Missed copying the definition of q: sage: q = QQbar(sum([sqrt(n) for n in range(10)])) David
On Mon, Jan 26, 2009 at 10:52 PM, David Roe <r...@math.harvard.edu> wrote: > 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 -~----------~----~----~----~------~----~------~--~---
