On Friday 26 October 2007, Robert Bradshaw wrote: > This is an interesting construction, but I am wondering if a uniform > distribution for all polynomials of specified degree < d, with a > specified number of terms, is the most natural one to give, and how > grave the impact is on efficiency. (Depending on the coefficient > ring, this goal may not even be achievable).
Yes, a random boolean multivariate polynomial will have $MM/2 monomials i.e. 1/2 of all possible monomials. That is okay, we are not enforcing #T to be achieved but we are enforcing that the coefficients determine if we get to #T or not rather than the implementation. Actually, Steffen jokingly proposed earlier to have .some_element() besides .random_element() which gives you a somewhat random element whereas .random_element() actually gives you something very random. > Also, rather than specifying maximum degree/number of terms, it might > make more sense (and be much after to implement) to use a > distribution with an expected degree and/or number of terms. can you elaborate on this, I don't really understand that point. Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
