Hi David, Thank you very much for your solution. I think it is enough for me as finally I want to see the result in normal basis. However, I changed the code a little to suite my purpose but it failed. Could you please tell me what should I use instead of "list" property in multivariate case (maybe we need some ordering like grobner basis):
sage: k = GF(7) # any coefficient ring here is okay sage: R = MPolynomialRing(k,2,x) # create polynomial ring over k in variable x sage: x = R.gens() sage: g = x[0]^3 + 2*x[1] + 5 # create some polynomial sage: print g.list() # list of coefficients of polynomial sage: [2*u for u in g.list()] # multiplies every elements of g.list() by 2 (mod 7), returns result as a list Traceback (most recent call last): ... AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular' object has no attribute 'list' I hope that you don't get the feeling that I just naging and challenging you for nothing. It is almost exactly the computation I need for my thesis as I'm working on GHS attack. I should look at a curve when its parameters and variables is represented in base field (so one equation become many equations) and then I should pass some hyper-plane through it in its base field. Thanx again. Ahmad On Nov 30, 8:20 am, David Harvey <[EMAIL PROTECTED]> wrote: > 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/ -~----------~----~----~----~------~----~------~--~---
