So, it's a little annoying in general, since something like sqrt(2) will have multiple embeddings into the number field. There's an argument to be made for square roots and quadratic number fields (both because this is a common use case and because quadratic number fields are often just defined by the polynomial x^2 - D, where there's an obvious distinguished root).
As for the question about a number field containing sqrt(2), sqrt(3)... sqrt(n), you need quite a large degree number field to contain all of those. Take a look at QQbar: depending on your desired application, it may be what you want. For example, sage: q.minpoly() x^16 - 96*x^15 + 4008*x^14 - 95328*x^13 + 1415500*x^12 - 13390560*x^11 + 76498488*x^10 - 193010400*x^9 - 528529098*x^8 + 6000127200*x^7 - 19169247528*x^6 + 16399249632*x^5 + 63008590252*x^4 - 213731811744*x^3 + 278799279816*x^2 - 170493467040*x + 39624448081 sage: q 19.30600052603573? But the degree of that minimal polynomial will look like 2^(n/ln(n)), which is bigger than you want. :-) David On Mon, Jan 26, 2009 at 10:33 PM, Franco Saliola <sali...@gmail.com> wrote: > > Here is a bug: one should be able to coerce the element that created > the number field into the number field: > > sage: R = QQ[sqrt(2)] > sage: R(sqrt(2)) > Traceback > ... > TypeError: <class 'sage.calculus.calculus.SymbolicComposition'> > > I came across this while playing around: I was trying to build a > number field containing sqrt(2), sqrt(3), ..., sqrt(n) to speed up > some code that needs to work with sqrts. If you have any suggestions, > that would be cool. > > Franco > > -- > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
