Note that 4.is_square?
and a=4 a.is_square? give different documentation strings. I don't know where the first is coming from. That looks like a strange glitch. It gives the documentation of the function is_square, which is not what the method on integers is. On Thursday, 9 October 2025 at 09:39:57 UTC-7 [email protected] wrote: > Thanks for that lesson in the English language, John. I obviously needed > it :-} > > As for #2, that’s something I did not know! > > Justin > > On Oct 9, 2025, at 01:54 , John Cremona <[email protected]> wrote: > > 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 > > <https://groups.google.com/d/msgid/sage-support/a67a94d8-8e79-4cc4-8974-1c3b6a0c9c22n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- > Justin C. Walker, Curmudgeon at Large > Director > Institute for the Enhancement of the Director's income > ----------- > Question 43: > What if the hokey pokey > really *is* what it’s all about? > -- > > -- 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/840532f1-83d6-48f1-bd02-2201f8b667fcn%40googlegroups.com.
