On Nov 30, 2007, at 2:45 AM, Ahmad wrote:
> > Dear Sage Supporters, > > As nobody continued to pay attention to the question I asked in sept 3 > about how I want to change the field basis "permanently", I am using > john Cremona's idea to ask my question in another way, in hope to > attract more attention: > > Suppose k is a field. Let define ring k[x]. I extend this ring by > adding variable 't' and taking quotient by polynomial 't^4 + t^3 + t^2 > + t + 1'. So, I have the ring k[x][t]/(t^4 + t^3 + t^2 + t + 1) which > is a free module over k[x]. But again sage use default basis (1, t, > t^2, t^3) to represent this ring over k[x]: > > sage: k = GF(2); > sage: R = k['x']; x = R.gen() > sage: S = R['t']; t = S.gen() > sage: SBar = S.quotient(t^4 + t^3 + t^2 + t + 1, 'a'); a = SBar.gen() > sage: print x*a^4 > x*a^3 + x*a^2 + x*a + x > > How can I change this basis to normal basis, so I get: > > sage: print x*a^4 > x*a^4 Hi Ahmad, I looked over the september thread, and the problem is that William's solution won't work in this more general case, since you can't create a polynomial ring with coefficients in a vector space, it just doesn't make sense. But if all you need is a list of the coordinates, then maybe we can make this work. All you need to be able to do is apply a function to each coefficient of a polynomial. Here's how you do that: sage: k = GF(7) # any coefficient ring here is okay sage: R.<x> = PolynomialRing(k) # create polynomial ring over k in variable x sage: g = x^3 + 2*x + 5 # create some polynomial sage: g.list() # list of coefficients of polynomial [5, 2, 0, 1] sage: [2*u for u in g.list()] # multiplies every elements of g.list () by 2 (mod 7), returns result as a list [3, 4, 0, 2] So you just need to replace "2*u" with whatever function William gave you to change basis representation. Of course, what you *really* want is to be able to create a field that prints elements of itself with respect to a different basis, but I don't think this is implemented in sage (yet). That sounds like it could be a useful thing to have. david --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
