This is to announce bugfix number 2 for GAP 4b5. The priority of this fix
is high.

You should not apply this fix to any version of GAP3.

This fix corrects:
1) Several problems with conversion of lists to finite field vectors.
2) It provides a workaround for a problem in the online help under Windows9x.
3) SpecialPcgs sometimes do not know to belong to finite groups.
4) It fixes the ``hard'' compatibility mode.
5) It adds a convenience function `Factorization' (for teaching purposes)
as existed in GAP3.

The errors under 1 can lead to wrong results and system crashes.
Errors 3,4 will lead to error messages,
Error 2 meant that the online help under Windows did not necessarily
display the right sections.

Many thanks to:

Tom McDonough for reporting on of the errors under 1, Stefan Kohl for
reporting error 2, J"urgen Ecker for reporting error 3, Igor Schein for
reporting error 4.

Load the zoo archive 'fix4b5n2.zoo' from the bugfixes web page
http://www-gap.dcs.st-and.ac.uk/~gap/Info4/bugfixes.html
Alternatively you can find this file in the 'bugfixes' directory of the
GAP4 ftp distribution.

Unpack the file in the home directory of your GAP distribution (the
directory containing the 'lib' and 'grp' directories) using
'unzoo -x fix4b5n2.zoo'
(On a PC or a Mac you will have to copy `unzoo' in the same directory and
enter the argument line after the call to 'unzoo'.) This will replace the
erraneous file by fixed versions.
Make sure you have write permissions when applying the fix.

This fix changes the kernel. You have to recompile by calling `make' in the
directory in which you unpacked the fix. Windows users can find a new binary
in the file win4b5f2.zoo in the `bugfixes' directory.
*NOTE: For technical reasons this file winbin2 will only be available next
week.*

You can remove the file 'description2' afterwards.

Alexander Hulpke, 3-Feb-99

#############################################################################
##
## These commands should run without error if the fix has been applied.
##
G := SmallGroup( 6, 1 );
A := AutomorphismGroup( G );
IsomorphismPermGroup(A);

g := Group( [ (1,2), (3,4,5,6), (4,6) ] );
Exponent(g);
h := SylowSystem(g)[1];
Exponent(h);
l:=[ 0*Z(2), Z(2)^0, Z(2^3), Z(2^3)^3 ];
if l[2]=0*l[2] then Error();fi;

x_1:=Indeterminate(GF(2));
f:=x_1^3+x_1^4+x_1^6+x_1^7+x_1^9+x_1^11+x_1^12;
Factors(f);

F:=GF(4);
F_root:=GeneratorsOfField(F)[1];
u := Indeterminate(F,1); SetName(u,"u");
o:=One(u);
p:=o+u^3+u^4;
q:=o+u^4+u^5;
r:=p/q;
v:=o*F_root;
p:=o+v*u^3+u^4;
q:=o+u^4+v*u^5;
r:=p/q;

l:=[ 0*Z(2), Z(2)^0, Z(2^3), Z(2^3)^3 ];
if l[2]=0*l[2] then Error();fi;

nd:=[];
nd[1]:=Z(3);
nd[4]:=Z(3);
Print(nd);
Print("\n");