2007/10/25, Mike Hansen <[EMAIL PROTECTED]>: > > > Since integers are chosen uniformly, this would guarantee (?) that the > > polynomial is generated uniformly. Only hitch is that I don't know if > > there is such inttovec is in in SAGE yet. mhansen, any idea? > > Yes, this is pretty much what I'm doing. While I don't have those > exact functions, they would be easy to implement. > > How fast do these need to be? Here's a rough function that uniformly > selects monomials without replacement from all possible monomials with > degree less than d.
Is this function in sage? Where is it located? didier > > def random_monomials(n, degree, terms): > #Get the counts of the total number of monomials > #of degree d > counts = [1] #degree 0 > for d in range(1, degree): > counts.append(binomial(n+d-1, d)) > total = sum(counts) > #Select a random indices > indices = sample(xrange(total), terms) > monomials = [] > for random_index in indices: > #Figure out which degree it corresponds to > d = 0 > while random_index >= counts[d]: > random_index -= counts[d] > d += 1 > #Generate the corresponding monomial > comb = choose_nk.from_rank(random_index, n+d-1, n-1) > monomial = [ comb[0] ] > monomial += map(lambda i: comb[i+1]-comb[i]-1, range(n-2)) > monomial.append( n+d-1-comb[-1]-1 ) > monomials.append(monomial) > return monomials > > Here's an example: > > sage: time random_monomials(20, 40, 20) > CPU times: user 0.09 s, sys: 0.00 s, total: 0.09 s > Wall time: 0.09 > > [[8, 1, 5, 0, 0, 1, 2, 0, 1, 1, 2, 0, 0, 2, 4, 2, 1, 4, 3, 1], > [0, 0, 9, 2, 0, 7, 2, 0, 3, 2, 1, 0, 3, 1, 0, 1, 4, 0, 4, 0], > [0, 0, 3, 0, 1, 4, 3, 1, 0, 2, 1, 3, 4, 1, 1, 0, 6, 7, 0, 0], > [0, 2, 3, 0, 0, 2, 1, 2, 5, 3, 0, 0, 1, 5, 2, 0, 1, 1, 9, 0], > [0, 1, 1, 7, 0, 1, 6, 0, 1, 0, 1, 0, 1, 6, 2, 0, 7, 0, 2, 1], > [7, 0, 3, 1, 0, 6, 1, 4, 0, 8, 0, 0, 0, 0, 0, 1, 3, 3, 0, 0], > [0, 0, 0, 4, 1, 5, 3, 1, 1, 0, 0, 2, 3, 3, 3, 1, 4, 0, 1, 6], > [1, 2, 5, 0, 5, 1, 1, 0, 0, 7, 0, 1, 1, 1, 1, 2, 3, 4, 1, 0], > [1, 7, 0, 0, 4, 3, 0, 2, 0, 0, 1, 8, 1, 1, 0, 0, 2, 5, 0, 0], > [0, 4, 0, 3, 5, 0, 0, 0, 1, 0, 1, 3, 2, 1, 8, 4, 0, 0, 1, 0], > [1, 0, 9, 0, 1, 7, 3, 1, 2, 0, 0, 1, 0, 0, 5, 1, 0, 6, 0, 0], > [1, 3, 0, 3, 5, 0, 1, 2, 0, 2, 4, 1, 0, 4, 1, 2, 3, 1, 4, 0], > [0, 2, 3, 8, 1, 0, 3, 1, 0, 1, 1, 1, 0, 1, 5, 5, 1, 5, 0, 0], > [3, 0, 4, 0, 8, 0, 3, 1, 0, 2, 0, 1, 0, 3, 1, 6, 2, 2, 0, 1], > [2, 5, 1, 0, 1, 0, 2, 5, 1, 2, 3, 3, 0, 0, 0, 4, 4, 0, 0, 0], > [1, 0, 6, 2, 5, 0, 0, 0, 1, 4, 2, 0, 5, 0, 1, 1, 0, 0, 3, 4], > [1, 1, 0, 2, 0, 1, 1, 1, 3, 3, 2, 2, 1, 0, 0, 1, 1, 1, 11, 7], > [7, 0, 3, 0, 4, 1, 2, 1, 6, 0, 0, 1, 3, 1, 0, 0, 7, 3, 0, 0], > [1, 2, 3, 1, 0, 1, 0, 0, 3, 3, 2, 0, 5, 0, 0, 0, 3, 1, 2, 7], > [0, 5, 0, 3, 1, 1, 2, 0, 1, 1, 0, 1, 4, 2, 8, 2, 2, 1, 0, 2]] > > > --Mike > > > > --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
