Hello, I think something like the following should get you going in the right direction:
sage: delta = lambda m, n: (m-1)*(n-1)/2 + gcd(m,n)-1/2 sage: m = 3 sage: n = 2 sage: for m_part in Partitions(m): ....: for n_part in Partitions(n): ....: print "%s, %s"%(m_part, n_part) ....: for mi in m_part: ....: for ni in n_part: ....: print "delta(%s,%s) = %s"%(mi,ni,delta(mi,ni)) ....: [3], [2] delta(3,2) = 3/2 [3], [1, 1] delta(3,1) = 1/2 delta(3,1) = 1/2 [2, 1], [2] delta(2,2) = 2 delta(1,2) = 1/2 [2, 1], [1, 1] delta(2,1) = 1/2 delta(2,1) = 1/2 delta(1,1) = 1/2 delta(1,1) = 1/2 [1, 1, 1], [2] delta(1,2) = 1/2 delta(1,2) = 1/2 delta(1,2) = 1/2 [1, 1, 1], [1, 1] delta(1,1) = 1/2 delta(1,1) = 1/2 delta(1,1) = 1/2 delta(1,1) = 1/2 delta(1,1) = 1/2 delta(1,1) = 1/2 You just need to combine the individual deltas in the appropriate way. --Mike On Thu, Apr 3, 2008 at 3:17 PM, Erick Galinkin <[EMAIL PROTECTED]> wrote: > > Mike, > Thank you for responding! > > delta is calculated by taking: > > delta(m,n) = ((m-1)(n-1)/2)+(gcd(m,n)-1/2) > > The issue I'm running into is getting sage to cycle these partitions > through this calculation. I can get the partitions and do it all by > hand, but that's an awful pain. > > ~Erick > > > > On Apr 3, 5:51 pm, "Mike Hansen" <[EMAIL PROTECTED]> wrote: > > Hi Erick, > > > > How do you calculate the delta invariant? (This is not my area of > > math.) How large of m and n do you want to work with? For example, > > here is some Sage code to generate all the integer partitions of 40: > > > > sage: time l = Partitions(40).list() > > CPU times: user 0.50 s, sys: 0.03 s, total: 0.53 s > > Wall time: 0.56 > > sage: len(l) > > 37338 > > sage: l[:5] > > [[40], [39, 1], [38, 2], [38, 1, 1], [37, 3]] > > > > --Mike > > > > > --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
