Dear Gap-Forum,

This is to announce bugfix number 5 for GAP 4b4. The priority of this fix
is high.

You should not apply this fix to any version of GAP3.
To apply the fix, you must have installed bugfixes 1 to 4 first.

This fix corrects:
1) An error in computing coefficients of a multivariate polynomail that
happens to be univariate.
2) A Problem with `GQuotient' when applied to free groups.
3) A too generous method installation for `MinimalGeneratingSet'. It also
adds redispatch methods for solvable permutation groups as a convenience.
4) A problem with forming factor groups of direct products
5) An error when creating finite fields by special polynomials
6) An error in `CharacterTableDirectProduct'
7) Recursion problems when computing with algebras.
8) A misleading error message in `ApplicableMethod'

Error 1 may lead to wrong results in the polynomial arithmetic.
Errors 2-8 lead to error messages.

Many thanks to:
David Hough for reporting error 1.
Esteban Crespi for reporting error 2 and problem 3.
Russell Blyth for reporting error 4.
Jacob Hirbawi for reporting error 5 and 6.
Craig Struble for reporting error 7.
Burkhard H"ofling for reporting problem 8.

Load the zoo archive 'fix4b4n5.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 fix4b4n5.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 does not change the kernel. You do not need to recompile. (Windows
users however should get the latest compiled binary in the file
`winbin2a.zoo' from the bugfixes page.)

You can remove the file 'description4' afterwards.

Alexander Hulpke, 6-Nov-98

#############################################################################
##
## These commands should run without error if the fix has been applied.
##
m:=[[3,3,3,3,3],[3,2,3,2,3],[3,3,2,2,3],[3,2,2,1,2],[3,3,3,2,2]];
r := Indeterminate(Rationals,"r");
mm := List(m,x->List(x,y->r^y));
d:=Determinant(mm);
if Length(Factors(d))<>15 then
  Error("arithmetic bug!");
fi;
G := Group((1,2,3),(1,2));
F := FreeGroup("a","b");
GQuotients(F,G);
G:=Group((1,4)(2,6)(3,5),(1,4)(2,5)(3,6),(1,3,2)(4,5,6),(1,2,3)(4,5,6)); 
MinimalGeneratingSet(G); 

G:=DirectProduct(AlternatingGroup(4),DihedralGroup(4));
C:=Centre(G);
F:=FactorGroup(G,C);

GF(2,UnivariatePolynomial(GF(2),Z(2)*[1,1,1,0,0,0,0,1,1],1));

c2:=CharacterTable("Cyclic",2);
c4:=CharacterTableDirectProduct(c2,c2);

A := FreeAlgebra(GF(7), 2);
x := GeneratorsOfAlgebra(A)[1];
y := GeneratorsOfAlgebra(A)[2];
I := Ideal(A, [x*y - y*x, x*x, y*y]);
B := A/I;