On Tuesday 3 September 2024 at 20:52:04 UTC-7 Kwankyu Lee wrote: If you mean "branch choice" in mathematical sense, the branch choice of Qbar (and CC and RR)
ln(z) = ln(r) + i * theta for z = r * exp(i * theta) with r > 0, -pi < theta <= pi (note <= at the end) is most natural for maximal continuity. I think this is more mathematical than choosing a "branch" that "does not require an extension of the parent". I think the opinion about what is "mathematical" is where the difference lies here and it may well depend on whether you're more algebraically or analytically oriented. As an algebraist, one does not tend to think of Qbar or AA explicitly embedded in CC, so there is no natural extension of exponents beyond QQ. Hence, QQ does not come with a particular topology on it, so there is no continuity to consider. Exponentiation on Qbar embedded in the p-adic C_p would work out *very* differently. For many (most?) applications of Qbar, its embedding into CC is only used to tell conjugates apart. Indeed, Magma's algebraic closure of QQ does not use an embedding into CC but instead tracks conjugate labels using a large finite field. -- 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/e0dbc77b-2978-492b-93c2-4b1866519795n%40googlegroups.com.
