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###############################################################################
##
#F Apps.gi The SymbCompCC package Dörte Feichtenschlager
##
###############################################################################
##
## AbelianInvariantsMultiplier( ParPres )
##
## Input: p-power-poly-pcp-groups ParPres
##
## Output: a list, describing the structure of the Schur multiplicators /
## multipliers of ParPres
##
InstallMethod(AbelianInvariantsMultiplier, [ IsPPPPcpGroups ],
function( ParPres )
local p, cc, name, pos, expo_vec, m, SchurMult, l_sm, i, Zero0, S, One1;
if ParPres!.m > 0 then
Error( "The function needs an infinite coclass sequence as input." );
fi;
p := ParPres!.prime;
cc := ParPres!.cc;
name := ParPres!.name;
Zero0 := Int2PPowerPoly( p, 0 );
One1 := Int2PPowerPoly( p, 1 );
if p = 2 and cc = 1 then
pos := Position( ParPresGlobalVar_2_1_Names, name );
if pos = fail then
Error( "Wrong name of presentations." );
fi;
S := GetMatrixPPowerPolySchurExt( ParPresGlobalVar_2_1[pos] );
S := PPowerPolyMat2PPowerPolyLocMat( S );
S := SmithNormalFormPPowerPoly( S );
expo_vec := [];
for i in [1..Length( S[1] )] do
expo_vec[i] := S[i][i]![1];
od;
m := Length( expo_vec );
elif p = 2 and cc = 2 then
pos := Position( ParPresGlobalVar_2_2_Names, name);
if pos = fail then
Error( "Wrong name of presentations." );
fi;
S := GetMatrixPPowerPolySchurExt( ParPresGlobalVar_2_2[pos] );
S := PPowerPolyMat2PPowerPolyLocMat( S );
S := SmithNormalFormPPowerPoly( S );
expo_vec := [];
for i in [1..Length( S[1] )] do
expo_vec[i] := S[i][i][1];
od;
m := Length( expo_vec );
elif p = 3 and cc = 1 then
pos := Position( ParPresGlobalVar_3_1_Names, name);
if pos = fail then
Error( "Wrong name of presentations." );
fi;
S := GetMatrixPPowerPolySchurExt( ParPresGlobalVar_3_1[pos] );
S := PPowerPolyMat2PPowerPolyLocMat( S );
S := SmithNormalFormPPowerPoly( S );
expo_vec := [];
for i in [1..Length( S[1] )] do
expo_vec[i] := S[i][i][1];
od;
m := Length( expo_vec );
else Error( "The parameter presentations are not yet in the data base." );
fi;
SchurMult := [];
l_sm := 0;
for i in [1..m] do
if not PPP_Equal( expo_vec[i], Zero0 ) and not PPP_Equal( expo_vec[i], One1 ) then
l_sm := l_sm + 1;
SchurMult[l_sm] := expo_vec[i];
fi;
od;
return SchurMult;
end);
###############################################################################
##
## SchurMultiplicatorPPPPcps( ParPres )
##
## Input: p-power-poly-pcp-groups ParPres
##
## Output: a list, describing the structure of the Schur multiplicators /
## multipliers of ParPres
##
InstallMethod( SchurMultiplicatorPPPPcps, [ IsPPPPcpGroups ],
function( G )
local SchurMult, SchurMultParPres, Zero0, One1, i, j, rel;
if G!.m > 0 then
Error( "The function needs an infinite coclass sequence as input." );
fi;
## get the structure describtion of the Schur Multiplier
SchurMult := AbelianInvariantsMultiplier( G );
## initalize
SchurMultParPres := rec( prime := G!.prime );
SchurMultParPres!.n := 0;
SchurMultParPres!.d := 0;
SchurMultParPres!.m := Length( SchurMult );
SchurMultParPres!.cc := fail;
SchurMultParPres!.expo := 1;
SchurMultParPres!.expo_vec := SchurMult;
SchurMultParPres!.name := Concatenation( "SchurMult", G!.name );
## get the relations
Zero0 := Int2PPowerPoly( G!.prime, 0 );
One1 := Int2PPowerPoly( G!.prime, 1 );
rel := [];
for i in [1..Length( SchurMult )] do
rel[i] := [];
for j in [1..i-1] do
rel[i][j] := [[ j, One1 ]];
od;
rel[i][i] := [[ i, Zero0 ]];
od;
SchurMultParPres!.rel := rel;
return PPPPcpGroups( SchurMultParPres );
end);
#E Apps.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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