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 [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/ -~----------~----~----~----~------~----~------~--~---
