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Original Message (ID '53750') By jf:
Left alone, they do reduce, In[5]:= P[Abs[1], Abs[-4]] Out[5]= P[1, 4] The problem is that If holds its second and third arguments so FullSimplify cannot access them. In[8]:= Attributes[If] Out[8]= {HoldRest, Protected} If S is defined, the test can be evaluated and the appropriate 2nd or 3rd argument evaluated.