Are you using ONAG for the main reference? In any case, I would appreciate a precise reference to a book or article on nimbers.
On 3/19/07, Michel <[EMAIL PROTECTED]> wrote: > > Hi, > > To acquant myself with sage's inner workings I have implemented > Conway's nimber field. > See > > http://alpha.uhasselt.be/Research/Algebra/Members/nimbers/ > > Recall that the nimbers form a field whose underlying set is the > natural numbers. The addition is bitwise exclusive or but the > multiplication is complicated. GF(2^(2^n)) is isomorphic to the > nimbers that are less than 2^(2^n). Thus the full nimber field is > isomorphic to the union of GF(2^(2^n)) for all n. > > Although my implenentation is still in pure python it seems to be not > much slower > than the standard finite fields GF(2^(2^n)) that one can create in > sage. However I didn't > do extensive testing. The basic arithmetic should be trivial to > rewrite in pyrex. > > This is still a prototype. The most glaring ommission is that > coercions from and to > standard Galois fields are missing. Nevertheless if there are remarks/ > comments I would > appreciate it very much. > > Regards, > Michel > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
