For the first one, 4*(x^6-3*x+3) = (2*x^3-3*x+3)^2 + 3*(2*x^2-x-1)^2. Warut On Thu, Dec 29, 2016 at 5:55 AM, Bill Gosper <billgosper@gmail.com> wrote:

irreducible, indecomposable, nonreciprocal, solvable: In[996]:= Factor@Decompose[MinimalPolynomial[I/Sqrt[3]-(I (1/2 (9 I-2 Sqrt[3]+3 3^(1/4) Sqrt[-4 I-3 Sqrt[3]]))^(1/3))/3^(2/3)+(I+Sqrt[3])/(2^(2/3) (27 I-6 Sqrt[3]+9 3^(1/4) Sqrt[-4 I-3 Sqrt[3]])^(1/3)),x],x] Out[996]= {3-3 x+x^6}

In[997]:= Factor@Decompose[MinimalPolynomial[1/12 (2-2^(2/3) (-29+3 Sqrt[321])^(1/3)+2^(2/3) (29+3 Sqrt[321])^(1/3)-2^(5/6) Sqrt[3 (7 2^(1/3)+(83-3 Sqrt[321])^(1/3)+(83+3 Sqrt[321])^(1/3))]),x],x] Out[997]= {-1-x-x^5+x^6} --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun