Bundle of manifold product

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Hi, I am quite new to SageMath and want to use it to help me on my diffgeo journey. I want to dive into fiber bundles but currently am stuck at the very basics: I want to create a bundle (M x N, pr, M) with pr: M x N -> M. For that I need to define two manifolds, which is no problem:

M = Manifold(3, 'M')

N = Manifold(3, 'N')

The total space is:

E = cartesian_product((M, N))

But how do I construct a, e.g., vector bundle E -> M?