Hi,
I just wanted to make you aware of a typo in the documentation of free modules [1]. The description of the function "echelon_coordinate_vector" of sage.modules.free_module.FreeModule_submodule_with_basis_pid says: "Write v in terms of the user basis for self." while it should correctly read: "Write v in terms of the echelonized basis for self."
[1] http://sagemath.org/doc/reference/sage/modules/free_module.html
Regards,
Philipp
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This is trac #13780 now. Thanks Philipp for reporting here. (I'll submit a patch now; but, I am ccing to the sage-devel to ask if issues that are so trivial to fix but still can be considered major, deserve a separate ticket).