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Basis elements in the incidence algebra. i.e. a single interval, are added like this:

R = posets.YoungDiagramPoset([2,2]).incidence_algebra(QQ)
f = R[(0,0),(0,0)]

.product_on_basis works as intended, but its arguments should be a pair of intervals in the poset, which translates to a pair of pairs of poset elements. With the same incidence algebra R as before, and the same poset, simply do

h=R.product_on_basis(((1,1),(1,1)),((1,1),(1,1)))