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The second import statement can indeed be removed since it is contained in the first. However, none of the first and third imply the other. With the first you can call the function have_same_parent() directly, while with the third you have to call the longer sage.structure.element.have_same_parent() but you will also be able to call some other functions such as sage.structure.element.make_element().

The second import statement can indeed be removed since it is contained in the first. However, none of the first and third imply the other. With the first you can call the function have_same_parent() directly, while with the third you have to call the longer sage.structure.element.have_same_parent() but you will also be able to call some the other functions of the sage.structure.element module such as sage.structure.element.make_element().

Note that it is also possible to get the benefits of both types of imports (short to write and get many functions of the same module) as follows:

sage: import sage.structure.element as el
sage: el.have_same_parent()
sage: el.make_element()