On Wednesday, August 28, 2024 at 7:57:43 PM UTC+9 john.c...@gmail.com wrote:
Surely the output of -1 for AA(-1)^(1/3) is correct: AA is the "Algebraic Real Field" and -1 has exactly one cube root in there, namely itself. On the other hand, QQbar(-1) has 3 cube roots and one is chosen (in some deterministic way). I do not think that AA(-1)^(1/3) should return a cubroot in another field/parent when there is one in the same field/parent. Compare sage: QQ(-1).nth_root(3) -1 sage: RR(-1).nth_root(3) -1.00000000000000 sage: CC(-1).nth_root(3) 0.500000000000000 + 0.866025403784439*I which is as it should be (in my opinion!) x^(1/n) and x.nth_root(n) do not behave in the same way. All x.nth_root(n) gives an n-th root in the same field to which x belongs while all x^(1/n) gives the primitive n-th root of unity, with the exception of AA(-1)^(1/n). -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/1941a3cc-5a33-4311-b2b5-1dfaa62557d5n%40googlegroups.com.
