pymsetmath contains methods for calculations using multisets.

Examples are included for estimating the probability of missing one or more of the top N results for any number of results returned by each of m workers.

>>> import pymsetmath
>>> pymsetmath.examples.print_cumulative_prob(20, 4)

Inputs are integers. Output is printed to stdout.

pymsetmath/
|-- LICENSE.txt
|-- README.rst
|-- setup.cfg
|-- setup.py
|-- pymsetmath/
|   |-- __init__.py
|   |-- multiset.py
|   |-- prob_of_missing.py
|-- tests/
|   |-- __init__.py
|   |-- test_pymsetmath.py

1. Add more to this overview
2. Add additional use case examples
3. Include support for groups of multisets which do not share a sum
4. Modify factorial to utilize memoization via a decorator

5. Annotate references including:

   • http://mathworld.wolfram.com/Partition.html
   • http://oeis.org/A008284
   • http://oeis.org/A026820
   • http://mail.python.org/pipermail/tutor/2001-August/008098.html
   • http://www.mathkb.com/Uwe/Forum.aspx/math/17470/Question-about-integer-partitions
   • http://code.activestate.com/recipes/218332/
   • http://mathworld.wolfram.com/PartitionFunctionQ.html
   • http://en.wikipedia.org/wiki/Multinomial_coefficient
   • http://en.wikipedia.org/wiki/Multiset#Counting_multisets

While the presently solved problem uses an assumption that each worker has an equal probability of finding a result, multiset methods could also be used to test the validity of that assumption by attempting to fit actual observed results by a multivariate hypergeometric distribution.