Dear forum,
I have written a program for the gauss algorithm, but it will run at the
second call:
gap> gauss:=function(A,m,n)
> local i,j,k,rcharind,B;
> k:=1;r:=0;charind:=[];
> repeat
>    for j in [1..n] do
>         if A[k][j]=0 then
>             for i in [k+1..m] do
>                 if A[i][j]<>0 then
>                     B:=A[i];A[i]:=A[k];A[k]:=B;
>                     break;
>                 fi;
>             od;
>         fi;
>         if A[k][j]<>0 then
>            r:=r+1;Add(charind,j);
>            A[k]:=A[k]*1/A[k][j];
>            for i in [k+1,m] do
>                 A[i]:=A[i]+A[k]*-A[i][j];
>            od;
>            k:=k+1;
>         fi;
>    od;
> until k=m;
> for k in [2..r] do
>    for i in [1..k-1] do
>       A[i]:=A[i]+A[k]*-A[i][charind[k]];
>    od;
> od;
> end;
function( A, m, n ) ... end

gap> A:=[ [ 1, -1, 1, 1, 1, 2 ], [ 0, 1, 2, 1, 5, 9 ], [ 0, 0, 0, 1, 2, 3
],
>   [ 0, 1, 2, -2, -1, 0 ], [ 0, 0, 0, 1, 2, -3 ] ];
[ [ 1, -1, 1, 1, 1, 2 ], [ 0, 1, 2, 1, 5, 9 ], [ 0, 0, 0, 1, 2, 3 ],
  [ 0, 1, 2, -2, -1, 0 ], [ 0, 0, 0, 1, 2, -3 ] ]

gap> gauss(A,5,6);

List Element: <list>[6] must have an assigned value at
A[i] := A[i] + A[k] * - A[i][j];
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop, you can 'quit;' to quit to outer loop,
or you can return after assigning a value to continue

now the second trial:

brk> quit;

gap> gauss(A,5,6);

gap> Display(A);
[ [  1,  0,  3,  0,  2,  0 ],
  [  0,  1,  2,  0,  3,  0 ],
  [  0,  0,  0,  1,  2,  0 ],
  [  0,  0,  0,  0,  0,  1 ],
  [  0,  0,  0,  0,  0,  0 ] ]

Who can explain that phenomen?

Best wishes

Kurt Ewald