Opened 7 years ago
Last modified 6 years ago
#16552 needs_work enhancement
oval in finite projective plane
Reported by:  vdelecroix  Owned by:  

Priority:  major  Milestone:  sage6.4 
Component:  combinatorial designs  Keywords:  
Cc:  ncohen, brett  Merged in:  
Authors:  Vincent Delecroix  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/vdelecroix/16552 (Commits)  Commit:  f7989eb77ceb0f23b07568e8433d7a27b74861de 
Dependencies:  #16500, #16553  Stopgaps: 
Description (last modified by )
Build oval from conics in Desarguesian projective plane and use MILP to look for ovals in nonDesarguesian ones.
We use it to speed up some of the Wilson construction which requires an oval.
To be rewritten over #16553
Change History (12)
comment:1 Changed 7 years ago by
comment:2 Changed 7 years ago by
 Branch set to u/vdelecroix/16552
 Commit set to f7989eb77ceb0f23b07568e8433d7a27b74861de
 Status changed from new to needs_review
Needs review.
And great speedup in the recursive constructions!!
Last 10 new commits:
9ff5062  trac #16423: Table of MOLS from the handbook and comparison with Sage

e64be98  trac #16423: tiny code improvement and alignment

e948cf6  trac #16423: Aligning the alignment

0a7d853  trac #16423: Broken doctests

b329351  trac #16499: Cheap speedup in the OA recursive constructions

a67c04f  trac #16500: New recursive constructions of Orthogonal Arrays

41c50d5  trac #16500: Simplified find_recursive_construction

e1992ce  trac #16500: doc + speedup

697dd0c  trac #16500: Typoes in the doc

f7989eb  trac #16552: implement oval for projective plane

comment:3 followup: ↓ 4 Changed 7 years ago by
and hyperovals are here too for GF(2^k)
;)
comment:4 in reply to: ↑ 3 ; followup: ↓ 5 Changed 7 years ago by
 Status changed from needs_review to needs_info
and hyperovals are here too for
GF(2^k)
;)
Ahem. Vincent, I thank you for the feature but the code really needs some reorganization :P
First, why wouldn't the system of coordinates be provided by DesarguesianProjectivePlane
when you create one ? Clearly getting the "coordinates" of the points can be useful, and the only reason why it is not already the case is that BlockDesign
only supports integers as a ground set. But you could return the dictionary along with the projective plane, couldn't you ?
additional question : is the _desarguesian_projective_plane_coordinates
properly defined anyway ? Or is that why it is just an internal function ?
Similarly, the oval functions have no reason to return integers. They can just return the triples of coordinates.
Besides, we can't just dump "Oval functions" like that in block_designs.py
. And... Well, though you were not the worst in the crowd, I think I can easily gather 50+ emails that were exchanged just because I created a ProjectivePlane
function which returned a desarguesian projective plane. How can you now create a function as well defined as OvalInDesarguesianProjectivePlaneDesign
?.. :P
Nathann
comment:5 in reply to: ↑ 4 ; followup: ↓ 7 Changed 7 years ago by
Replying to ncohen:
and hyperovals are here too for
GF(2^k)
;)Ahem. Vincent, I thank you for the feature but the code really needs some reorganization
:P
First, why wouldn't the system of coordinates be provided by
DesarguesianProjectivePlane
when you create one ? Clearly getting the "coordinates" of the points can be useful, and the only reason why it is not already the case is thatBlockDesign
only supports integers as a ground set. But you could return the dictionary along with the projective plane, couldn't you ?
doable... You would like the answer of DesarguesianProjectivePlane
to be a pair (projective plane, coordinates)
. But not very standardized with comparison to BIBD, OA, MOLS, etc.
I would rather create a class
class DesarguesianProjectivePlaneDesign(IncidenceStructure): def label(self, x, y, z): r""" Return the label of the class `[x:y:z]` """
but it is too much work for this ticket.
additional question : is the
_desarguesian_projective_plane_coordinates
properly defined anyway ? Or is that why it is just an internal function ?
No. What is well defined are the classes [x:y:z]
which are elements of K^3 \ {0}
up to multiplication by a nonzero scalar (i.e. lines in K^3
). The labeling choice mapping it to integers is not canonical.
Similarly, the oval functions have no reason to return integers. They can just return the triples of coordinates.
Right, but in that case there is no need for a function:
sage: K = GF(17) sage: oval = [(t,t^2,K.one()) for t in K] + [(K.zero(),K.one(),K.zero())]
Besides, we can't just dump "Oval functions" like that in
block_designs.py
. And... Well, though you were not the worst in the crowd, I think I can easily gather 50+ emails that were exchanged just because I created aProjectivePlane
function which returned a desarguesian projective plane. How can you now create a function as well defined asOvalInDesarguesianProjectivePlaneDesign
?..:P
The name is not quite appropriate for sure. I can call them PointOfTheConic_t_t2_1
if you prefer but if we would return triple of elements of GF(q)
then there is no need for these functions.
Vincent
comment:6 Changed 7 years ago by
And note that we already have from sage.schemes.projective.projective_space
sage: list(ProjectiveSpace(2,GF(2))) [(0 : 0 : 1), (1 : 0 : 1), (0 : 1 : 1), (1 : 1 : 1), (0 : 1 : 0), (1 : 1 : 0), (1 : 0 : 0)]
comment:7 in reply to: ↑ 5 ; followup: ↓ 8 Changed 7 years ago by
Yo !
doable... You would like the answer of
DesarguesianProjectivePlane
to be a pair(projective plane, coordinates)
. But not very standardized with comparison to BIBD, OA, MOLS, etc.
Well.... You know how I would do it ... :P
designs.DesarguesianProjectivePlane(return_coordinates=True)
I would rather create a class
That would the "most proper way".
but it is too much work for this ticket.
Hmmmm... Well, we will have to do that someday for many objects, it is just weird that we somehow need the objects and do not have so many functions to add to them...
Right, but in that case there is no need for a function:
sage: K = GF(17) sage: oval = [(t,t^2,K.one()) for t in K] + [(K.zero(),K.one(),K.zero())]
Well, those three lines are all that the function should do. And as it is, it already helps dumb guys like me who did not even know (what ovals were) how to build an oval.
The name is not quite appropriate for sure. I can call them
PointOfTheConic_t_t2_1
if you prefer but if we would return triple of elements ofGF(q)
then there is no need for these functions.
HMmmmmmmm.. I don't know how to implement that properly :/
Nathann
comment:8 in reply to: ↑ 7 ; followup: ↓ 10 Changed 7 years ago by
Replying to ncohen:
Yo !
doable... You would like the answer of
DesarguesianProjectivePlane
to be a pair(projective plane, coordinates)
. But not very standardized with comparison to BIBD, OA, MOLS, etc.Well.... You know how I would do it ...
:P
designs.DesarguesianProjectivePlane(return_coordinates=True)
I will create a decorator @output_type_depends_on_input
especially for you!
I would rather create a class
That would the "most proper way".
If I do this I would rewrite partly the IncidenceStructure
class (especially hide the attributes). For a class DesarguesianProjectivePlane
there is no need to store the points or the blocks. It will be as fast as you whish to do it on the fly...
But then comes from the problem with labels... should we steal the implementation that is in graph?
Right, but in that case there is no need for a function:
sage: K = GF(17) sage: oval = [(t,t^2,K.one()) for t in K] + [(K.zero(),K.one(),K.zero())]Well, those three lines are all that the function should do. And as it is, it already helps dumb guys like me who did not even know (what ovals were) how to build an oval.
I was dump and wikipedia was my friend in that particular case.
The name is not quite appropriate for sure. I can call them
PointOfTheConic_t_t2_1
if you prefer but if we would return triple of elements ofGF(q)
then there is no need for these functions.HMmmmmmmm.. I don't know how to implement that properly
:/
For example:
sage: K = GF(3) sage: P = designs.ProjectivePlane(K) sage: R.<t> = K[t] sage: oval = P.points_of_parametrized_curve((t,t^2))
Vincent
comment:9 Changed 7 years ago by
and rewriting IncidenceStructure
might overlap with #16534.
comment:10 in reply to: ↑ 8 Changed 7 years ago by
Yo !
I will create a decorator
@output_type_depends_on_input
especially for you!
We need a category of functions whose output depends on the input and combinatorial maps from there to everywhere else.
If I do this I would rewrite partly the
IncidenceStructure
class (especially hide the attributes).
Honestly, if you feel like working on IncidenceStructure
we can rewrite it together. Up to now I have been alternatively 1) scared to use it because of the bugs I already found there 2) not sufficienty stuck to need to rewrite it.
For a class
DesarguesianProjectivePlane
there is no need to store the points or the blocks. It will be as fast as you whish to do it on the fly...
Ahahahah. Well, if you want to get better performances on this kind of stuff ...
But then comes from the problem with labels... should we steal the implementation that is in graph?
T_T
Well. If we .... sigh .... let block designs have a different ground set, we should do it in such a way that we can work with integers when we want to without being in trouble. Perhaps it just means that we need to have "integer" counterparts to every "labelled" function.
For example:
sage: K = GF(3) sage: P = designs.ProjectivePlane(K) sage: R.<t> = K[t] sage: oval = P.points_of_parametrized_curve((t,t^2))
HMmmmm... I have no idea if it is the right place O_o
I really have no idea.... O_o
Nathann
comment:11 Changed 7 years ago by
 Dependencies changed from #16500 to #16500, #16553
 Description modified (diff)
 Status changed from needs_info to needs_work
Ok. Let us do that in #16553
comment:12 Changed 6 years ago by
 Milestone changed from sage6.3 to sage6.4
Oh... And would you know how to compute hyperovals too ? I used a LP to compute the one I needed in #16528. It's precomputer so it does not matter, but well...
:)
Nathann
P.S. : Some day, all these functions will become methods of something, but I am really scared to know "what"
:D