Dear Forum,

This is to announce bugfix number 2 for GAP 4.1. The priority of this fix
is high.

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

This fix corrects:
1) Problems with the 0 Laurent polynomial. (reported by Craig Struble)
2) Problems with `BinaryRelationByListOfImagesNC'. (rep. Robert Morse)
3) A problems with `AllPrimitiveGroups'. (Christian Pech)
4) A problem with `ConjugacyClasses'. (rep. H. Pahlings)
5) A problem with the tables of marks. (Davide Ferrario)
6) A problem with `CompanionMat'. (Craig Struble)
7) A problem with ideals of ideals in group rings. (Craig Struble)
8) A problem with `DirectSumMat' over finite fields. (Craig Struble)
9) A problem with `MaximalAbelianQuotient', causing `IdGroup' to break
down.

Error 3 and 8 might produce wrong results.

Many thanks to:
Craig Struble for reporting errors 1, 6, 7, 8.
Peter Prohle for reporting error 9.
Robert Morse for reporting error 2.
Christian Pech for reporting error 3.
Herbert Pahlings for reporting error 4.
Davide Ferrario for reporting error 5.

Load the zoo archive 'fix4r1n2.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
fix4r1n2.zoo'. `unzoo' may ask you for permissions to overwrite files,
answer this with Y)es or A)ll. This will replace the erraneous file by
fixed versions.

(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'.)
Make sure you have write permissions when applying the fix.

This fix does *not* change the kernel. So Windows and Mac users do not
need a new binary.

You can remove the file 'description2' afterwards.

Alexander Hulpke, Willem de Graaf, 27-Aug-99

#############################################################################
##
## These commands should run without trouble or error if the fix has been 
## applied.
##
F := GF(3);;
fam := ElementsFamily(FamilyObj(F));;
p := LaurentPolynomialByCoefficients( fam, [One(F)], 0 );
Derivative(p);
Gcd( p, Derivative(p) );
AllPrimitiveGroups(DegreeOperation,64);
gens:=                                                                          
[ (  3, 10)(  6, 18)( 11, 26)( 12, 27)( 13, 28)( 19, 40)( 20, 41)( 24, 32)      
    ( 29, 53)( 30, 54)( 31, 55)( 33, 57)( 42, 69)( 43, 70)( 45, 71)( 49, 61)    
    ( 51, 63)( 58, 83)( 59, 84)( 60, 85)( 62, 86)( 64, 87)( 68, 82)( 72, 91)    
    ( 73, 92)( 75, 93)( 78, 94)( 80, 89)( 81, 90)( 88, 99),                     
  (  1,  2)(  3,  6)(  4,  7)(  9, 17)( 10, 18)( 11, 19)( 13, 32)( 14, 21)      
    ( 23, 37)( 24, 28)( 25, 38)( 26, 40)( 29, 42)( 31, 61)( 33, 63)( 34, 46)    
    ( 39, 65)( 48, 66)( 49, 55)( 50, 67)( 51, 57)( 53, 69)( 58, 72)( 60, 89)    
    ( 62, 90)( 68, 78)( 80, 85)( 81, 86)( 82, 94)( 83, 91),                     
  (  1,  3)(  2,  6)(  4, 11)(  7, 19)(  9, 24)( 14, 29)( 17, 28)( 20, 44)      
    ( 21, 42)( 23, 49)( 25, 51)( 27, 56)( 34, 58)( 37, 55)( 38, 57)( 39, 68)    
    ( 43, 74)( 45, 76)( 46, 72)( 48, 80)( 50, 81)( 54, 77)( 65, 78)( 66, 85)    
    ( 67, 86)( 73, 95)( 75, 96)( 84, 98)( 87, 97)( 99,100),                     
  (  1,  4)(  2,  7)(  3, 11)(  6, 19)(  8, 22)( 10, 26)( 12, 30)( 18, 40)      
    ( 27, 54)( 35, 36)( 48, 50)( 56, 77)( 60, 62)( 66, 67)( 73, 75)( 80, 81)    
    ( 85, 86)( 89, 90)( 92, 93)( 95, 96), (  4, 14)(  7, 21)( 11, 29)( 15, 36)  
    ( 19, 42)( 22, 47)( 23, 50)( 26, 53)( 30, 59)( 31, 62)( 37, 67)( 40, 69)    
    ( 43, 75)( 49, 81)( 54, 84)( 55, 86)( 61, 90)( 70, 93)( 74, 96)( 77, 98),   
  (  5, 15)(  9, 23)( 13, 31)( 14, 34)( 17, 37)( 20, 43)( 21, 46)( 24, 49)      
    ( 28, 55)( 29, 58)( 32, 61)( 41, 70)( 42, 72)( 44, 74)( 47, 79)( 53, 83)    
    ( 59, 88)( 69, 91)( 84, 99)( 98,100), (  5, 16)(  9, 25)( 13, 33)( 17, 38)  
    ( 20, 45)( 24, 51)( 28, 57)( 32, 63)( 34, 65)( 39, 46)( 41, 71)( 44, 76)    
    ( 52, 79)( 58, 78)( 64, 88)( 68, 72)( 82, 91)( 83, 94)( 87, 99)( 97,100),   
  (  2,  8)(  3, 12)(  5, 17)(  7, 22)( 10, 27)( 11, 30)( 15, 37)( 16, 38)      
    ( 20, 32)( 21, 47)( 24, 41)( 26, 54)( 29, 59)( 35, 66)( 36, 67)( 39, 52)    
    ( 43, 61)( 45, 63)( 46, 79)( 49, 70)( 51, 71)( 53, 84)( 58, 88)( 64, 78)    
    ( 73, 89)( 75, 90)( 80, 92)( 81, 93)( 83, 99)( 87, 94)];;                   
g:=Group(gens); 
c:=ConjugacyClasses(g);
a:=
[ [ 1, 2, -1, 3, 3/4, 3 ], [ 2, 1, 3/4, 3, -1, 3 ], [ -1, 3, 1, 2, 3, 3/4 ],
  [ 3/4, 3, 2, 1, 3, -1 ], [ 3, -1, 3, 3/4, 1, 2 ], [ 3, 3/4, 3, -1, 2, 1 ] ];
mp:=MinimalPolynomial(Rationals, a, 1);
CompanionMat(mp);
g := GroupRing(GF(7), SymmetricGroup(4));
I:= Ideal( g, [ Basis(g)[1] ] );
J:= Ideal( g, [ Basis(I)[1] ] );
m:= IdentityMat( 2, GF(3) );
if not DirectSumMat( m,m)=
[ [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], 
  [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ] ]
then print( "ERROR-diretcsummat" ); fi;

b := BinaryRelationByListOfImagesNC([[1],[2],[3]]);
if not IsDomain(Source(b)) then Print(" ERROR-bin_rel" ); fi;

# The following command requires the tables of marks to be installed. If
# they are not installed it will issue a - then harmless - error.
G:=DihedralGroup(6);
tm:=TableOfMarks(G);
H:=RepresentativeTom(tm,2);
th:=CharacterTable(H);
Size(H);
SizesConjugacyClasses(th);
Display(tm);
Display(th);