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]> 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]. > 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/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/CAKgW%3D6%2B%3Dj96WtGshe_gK2k98pKca5pQgQVGR80NbinEVabpbhA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
