#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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Comment (by vdelecroix):
Replying to [comment:4 ncohen]:
> - 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.
I will put it back if you prefer. I just remarked that I removed an
important comment about PG2 being the set of points = 0 mod 39.
But note that it is faster to test "x%39 == 0" rather than building PG2
and then test "x in PG2".
> - {{{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.
No, `GF(q)` is not a number but a field. It refers to line as line in a
vector space over `GF(q)`. The very same way you would speak about `RR`
lines in `CC`. Isn't that clear enough?
> - {{{+ 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.
It is stupid. You will have to first build the projective space, then
compute its automorphism group that we already know and then apply a big
hammer.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16597#comment:5>
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