#15310: Wilson's construction of Transversal Designs/Orthogonal Arrays/MOLS
-------------------------+-------------------------------------------------
Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | f23fa885ee5a080f2a8051f23f7fc9f130541849
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/15310 |
Dependencies: |
#15287, #15431 |
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Comment (by vdelecroix):
Hi Nathann,
I am not sure I would be able to do the full review. Nevertheless, you can
can speed up '''a lot''' the function `find_wilson_decomposition` using
the fact that if a TD(k,n) exists then we have the inequality `k <= n+1`.
Here is a sample version of what can be done:
{{{
def find_wilson_decomposition(k,n):
# we can start from k-1 since we need a TD(k+1,t)
for t in range(max(1,k-1),n-1):
u = n%t
# We ensure that 1<=u and
# u <= k-2 since we need a TD(k,u)
if u == 0 or u <= k-2:
continue
m = n//t
# k < m+2 since we need a TD(k,m)
if k >= m+2:
break
if (transversal_design(k ,m , availability=True) and
transversal_design(k ,m+1, availability=True) and
transversal_design(k+1,t , availability=True) and
transversal_design(k ,u , availability=True)):
return k,m,t,u
return False
}}}
You can check that there is no stupid call to `find_wilson_decomposition`
with the following
{{{
sage: from sage.combinat.designs.orthogonal_arrays import
find_wilson_decomposition
sage: find_wilson_decomposition(7,71)
(7, 8, 8, 7)
sage: find_wilson_decomposition.get_cache() # get the list of cached
values
...
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15310#comment:15>
Sage <http://www.sagemath.org>
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