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Note that sage.calculus.var.var and sage.calculus.var.function are just convenience wrappers of SR.var and sage.symbolic.function_factory.function_factory respectively. Both are augmented to inject the name they define into the global namespace and are therefore only suited for interactive use at sage's toplevel. In any more elaborate program or in library code, you should use the original functions.
The documentation of any of those can use improvement, but I'm not sure you want to explain all options in all of their docstrings. Perhaps a good cross reference can save some work.
This could potentially be useful, but the docs only mention the following inputs:
Component: documentation
Reviewer: Lorenz Panny
Issue created by migration from https://trac.sagemath.org/ticket/12817
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