No, not a typo but an oversight from me. Is a polynomial "irreducible" if `factor_list(Poly(...))` is exactly of length 1?
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] <javascript:>> 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] <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/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/4250f620-c732-4b99-873c-6e8221a4a403%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
