[GAP Forum] How to obtain the incidence matrix of a partial geometry?

[Sven Reichard]

Hello Felix,

the geometry is returned as an incidence graph in GRAPE format. For each
vertex x of that graph, Adjacency(haemers, x) will give you its
neighbours. From that you can reconstruct the adjacency matrix if you want.

For example with the following function:

AdjacencyMatrix := function ( gamma )
    local  result, x, y;
    result := NullMat( gamma.order, gamma.order );
    for x  in [ 1 .. gamma.order ]  do
        for y  in Adjacency( gamma, x )  do
            result[x][y] := 1;
        od;
    od;
    return result;
end

However it could be worth your while working with the graph format as it is.

"delta" just refers to the incidence graph. PartialLinearSpaces returns
a list of those.

Hope this helps,

Sven Reichard
Institut für Algebra
TU Dresden


On 01/21/2015 01:33 PM, Felix Goldberg wrote:
> Hello all,
> 
> I am running the code in the example in Section 9.2 of the GRAPE manual (
> http://www.maths.qmul.ac.uk/~leonard/grape/manual/CHAP009.htm) , which
> generates the Haemers partial geometry pg(4,17,2).
> 
> All works well but I cannot understand where exactly the incidence matrix
> is stored and how to access it. The manual (referred to above) says that
> there is a *delta* associated to the geometry output by the function
> PartialLinearSpaces
> but I can't find it.
> 
> I tried to run RecNames on the output (the variable called *haemers*) and
> got this:
> 
> [ "names", "group", "order", "representatives", "isSimple", "isGraph",
> "schreierVector", "adjacencies" ]
> 
> No sign of *delta* and apparently no incidence matrix.
> 
> Any help will be greatly appreciated.
> 
> Thanks,
> Felix
> 
> 
> 
>