For the record: I always thought that InputForm would be intended to 
provide a means to obtain a construction of an object.  Put differently, 
converting an object x to InputForm and evaluating the result should equal 
x.

With this idea in mind, I wrote several testcases in FriCAS, and recently 
the sage interface.

So, in case this is changed, the sage interface will have to be adapted.

I can see that the original authors may have had a different idea of its 
meaning, but the name InputForm is actually very telling.

Concerning UP and SUP: with the above the definition of InputForm, yes it 
would be great if they had InputForm (and they should be different, as 
Waldek pointed out).  It's a major annoyance in the interface.

Martin

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