[GAP Forum] ZeroMutable for a group ring module

[Max Horn]

Dear Forum members,

I am doing some work in GAP with integral group rings, specifically with modules over those. For this, I wanted to get a mutable zero "vector" of a module M (to be modified later on). However, it turns out that ZeroMutable(M) does not work (in GAP 4.4.12) for my case. To my confusion, ZeroMutable(Zero(M)) *does* work.  Am I doing something wrong? Is this intentional or a bug?


Here's an explicit example

gap> G:=SymmetricGroup(3);	# Some group, doesn't matter which
Sym( [ 1 .. 3 ] )
gap> ZG:=GroupRing(Integers,G); # integral group ring of G
<free left module over Integers, and ring-with-one, with 2 generators>
gap> M:=ZG^3;			# some ZG module
( <free left module over Integers, and ring-with-one, with 2 generators>^3 )
gap> Zero(M); IsMutable(last);
[ <zero> of ..., <zero> of ..., <zero> of ... ]
false
gap> ZeroMutable(Zero(M)); IsMutable(last);
[ <zero> of ..., <zero> of ..., <zero> of ... ]
true
gap> ZeroMutable(M);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `ZERO_MUT' on 1 arguments called from
<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;' to continue
brk> 


Best regards,
Max