As for #1, 4 is certainly a square, and is also not square-free (begin divisible by a square >1) so I don't see any problem.
For #2, K is a real quadratic field, and the conjugate method is *not* Galois conjugation, but complex conjugation (with respect to either of the embeddings of K into CC); for that, use v.galois_conjugate(). John Cremona On Thursday, 9 October 2025 at 00:17:54 UTC+1 [email protected] wrote: > 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. > > > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/sage-support/a67a94d8-8e79-4cc4-8974-1c3b6a0c9c22n%40googlegroups.com.
