#16391: Helper functions for OA constructions
-------------------------------------+-------------------------------------
Reporter: ncohen | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.3
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/16391 | 90f828fb2904fc5083baa8b45af97d6dc7740f54
Dependencies: #16370 | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by vdelecroix):
* status: needs_review => needs_info
Comment:
Hi,
1) What you called OA with holes are "incomplete orthogonal array" in the
Handbook (as well as their sisters "incomplete transversal design" and
"incomplete set of MOLS"). See p 193-194. And the one you are interested
in, the "OA(k,n) - x.OA(k,1)", are also denoted "OA(k,n; 1, ..., 1)". Am I
right? If this is true, I would rather write a function
`incomplete_orthogonal_array(k,n,holes)` where holes is a tuple of
integers to fit with the standard names and notations. I also saw some
general results in the Handbook (Theorems 4.16 and 4.17) about one hole
and k=4,5... and a beautiful table of IMOLS.
2) From the function you wrote, it is very easy to
- allow `x` as None, in which case the function tries to optimize the
number of holes
- have an optional argument `OA` such that, if it is provided, the
function looks for holes inside this orthogonal array.
I did the change myself but the function looks a bit uglier so I am not
sure what to do. I would like to have those two functions to study the
number of holes depending on the OA. But on the other hand, I tried with
the OA(10,4) that we have but it took lifetime to obtain the answer 9.
A perhaps cleaner way to do things is to have two functions that would
looks like
- `incomplete_orthogonal_array(k,n,holes)` (this function would be
available from the global namespace)
- `look_for_holes_in_my_OA(OA,k,n,holes)`
What do you think?
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/16391#comment:13>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
