is there a way of doing what uve done except considering the pair of polynomials x^2+a1*x+a0 x^2+b1*x+b0 where a0,a1,b0,b1 lie in QQ but their exact values r not known and al is a root of the first and be is a root of the second?
On Sun, Oct 24, 2010 at 5:22 PM, Yann <[email protected]> wrote: > On Oct 23, 9:39 pm, andrew ewart <[email protected]> wrote: > > if alpha is a root of x^2+a_1*x+a_0 and beta is a root of x^2+b_1*x > > +b_0 (both polynomials r in QQ), then how do i construct code such > > that it can tell me the minimum polynomials of the following roots > > alpha+beta > > and > > alpha*beta > > Hi, I'm not sure if I understood your question, but this might be what > you want: > > sage: R.<x> = QQbar[] > sage: p = 1/7*x^2-x+4 > sage: q = x^2+x+1/3 > sage: p.roots() > [(3.500000000000000? - 3.968626966596886?*I, 1), (3.500000000000000? + > 3.968626966596886?*I, 1)] > sage: a = p.roots()[0][0] > sage: b = q.roots()[0][0] > sage: (a+b).minpoly() > x^4 - 12*x^3 + 257/3*x^2 - 298*x + 5503/9 > sage: (a*b).minpoly() > x^4 + 7*x^3 + 77/3*x^2 + 196/3*x + 784/9 > > I hope this helps. > > Yann > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected]<sage-support%[email protected]> > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
