#16272: redesign transversal designs
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Reporter: vdelecroix | Owner: Vincent
Type: enhancement | Delecroix
Priority: major | Status: new
Component: PLEASE CHANGE | Milestone: sage-6.2
Keywords: designs, orthogona arrays | Resolution:
Authors: Vincent Delecroix | Merged in:
Report Upstream: N/A | Reviewers:
Branch: | Work issues:
Dependencies: #15310, #16227 | Commit:
| Stopgaps:
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Description changed by vdelecroix:
Old description:
> The tickets #15310 and #16227 introduce a nice `availability` keywords to
> the function `transversal_design`. With `availability=True` the return
> value is the answer to the question "Does Sage know how to build a
> TD(k,n)"? Using `Unknown` from `sage.misc.unknown` we can turn the
> question into "Do we know mathematically that a TD(k,n) exist?" whose
> answer would be:
> - `True` if Sage knows how to do it
> - `Unknwon` if neither Sage nor mathematics can help
> - `False` if we know mathematically that such construction does not
> exist
>
> As the semantic changes, we will also turn the keyword `availability`
> into `existence` (or maybe have both).
>
> In the same ticket, we will include some of the known non existence of
> transversal designs.
New description:
The tickets #15310 and #16227 introduce a nice `availability` keywords to
the function `transversal_design`. With `availability=True` the return
value is the answer to the question "Does Sage know how to build a
TD(k,n)"? Using `Unknown` from `sage.misc.unknown` we can turn the
question into "Do we know mathematically that a TD(k,n) exist?" whose
answer would be:
- `True` if Sage knows how to do it
- `Unknwon` if neither Sage nor mathematics can help
- `False` if we know mathematically that such construction does not exist
As the semantic changes, we will also turn the keyword `availability` into
`existence` (or maybe have both).
In the same ticket, we will include some of the known non existence of
transversal designs:
- The
[http://en.wikipedia.org/wiki/Bruck%E2%80%93Ryser%E2%80%93Chowla_theorem
Bruck Ryser Chowla Theorm] gives the non-existence of many TD(n+1,n)
- C. Lam in Lam, "The Search for a Finite Projective Plane of Order 10"
(1991) proved that TD(11,10) cannot exist
- there is some work (?) that shows that if $k$ is large enough then the
existence of TD(k,n) implies the existence of TD(n+1,n) and so the non-
existence results can percolate downwards in k
--
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Ticket URL: <http://trac.sagemath.org/ticket/16272#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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