Couldn't we still just number the roots? Or would that lead to inconsistencies?
Aaron Meurer On Fri, Feb 27, 2015 at 5:02 AM, Kalevi Suominen <[email protected]> wrote: > It should not be necessary to lose any of the current functionality of > RootOf. A call will now return a complex value. > It could be replaced with a call to rootof() which would do exactly the > same. > (Some editing would be needed in solvers, of course.) > > The field of complex numbers is special because its elements can be > identified by their position in the complex plane. Hence it is possible to > have them labelled. This is essentially what RootOf does now. > > In other fields it is practically impossible to tell different roots apart > by some inherent property. Algebraically they all > appear equivalent (at least if the polynomial is irreducible). Hence an > object of the RootOf class could represent any > one of them. An algebraic field extension could be constructed by just > adjoining a suitable object of RootOf class. > Note that this would be a new object, not one belonging to a pre-established > domain. > > (If, for some reason, it were necessary to have several roots one should > divide the polynomial by the linear > factors X - a, for all roots a found so far, and then take the RootOf of > the remaining quotient or of a factor of it.) > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/01db05d9-689e-407c-bae3-1b369d2b753f%40googlegroups.com. > > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6KrdUGsCSFS%3DjjTn4nhKfULYHoOw2M%2BiMesbK6FYfotNQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
