On Friday 16 March 2007 13:57, David Harvey wrote: > All number fields can be defined in terms of a monic polynomial with > integer coefficients. Suppose you start with a defining polynomial > which is monic but has non-integral coefficients. Multiply the whole > polynomial by L^d, where d is the degree and L is the LCM of the > denominators of the coefficients. Then you can absorb L into the > variable. (Another way to say this is to take any generator of K/k > and then multiply it by an appropriate integer to make it an > algebraic integer.)
Oh, clever, I didn't catch the L^d and absorbing trick. I didn't read this e-mail very well before writing one of my other e-mails. This means that it will in fact be monic in the end. I will so implement unless I hear otherwise. -- Joel --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
