Using sage 9.7 and 10.3 (on an oldish iMac), I ran into some puzzling results, 
of which the following are minimal examples:

#1:
sage: 4.is_square()
True
sage: 4.is_squarefree()
False

#2:
sage: f=x^2-3
sage: K.<a>=NumberField(f)
sage: OK=K.maximal_order()
sage: v=OK.random_element()
sage: v
2*a + 1
sage: v==v.conjugate()
True

#1 I don’t get (and it seems to contradict the “?” doc); while #2 may be a 
misunderstanding on my part.

Thoughts?  Pointers?

Thanks, for any help.

Justin

--
Justin C. Walker, Curmudgeon at Large
Institute for the Absorption of Federal Funds
-----------
I want to die, peacefully in my sleep, like my grandfather;
not screaming in terror, like his passengers.




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