I suppose it comes down to this:
from sage.combinat.designs import design_catalog as designs
PG = designs.ProjectiveGeometryDesign(4 - 1, 2 - 1, 5)
PG.blocks()[0]
[(1, 0, 0, 0), (1, 0, 0, 1), (1, 0, 0, 2), (1, 0, 0, 3), (1, 0, 0, 4), (0,
0, 0, 1)]
On Tue, Mar 25, 2025 at 6:23 PM Jackson Walters <jacksonwalt...@gmail.com>
wrote:
> I guess they are projective lines with q+1 points arising
> from designs.ProjectiveGeometryDesign. However, the blocks (the
> 2-subspaces) should be in one-to-one correspondence with the vertices.
>
> On Tue, Mar 25, 2025 at 6:04 PM Jackson Walters <jacksonwalt...@gmail.com>
> wrote:
>
>> Thanks, that's helpful.
>>
>> G = graphs.GrassmannGraph(5, 4, 2); G
>>
>> gives 806 vertices, as expected, but why do the vertices seem to have six
>> points?
>>
>> G.vertices()[0]
>> {(0, 0, 0, 1), (1, 0, 0, 1), (1, 0, 0, 2), (1, 0, 0, 4), (1, 0, 0, 0),
>> (1, 0, 0, 3)}
>>
>> I don't see anything about this in the documentation. Shouldn't it be
>> just two basis vectors that span the subspace?
>>
>> Thanks,
>> Jackson
>>
>> On Tue, Mar 25, 2025 at 5:33 PM Dima Pasechnik <dimp...@gmail.com> wrote:
>>
>>> We have functionality to build Grassmann graphs. See GrassmannGraph in
>>>
>>> <
>>> https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_generators.html#sage.graphs.graph_generators.graphgenerators.paleygraph
>>> >
>>>
>>>
>>> On 25 March 2025 12:46:56 GMT-05:00, Jackson Walters <
>>> jacksonwalt...@gmail.com> wrote:
>>>
>>>> Does Sage support computing Gr_{F_q}(k,r), the space of k-hyperplanes
>>>> through the origin in GF(q**r)? I looked around for things like Schubert
>>>> cells and didn't see anything immediately relevant. I've started to write
>>>> some stuff for k=2. I may do a PR if it's not already available.
>>>>
>>>> Thanks,
>>>> Jackson
>>>>
>>>> --
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>>
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