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I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

EDIT: EDIT (2020-10-26): Problem not solved, but I found an issue that may be related https://trac.sagemath.org/ticket/6100 Namely, chain_complex().homology(generators=true) uses a basis in which the simplices are listed in an order that seems untractable (especially, not the lexicographic order). If one could guess in which order the simplices are listed, I could compute the cup products.

I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

EDIT (2020-10-26): Problem not solved, but I found an issue that may be a seempingly related https://trac.sagemath.org/ticket/6100 issue: https://trac.sagemath.org/ticket/6100 . Namely, chain_complex().homology(generators=true) uses a basis in which the simplices are listed in an order that seems untractable (especially, not the lexicographic order). If one could guess in which order the simplices are listed, I could then I would be able to compute the cup products.

I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

EDIT (2020-10-26): Problem not solved, but I found a seempingly seemingly related issue: https://trac.sagemath.org/ticket/6100 . Namely, chain_complex().homology(generators=true) uses a basis in which the simplices are listed in an order that seems untractable intractable (especially, not the lexicographic order). If one could guess in which order the simplices are listed, then I would be able to compute the cup products.

I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

EDIT (2020-10-26): Problem not solved, but I found a seemingly related issue: https://trac.sagemath.org/ticket/6100 . Namely, chain_complex().homology(generators=true) uses a basis in which the simplices are listed in an order that seems intractable (especially, not the lexicographic order). If one could guess in which order the simplices are listed, then I would be able to compute the cup products.

I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

EDIT (2020-10-26): Problem not solved, but I found a seemingly related issue: https://trac.sagemath.org/ticket/6100 . Namely, chain_complex().homology(generators=true) uses a basis in which the simplices are listed in an order that seems intractable (especially, not the lexicographic order). If one could guess in which order the simplices are listed, then I would be able to compute the cup products.