On Monday, 13 July 2015 19:15:40 UTC+2, Simon King wrote: > > Hi! > > On 2015-07-13, Nathann Cohen <nathan...@gmail.com <javascript:>> wrote: > > sage: sqrt(2) # a symbolic ring element > > sqrt(2) > > sage: QQbar(sqrt(2)) # an algebraic value > > 1.414213562373095? > > > > It is true that this final '?' sounds more like a '...', as if some > additional > > digits were hidden in a value stored as a float/double. Yet it is exact. > > > > How could we replace it? Ideally, that would be a 'sqrt(2)' but can we > always > > provide such a representation cheaply? Could we display it as 'sqrt(2)' > at least > > when it is free to do so? > > The elements of QQbar are the solutions of algebraic equations. As you > probably know, the solutions of algebraic equations of degree > 4 can, in > general, not be expressed that nicely. >
This is slightly incorrect. The general quintic can be solved in terms of Jacobi theta functions, the general sextic in terms of Kampe de Feriet functions, amongst others. In general Mellin integrals, Fuchsian functions and theta functions can be used to solve general equations of degree n. Bill. -- 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 post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
