> Couldn't we still just number the roots? Or would that lead to > inconsistencies? >
It would be fairly complicated to do in full generality. It is necessary to construct one root at a time. (This is essentially so in the complex case, too.) For each root one has to remove those that have already been constructed by the process I described above: > (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.) So it can be done. However, the numbering of the roots will not always be unique since a choice has to be made between the factors of remaining polynomial if it happens to be reducible. Fortunately it is seldom necessary to have a representation for all of the roots at once. For example, for the construction of function field extensions, or even differential extensions, just one root at a time will suffice in general. The same is true for finite fields. It is enough to have one primitive element generating the whole field. -- 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/857a7998-587e-4f60-aa49-40280b7a5e2f%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
