Is there a typo below? Those polynomials aren't minimal polynomials because they aren't irrreducible.
Aaron Meurer On Wed, Jan 4, 2017 at 9:25 AM <[email protected]> wrote: > I have two algebraic numbers defined by minimal polynomials: > > x, z = symbols('x, z') > p = Poly((x-1)*(x-2)*(x-3)*(x-4)) > q = Poly((x-5)*(x-6)*(x-7)*(x-8)) > > > > and I would like to compute the sum of these numbers. I [found]( > http://math.stackexchange.com/a/155132/327863) that I need to "`z=x+y` is > a root of the resultant of `P(x)` and `Q(z−x)` (where we take this > resultant by regarding `Q` as a polynomial in only `x`)". > > I'm totally new to all this algebraic numbers thing so I don't quite > understand the advice but I tried: > > resultant(p, q.subs(x, z-x)) > > but then I got stuck. Please, could someone explain to me: > > - I would like to see the steps that lead to the computation of desired > minimal polynomial with the help of resultant. I think I defined the two > numbers properly but I don't know how to express that `Q(z−x)`. > > - As it stands now, the `resultant` function returns bivariate polynomial > but I would've assumed that the resulting minimal polynomial should be > univariate. How do I get rid of the second variable? > > - The above link also says "`P(x) = Q(y) = 0`". Does it mean that `p` and > `q` can't be both `Poly((x-1)*(x-2)*(x-3)*(x-4))`? What if I would like to > add the same two numbers? > > Thank you very much in advance! > > > > > > > > > -- > > > 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 https://groups.google.com/group/sympy. > > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/1ed9b3a3-d5cf-4343-9674-99560c14400f%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/1ed9b3a3-d5cf-4343-9674-99560c14400f%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > 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 https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6L%3DSCXtBtXAv5QGDkZ_app%2BjDMYgHAQH6xpzSTW6WzVvQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
