Understood, thank you all!
On Thursday, January 5, 2017 at 10:52:49 PM UTC+1, Aaron Meurer wrote: > > You can also check p.is_irreducible. And to be clear, yes, the factors > from factor_list are guaranteed to be irreducible. > > Aaron Meurer > > On Thu, Jan 5, 2017 at 4:24 AM, Kalevi Suominen <[email protected] > <javascript:>> wrote: > > > > > > On Thursday, January 5, 2017 at 1:08:22 PM UTC+2, [email protected] > wrote: > >> > >> No, not a typo but an oversight from me. > >> > >> Is a polynomial "irreducible" if `factor_list(Poly(...))` is exactly of > >> length 1? > > > > > > It is irreducible if there is only one factor and its exponent is 1. The > > square of an irreducible polynomial is not irreducible. > >> > >> > >> > >> On Thursday, January 5, 2017 at 12:23:57 AM UTC+1, Aaron Meurer wrote: > >>> > >>> 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. > > > >>>> > >>>> > >>>> 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] <javascript:>. > > To post to this group, send email to [email protected] > <javascript:>. > > 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/d47d09c1-4afb-40b3-a13c-9a971057cc18%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 https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/2924dccd-e4c9-4262-a1aa-4b275354d6b9%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
