On Wed, 4 Sept 2024 at 11:06, Kwankyu Lee <ekwan...@gmail.com> wrote: > > On Wednesday, September 4, 2024 at 1:41:30 PM UTC+9 Nils Bruin wrote: > > ... it may well depend on whether you're more algebraically or analytically > oriented. > > > Yes. That may be a way to reconcile the conflicting views. > > We may explicitly introduce technical distinction of "analytical fields" and > "algebraic fields". > > Analytical fields are : RR, RDF, RBF, ..., CC > Algebraic fields are: AA, QQbar, GF, Qp, ... > > 1. For an element x in analytical field P, x^(1/n) returns the principal > n-th root of x in P or in CC. > 2. For an element x in algebraic field A, x^(1/n) returns an n-th root of x > in A or raises an error if there is none. > > and we live happily ever after.
Until it is discovered that coercions exist that go from algebraic fields to analytic ones or that there are very common rings that could be viewed as being subrings of either analytic or algebraic fields: >>> ZZ(-8)^(1/3) 2*(-1)^(1/3) >>> RR(ZZ(-8)^(1/3)) ... TypeError: unable to convert '1.00000000000000+1.73205080756888*I' to a real number This coercion also seems questionable: >>> parent(ZZ(8)^(1/3)) Rational Field There is no case where an element of ZZ raised to an element of QQ will give a non-integer rational number. Probably as alluded above exponentiation should not use a general coercion and the type of the exponent should be treated differently from the type of the base. -- Oscar -- 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/CAHVvXxQEYMKxCPsomxCeznHGsFgdSXTpBJ-RTwON3QHxFQJg8Q%40mail.gmail.com.
