do not change n_dim but _n_dim. We should raise an error if a user try to specify both n_dim and dim.

I assume that the time of the deprecation, we need to have n_dim=None to detect explicitely if a user pass n_dim=1 or not. This is annoying but I don't see how to detect this case otherwise. This would not change the default value because None would default to 1. Somehow, we can omit to document it explicitely, and make a more silent deprecation because I don't think that any user will use n_dim=Noe explicitely to set it to 1.