> .map_coefficients doesn't produce an element of the same parent in this 
case (here it is returning a malformed Sage object).  In this example it is 
sending a symmetric function with coefficients in the ring QQ to a 
symmetric function with coefficients that are factor objects.  It however 
is not aware that the object that it is producing is not valid.  What is 
going "wrong" is that it is throwing away empty factors (or in this case 
factor(1) or even factor(-1)).  Technically this is also not wrong either 
because you want empty factors to be 'False' for other applications.

Sorry, I should have made myself clearer: I do not understand the design 
decision behind the way map_coefficients works.

Shouldn't it rather check whether the function actually produces something 
in the coefficient ring?

Martin

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