vector space. Then the associate cluster algebra is
sage: A = ClusterAlgebra( matrix(5,[0,1,-1,1,-1]), cluster_variable_names=['p13'], coefficient_names=['p12','p23','p34','p41'], scalars=QQbar); A
A Cluster Algebra with cluster variable p13 and coefficients p12, p23, p34, p41 over Algebraic Field

Swapping out p13 from the initial seed should give p24 or, at the very least *not* p13. Getting p24 requires some understanding of what the ring in question really is that goes beyond the scope of this class. Currently we get

sage: A.mutate_initial(0)
A Cluster Algebra with cluster variable p13 and coefficients p12, p23, p34, p41 over Algebraic Field
• mutate_initial does not compute all the required F-polynomials and it does not enforce the fact that they are not rational expressions
sage: A1 = ClusterAlgebra(['A',[2,1],1])
sage: A2 = A1.mutate_initial([0,1,0])
sage: len(A2.g_vectors_so_far()) == len(A2.F_polynomials_so_far())
False
sage: all(parent(f) == A2._U for f in A2.F_polynomials_so_far())
False
• finally mutate_initial does not enforce the fact that initial g-vectors belong to the initial cluster but rather prepend the performed mutation sequence to all the paths already known.
sage: A2.find_g_vector((0,0,1))
[0, 1, 0]

This, while technically not false, may generate confusion.

This ticket deals with all these issues.

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