I need to compute the homology of a chain complex whose graded basis is a collection of formal symbols, say {a,b,c,…}. Does Sage have the capability to store a basis of symbols and express a homology class in terms of a symbolic class representative?
I have been able to able to create a ChainComplex instance using matrices for the boundary maps. For example,
TorusComplex = ChainComplex({0: matrix(Z_2,2,1,[0,0],sparse=True),1: matrix(Z_2,1,2,[0,0],sparse=True)})
"Chain complex with at most 3 nonzero terms over Ring of integers modulo 2"
TorusComplex.homology(generators=true)
"{0: (Vector space of dimension 1 over Ring of integers modulo 2, [(1)]), 1: (Vector space of dimension 2 over Ring of integers modulo 2, [(1, 0), (0, 1)]), 2: (Vector space of dimension 1 over Ring of integers modulo 2, [(1)])}"
However, I can't figure out how define symbols so that the resulting generators are symbols. Any ideas?
