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Remove NameIsomorphismClass #597

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Feb 9, 2016
Merged

Remove NameIsomorphismClass #597

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13 changes: 0 additions & 13 deletions grp/basicpcg.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -101,22 +101,10 @@ local pis, f, g, r, k, pi, i, geni, j, name, ps;
od;
if not HasIsCyclic( k ) then
SetIsCyclic( k, true );
SetNameIsomorphismClass( k, Concatenation( "c", String( Size( f ))));
return k;
fi;
Sort( pis );
SetAbelianInvariants( k, pis );
pis := Collected( pis );
name := "";
for i in pis do
Append( name, String( i[ 1 ] ) );
if i[ 2 ] > 1 then
name := Concatenation( name, "^", String( i[ 2 ] ) );
fi;
Append( name, "x" );
od;
Unbind( name[ Length( name ) ] );
SetNameIsomorphismClass( k, name );
return k;
end );

Expand Down Expand Up @@ -182,7 +170,6 @@ function( filter, n )

SetSize( f, n );
SetIsCyclic( f, true );
SetNameIsomorphismClass( f, Concatenation( "c", String( n ) ) );
return f;
end );

Expand Down
14 changes: 0 additions & 14 deletions lib/grp.gd
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Expand Up @@ -138,20 +138,6 @@ DeclareSynonymAttr( "GeneratorsOfGroup", GeneratorsOfMagmaWithInverses );
DeclareOperation( "GroupString", [IsGroup,IsString] );


#############################################################################
##
#A NameIsomorphismClass( <G> ) . . . . . . . . . . . . . . . . experimental
##
## <ManSection>
## <Attr Name="NameIsomorphismClass" Arg='G'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareAttribute( "NameIsomorphismClass", IsGroup );


#############################################################################
##
#P IsCyclic( <G> )
Expand Down
80 changes: 4 additions & 76 deletions small/smlgp1.g
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Expand Up @@ -68,11 +68,6 @@ SMALL_GROUP_FUNCS[ 1 ] := function( size, i, inforec )
if i > 1 then
Error( "there is just 1 group of size ", size );
fi;
if size = 1 then
g := TrivialGroup( IsPcGroup );
SetNameIsomorphismClass( g, Concatenation( "c", String( size ) ) );
return g;
fi;
return CyclicGroup( size );
end;

Expand Down Expand Up @@ -126,15 +121,6 @@ SMALL_GROUP_FUNCS[ 3 ] := function( size, i, inforec )

g := PcGroupFpGroup( F / rels );

if typ = "pq" then
SetNameIsomorphismClass( g, Concatenation( "c", String( size ) ) );
elif size = 6 then
SetNameIsomorphismClass( g, "S3" );
elif p = 2 then
SetNameIsomorphismClass( g, Concatenation( "D", String( size ) ) );
else
SetNameIsomorphismClass( g, Concatenation(String(q),":",String(p)) );
fi;
return g;
end;

Expand All @@ -145,7 +131,7 @@ end;
## order p^3
##
SMALL_GROUP_FUNCS[ 4 ] := function( size, i, inforec )
local F, gens, p, rels, g, name;
local F, gens, p, rels, g;

if i > 5 then
Error( "there are just 5 groups of size ", size );
Expand All @@ -157,34 +143,19 @@ SMALL_GROUP_FUNCS[ 4 ] := function( size, i, inforec )

if i = 1 then
rels := [ gens[1]^p / gens[2], gens[2]^p / gens[3], gens[3]^p ];
name := Concatenation( "c", String( size ) );
elif i = 2 then
rels := [ gens[1]^p / gens[3], gens[2]^p, gens[3]^p ];
name := Concatenation( String( p ), "x", String( p^2 ) );
elif i = 3 then
rels := [ gens[1]^p, gens[2]^p, gens[3]^p,
Comm( gens[2], gens[1] ) / gens[3] ];
if size = 8 then
name := "D8";
else
name := Concatenation( String( p ), "^2:", String( p ) );
fi;
elif i = 4 then
rels := [ gens[1]^p/gens[3], gens[2]^p, gens[3]^p,
Comm( gens[2], gens[1] ) / gens[3] ];
if size = 8 then
rels[ 2 ] := gens[2]^2/gens[3];
name := "Q8";
else
name := Concatenation( String( p^2 ), ":", String( p ) );
fi;
elif i = 5 then
rels := [ gens[1]^p, gens[2]^p, gens[3]^p ];
name := Concatenation( String( p ), "^3" );
fi;

g := PcGroupFpGroup( F / rels );
SetNameIsomorphismClass( g, name );
return g;
end;

Expand All @@ -196,7 +167,7 @@ end;
## order p ^ 2 * q
##
SMALL_GROUP_FUNCS[ 5 ] := function( size, i, inforec )
local n, typ, F, gens, rels, p, q, co, root, name, g;
local n, typ, F, gens, rels, p, q, co, root, g;

if not IsBound( inforec.types ) then
inforec := NUMBER_SMALL_GROUPS_FUNCS[ 5 ]( size, inforec );
Expand All @@ -214,30 +185,21 @@ SMALL_GROUP_FUNCS[ 5 ] := function( size, i, inforec )
typ := inforec.types[ i ];
if typ = "ppq" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ p, gens[ 3 ] ^ q ];
name := Concatenation( String( p ), "^2x", String( q ) );
elif typ = "p2q" then
rels := [ gens[ 1 ] ^ p / gens[ 3 ] , gens[ 2 ] ^ q, gens[ 3 ] ^ p ];
name := Concatenation( "c", String( size ) );
elif typ = "Dpqxp" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ p, gens[ 3 ] ^ q,
gens[3] ^ gens[1] /
gens[3] ^ ( PrimitiveRootMod(q) ^ ( (q-1)/p ) mod q ) ];
if p = 2 then
name := Concatenation( "D", String( size ) );
else
name := Concatenation( String(q),":", String(p),"x", String(p) );
fi;
elif typ = "a4" then
rels := [ gens[ 1 ] ^ 3, gens[ 2 ] ^ 2, gens[ 3 ] ^ 2,
gens[ 2 ] ^ gens[ 1 ] / gens[ 3 ],
gens[ 3 ] ^ gens[ 1 ] / gens[ 2 ] * gens[ 3 ] ];
name := "A4";
elif typ = "Gp2q" then
rels := [ gens[ 1 ] ^ p / gens[ 2 ], gens[ 2 ] ^ p,
gens[ 3 ] ^ q,
gens[3] ^ gens[1] /
gens[3] ^ ( PrimitiveRootMod(q) ^ ( (q-1)/p ) mod q ) ];
name := Concatenation( String( p*q ), ".", String( p ) );
else
# Hp2q
root := PrimitiveRootMod(q);
Expand All @@ -247,11 +209,9 @@ SMALL_GROUP_FUNCS[ 5 ] := function( size, i, inforec )
gens[3] ^ ( root ^ ( (q-1)/p^2 ) mod q ),
gens[3] ^ gens[2] /
gens[3] ^ ( root ^ ( (q-1)/p ) mod q ) ];
name := Concatenation( String( q ), ":", String( p*p ) );
fi;

g := PcGroupFpGroup( F / rels );
SetNameIsomorphismClass( g, name );
return g;
end;

Expand All @@ -262,7 +222,7 @@ end;
## order p * q ^ 2
##
SMALL_GROUP_FUNCS[ 6 ] := function( size, i, inforec )
local n, typ, F, gens, rels, p, q, root, base, vec, name, g;
local n, typ, F, gens, rels, p, q, root, base, vec, g;

if not IsBound( inforec.types ) then
inforec := NUMBER_SMALL_GROUPS_FUNCS[ 6 ]( size, inforec );
Expand All @@ -280,21 +240,12 @@ SMALL_GROUP_FUNCS[ 6 ] := function( size, i, inforec )
typ := inforec.types[ i ];
if typ = "pqq" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q, gens[ 3 ] ^ q ];
name := Concatenation( String( p ), "x", String( q ), "^2" );
elif typ = "pq2" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q / gens[ 3 ], gens[ 3 ] ^ q ];
name := Concatenation( "c", String( size ) );
elif typ = "Dpqxq" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q, gens[ 3 ] ^ q,
gens[3] ^ gens[1] /
gens[3] ^ ( PrimitiveRootMod(q) ^ ( (q-1)/p ) mod q ) ];
if q = 3 then
name := "S3x3";
elif p = 2 then
name := Concatenation( "D", String( p*q ), "x", String( q ) );
else
name := Concatenation( String(q),":", String(p),"x", String(q) );
fi;
elif typ = "Mpq2" then
root := PrimitiveRootMod( q ^ 2 );
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q / gens[ 3 ], gens[ 3 ] ^ q,
Expand All @@ -303,15 +254,13 @@ SMALL_GROUP_FUNCS[ 6 ] := function( size, i, inforec )
gens[3] ^ QuoInt( root ^ ( q*(q-1)/p ) mod ( q^2 ), q ) ),
gens[3] ^ gens[1] /
gens[3] ^ ( root ^ ( (q-1)/p ) mod q ) ];
name := Concatenation( String( q^2 ), ":", String( p ) );
elif typ = "Npq2" then
base := CanonicalBasis( GF( q ^ 2 ) );
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q, gens[ 3 ] ^ q ];
vec := IntVecFFE( Coefficients( base, Z(q^2) ^ ( (q^2-1)/p ) ) );
Add( rels, gens[2]^gens[1] / ( gens[2]^vec[1] * gens[3]^vec[2] ) );
vec := IntVecFFE( Coefficients( base, Z(q^2) ^ ( (q^2-1)/p+1 ) ) );
Add( rels, gens[3]^gens[1] / ( gens[2]^vec[1] * gens[3]^vec[2] ) );
name := Concatenation( String( q ), "^2:", String( p ) );
elif IsInt( typ ) then
# Kpq2( 1 ) or Lpq2( >1 )
root := PrimitiveRootMod( q ) ^ ( (q-1)/p );
Expand All @@ -321,9 +270,6 @@ SMALL_GROUP_FUNCS[ 6 ] := function( size, i, inforec )
fi;

g := PcGroupFpGroup( F / rels );
if IsBound( name ) then
SetNameIsomorphismClass( g, name );
fi;
return g;
end;

Expand All @@ -334,7 +280,7 @@ end;
## order p * q * r
##
SMALL_GROUP_FUNCS[ 7 ] := function( size, i, inforec )
local n, typ, F, gens, rels, p, q, r, root, r1, r2, g, name;
local n, typ, F, gens, rels, p, q, r, root, r1, r2, g;

if not IsBound( inforec.types ) then
inforec := NUMBER_SMALL_GROUPS_FUNCS[ 7 ]( size, inforec );
Expand All @@ -353,38 +299,23 @@ SMALL_GROUP_FUNCS[ 7 ] := function( size, i, inforec )
typ := inforec.types[ i ];
if typ = "pqr" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q, gens[ 3 ] ^ r ];
name := Concatenation( "c", String( size ) );
elif typ = "Dpqxr" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ r, gens[ 3 ] ^ q,
gens[3] ^ gens[1] /
gens[3] ^ ( PrimitiveRootMod(q) ^ ( (q-1)/p ) mod q ) ];
if q = 3 then
name := Concatenation( "S3x", String( r ) );
elif p = 2 then
name := Concatenation( "D", String( p*q ), "x", String( r ) );
else
name := Concatenation( String(q),":",String(p),"x",String(r) );
fi;
elif typ = "Dprxq" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q, gens[ 3 ] ^ r,
gens[3] ^ gens[1] /
gens[3] ^ ( PrimitiveRootMod(r) ^ ( (r-1)/p ) mod r ) ];
if p = 2 then
name := Concatenation( "D", String( p*r ), "x", String( q ) );
else
name := Concatenation( String(r),":",String(p),"x",String(q) );
fi;
elif typ = "Dqrxp" then
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q, gens[ 3 ] ^ r,
gens[3] ^ gens[2] /
gens[3] ^ ( PrimitiveRootMod(r) ^ ( (r-1)/q ) mod r ) ];
name := Concatenation( String(r),":",String(q),"x",String(p) );
elif typ = "Hpqr" then
root := PrimitiveRootMod( r );
rels := [ gens[ 1 ] ^ p, gens[ 2 ] ^ q, gens[ 3 ] ^ r,
gens[3] ^ gens[1] / gens[ 3 ] ^ ( root^((r-1)/p) mod r ),
gens[3] ^ gens[2] / gens[ 3 ] ^ ( root^((r-1)/q) mod r ) ];
name := Concatenation( String(r),":",String(p*q) );
elif IsInt( typ ) then
# Gpqr
r1 := First( [2..r-1], t -> t^p mod r = 1 );
Expand All @@ -395,9 +326,6 @@ SMALL_GROUP_FUNCS[ 7 ] := function( size, i, inforec )
fi;

g := PcGroupFpGroup( F / rels );
if IsBound( name ) then
SetNameIsomorphismClass( g, name );
fi;
return g;
end;

Expand Down
18 changes: 0 additions & 18 deletions small/smlinfo.gi
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Expand Up @@ -67,24 +67,6 @@ end );
#F SMALL_GROUPS_INFORMATION[ 1 ]( size, smav, num )
##
SMALL_GROUPS_INFORMATION[ 1 ] := function( size, smav, num )
local all, i;

all := AllSmallGroups( size );
for i in [ 1 .. Length( all ) ] do
if HasNameIsomorphismClass( all[ i ] ) then
Print(" ",i," is of type ",NameIsomorphismClass(all[i]),".\n");
else
if HasNameIsomorphismClass( all[ i - 1 ] ) then
Print( " ", i, " - ", Length(all)-1, " are of types " );
if smav.func = 6 then
Print( smav.q,":",smav.p,"+",smav.q,":",smav.p,".\n" );
else
Print( smav.q,":",smav.p,"+",smav.r,":",smav.p,".\n" );
fi;
fi;
fi;
od;

Print("\n");
Print(" The groups whose order factorises in at most 3 primes \n");
Print(" have been classified by O. Hoelder. This classification is \n");
Expand Down