[GAP Forum] Creating block matrices

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear Katie,
it's not clear from your message what you mean by "efficiently".
You mean, a special function that can do it for you?

Here is one way to accomplish it:

sgrp:=function(q,n0)
local g, eij, i, j,n, d;

 eij:=function(i,j)
   local M;
   M:=IdentityMat(n,GF(q));
   M[i][j]:=Z(q)^0;
  return M;
 end;

g:=[];
n:=2*n0;
for i in [1..n-1] do
  Add(g,eij(i+1,i));
  d:=IdentityMat(n,GF(q));
  d[i][i]:=Z(q);
  Add(g,d);
od;
for i in [1..n0-1] do
  Add(g,eij(i,i+1));
  Add(g,eij(n0+i,n0+i+1));
od;

return Group(g);
end;

Hope this helps,
Dmitrii

On 17 January 2011 12:21, Katie Morrison <kmorris2 at gmail.com> wrote:
> Hi all, I was wondering if there's an efficient way to create the subgroup
> of GL(2n, q) consisting of block matrices of the form:
> [A 0
> B C]
> where A and C are in GL(n,q) and B is in M(n,q) (i.e. B is an arbitrary nxn
> matrix).  Thanks for the help.
>
> Katie
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> Forum mailing list
> Forum at mail.gap-system.org
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>



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Dmitrii Pasechnik
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