#16597: Singer difference set and fix OA_9_135
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.3
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | ec6df26f4d72c5eb939a9b02cd3ad809feacb105
u/vdelecroix/16597 | Stopgaps:
Dependencies: |
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Changes (by ncohen):
* status: needs_review => needs_work
Comment:
- In `OA_9_135` you remove the definition of `PG2 = set([x*39 for x in
range(7)])` but it still appears in the documentation. And it is nice to
have an object representing that to describe more clearly what the
function does.
And you repeat this %39 everywhere right now.
- {{{The set of `GF(q)` lines in `V` is a projective plane}}}. The set of
`(q^3-1)/(q-1)=q^2+q+1` lines ? Either way `GF(q)` is not an integer.
- {{{+ spaces/.}}}
- {{{ Kq (i.e the (q-1)-th root of unity}}}
- About the second part of function `singer_difference_set` : what would
you think of implementing 3.16 instead ? It builds the cyclic difference
set from a cyclic automorphism of a BIBD... And it could be useful later,
like when we will have a `BIBD.is_cyclic` function.
Which we can write easily now that BIBD are a class `:-D`
{{{
sage: def is_cyclic(BIBD):
....: repr =
BIBD.automorphism_group().conjugacy_classes_representatives()
....: repr = [x.cycles() for x in repr]
....: for x in repr:
....: if len(x) == 1 and len(x[0].tuple()) == BIBD.num_points():
....: return x[0].tuple()
....: return False
sage: is_cyclic(designs.balanced_incomplete_block_design(13,3))
(1, 9, 8, 7, 12, 10, 5, 2, 11, 3, 0, 4, 6)
}}}
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/16597#comment:4>
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