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How to create a Sage directory of all functions?

Can one easily get the list of all defined functions in Sage to something like a directory including at least following information:


  • function name
  • allowed input argument numbers (possibly several)
  • allowed input argument types for each allowed input argument
  • function result values numbers (possibly several depending on input arguments)
  • function result values types for each result value


  • next similar etc.


so that for example one could easily construct an expression-set having all allowed functions in function argument places up to a given level?

For example:

Expression-set for 3 levels is something like:










(All combinations. Here only 3 levels given as an example. Here function myfun may have several return variables each can be a variable, vector, matrix, function name etc.)