# Inner products with dimension $n$.

Is there a way to work with inner products with unspecified dimension in Sage? All the options that I've been able to find e.g. FreeModule have a required argument that asks for a dimension, basis or rank of some sort.

Ideally, what I need would work like:

INN = InnerProdSpace(RR); u, v = INN(u,v); u.dot(v)

and it would be able to perform basic simplifications like:

u.dot(v + ru) = u.dot(v) + ru.dot(u)

I know that some modules like VectorSpace already do this and much more; but I would like to do it without needing to specify the dimension.

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