On 13 May 2012 18:00, mmarco <[email protected]> wrote: > > >> As motivation, what is a good example of what *you* want to do with >> symbolics + algebraic numbers. >> > > What motivated my question was the following problem. I have a > polynomial f(x,y) with algebbraic coeffcients. If i fix a value for x, > the roots of f as a polynomial in y are algebraic numbers. By the > implicit function theorem, around each pair (x,y) i have a function, > and i need its taylor expansion. That means i need to take the > derivatives of this function using implicit derivation. That's why i > wanted to move algebraic numbers from a polynomial ring to the > symbolic ring and back. >
There's no reason not to differentiate polynomials with number field coefficients: sage: K.<a> = NumberField(x^3-2) sage: R.<x> = K[] sage: f = x^2-a*x+1 sage: f.derivative() 2*x - a sage: R.<x,y> = K[] sage: f = x^2-a*x*y+y^2 sage: f.derivative(x) 2*x + (-a)*y sage: R.<x,y> = QQbar[] sage: f = x^2-QQbar(sqrt(3))*x*y+y^2 sage: f.derivative(x) 2*x + (-1.732050807568878?)*y John > -- > To post to this group, send an email to [email protected] > To unsubscribe from this group, send an email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
