[GAP Forum] Orbit of group action on matrices

[Keshav Rao Kini]

Hello,

As the message states, you cannot assign values to elements of an immutable list. When you tested your act function at the prompt, you passed it a list literal, which is mutable. Presumably Orbit() is passing your function an immutable list (which is wise as it preserves the arguments you sent to Orbit()), which your function then chokes on. You could try for example using ShallowCopy() on the list x which is passed to your function:

gap> act:=function(x,g)
>     local i,y;
>     y:=ShallowCopy(x);
>     for i in [1..Length(y[1])] do y[i]:=Permuted(y[i],g); od;
>     return Permuted(y,g);
> end;
function( x, g ) ... end
gap> act([[1,2],[3,4]],(1,2));
[ [ 4, 3 ], [ 2, 1 ] ]
gap> Orbit(Group((1,2)),[[1,2],[3,4]],act);
[ [ [ 1, 2 ], [ 3, 4 ] ], [ [ 4, 3 ], [ 2, 1 ] ] ]
gap>

As I am a GAP beginner, I can't guarantee that there isn't a better way to do this, but it seems to work ;) Here is some more information about mutability: http://www.gap-system.org/Manuals/doc/htm/ref/CHAP012.htm#SECT006

Yours,
    Keshav

On Sat, Sep 25, 2010 at 14:36, Benjamin Sambale <bsambale at gmx.de<mailto:bsambale at gmx.de>> wrote:

 Dear Forum,

I've defined an action of a permutation group on a set of square
matrices in the following way:

act:=function(x,g)
    local i;
    for i in [1..Length(x[1])] do x[i]:=Permuted(x[i],g); od;
    return Permuted(x,g);
end;

This works as expected, for example:

gap> act([[1,2],[3,4]],(1,2));
[ [ 4, 3 ], [ 2, 1 ] ]

However, using the Orbit command gives

gap> Orbit(Group((1,2)),[[1,2],[3,4]],act);
Lists Assignment: <list> must be a mutable list

What is wrong here?

Thanks,
Benjamin Sambale

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