[sage-support] Irreducibility of a polynomial
How one can check weather a polynomial f(x,y) is irreducible over rational or not? -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Irreducibility of a polynomial
On Fri, Jan 29, 2010 at 5:06 AM, Santanu Sarkar sarkar.santanu@gmail.com wrote: How one can check weather a polynomial f(x,y) is irreducible over rational or not? sage: R.x,y = QQ[] sage: f = (x^3-x*y+y^2-x)*(x^5-3/2*x-y); f x^8 - x^6*y + x^5*y^2 - x^6 - 3/2*x^4 - x^3*y + 3/2*x^2*y - 1/2*x*y^2 - y^3 + 3/2*x^2 + x*y sage: f.factor() (1/2) * (x^3 - x*y + y^2 - x) * (2*x^5 - 3*x - 2*y) sage: len(f.factor()) 2 We should have len(f.factor()) == 1 when f is irreducible. I'm skeptical that the above function is provably correct, by the way, since it calls singular, and I don't trust singular's factor function, personally... William -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Irreducibility of a polynomial
On Jan 29, 2010, at 11:55 AM, William Stein wrote: On Fri, Jan 29, 2010 at 5:06 AM, Santanu Sarkar sarkar.santanu@gmail.com wrote: How one can check weather a polynomial f(x,y) is irreducible over rational or not? sage: R.x,y = QQ[] sage: f = (x^3-x*y+y^2-x)*(x^5-3/2*x-y); f x^8 - x^6*y + x^5*y^2 - x^6 - 3/2*x^4 - x^3*y + 3/2*x^2*y - 1/2*x*y^2 - y^3 + 3/2*x^2 + x*y sage: f.factor() (1/2) * (x^3 - x*y + y^2 - x) * (2*x^5 - 3*x - 2*y) sage: len(f.factor()) 2 We should have len(f.factor()) == 1 when f is irreducible. I'm skeptical that the above function is provably correct, by the way, since it calls singular, and I don't trust singular's factor function, personally... To check if f (or one if its factors) is actually irreducible one could find a specialization down one variable that is irreducible (I think the univariate case uses Pari). sage: f = R.random_element() + R.random_element(5) sage: len(f.factor()) 1 sage: g = QQ['x'](f.subs(y=5)) sage: g.is_irreducible() True - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
