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###############################################################################
##
#F RelGroups.gi The SymbCompCC package Dörte Feichtenschlager
##
###############################################################################
##
## GetRelAsWord( rel, n, d, p, m, FSet )
##
## Input: a relation rel, number of generators n, d, m, a prime p and a set of
## free generators FSet
##
## Output: the relation rel as word
##
InstallMethod( GetRelAsWord,
"take rel and make a word out of it",
[ IsList, IsInt, IsInt, IsPosInt, IsInt, IsList ],
function( rel, n, d, p, m, FSet )
local exp, word, i;
if not IsPrime( p ) then
Error( "Wrong input, the fourth parameter has to be a prime." );
fi;
## get first
if rel[1][1] <= n then
exp := rel[1][2];
else exp := EvaluatePPowerPoly( rel[1][2], m );
fi;
word := FSet[rel[1][1]]^exp;
## get rest
for i in [2..Length( rel )] do
if rel[i][1] <= n then
exp := rel[i][2];
else exp := EvaluatePPowerPoly( rel[i][2], m );
fi;
word := word*FSet[rel[i][1]]^exp;
od;
return word;
end);
###############################################################################
##
## GetPcGroupPPowerPoly( ParPres, m )
##
## Input: a record ParPres, presententing p-power-poly-pcp-groups, and an
## integer m
##
## Ouput: a pc-group which corresponds to ParPres evaluated at m
##
InstallMethod( GetPcGroupPPowerPoly,
"take rels and get a pc-presentation for the group",
[ IsRecord, IsInt],
function( ParPres, m )
local p, n, d, rel, expo, F, FSet, relord, i, coll, word, j, G,
Zero0, One1;
if not IsPrime( ParPres!.prime ) then Error("Wrong input." ); fi;
p := ParPres!.prime;
n := ParPres!.n;
d := ParPres!.d;
rel := ParPres!.rel;
expo := ParPres!.expo;
Zero0 := Int2PPowerPoly( p, 0 );
One1 := Int2PPowerPoly( p, 1 );
## initalize free group
F := FreeGroup( n+d );
FSet := GeneratorsOfGroup( F );
## get relative order vector
relord := [];
for i in [1..n] do
relord[i] := p;
od;
for i in [n+1..n+d] do
relord[i] := EvaluatePPowerPoly( expo, m );
od;
## initalize collector
coll := SingleCollector( F, relord );
## get powers
for i in [1..n] do
if rel[i][i] <> [[i,0]] then
word := GetRelAsWord( rel[i][i], n, d, p, m, FSet );
SetPower( coll, i, word );
fi;
od;
for i in [n+1..n+d] do
if rel[i][i] <> [[i,Zero0]] then
word := GetRelAsWord( rel[i][i], n, d, p, m, FSet );
SetPower( coll, i, word );
fi;
od;
## get conjugates
for i in [1..n] do
for j in [1..i-1] do
if rel[i][j] <> [[i,1]] then
word := GetRelAsWord( rel[i][j], n, d, p, m, FSet );
SetConjugate( coll, i, j, word );
fi;
od;
od;
for i in [n+1..n+d] do
for j in [1..i-1] do
if rel[i][j] <> [[i,One1]] then
word := GetRelAsWord( rel[i][j], n, d, p, m, FSet );
SetConjugate( coll, i, j, word );
fi;
od;
od;
G := GroupByRws( coll );
return G;
end);
###############################################################################
##
## GetPcGroupPPowerPoly( G, m )
##
## Input: p-power-poly-pcp-groups G and an integer m
##
## Ouput: a pc-group which corresponds to G evaluated at m
##
InstallMethod( GetPcGroupPPowerPoly,
"take rels and get a pc-presentation for the group",
[ IsPPPPcpGroups, IsInt],
function( G, m )
local ParPres;
ParPres := rec( prime := G!.prime );
ParPres!.rel := G!.rel;
ParPres!.n := G!.n;
ParPres!.d := G!.d;
ParPres!.m := G!.m;
ParPres!.expo := G!.expo;
ParPres!.expo_vec := G!.expo_vec;
ParPres!.cc := G!.cc;
ParPres!.name := G!.name;
return GetPcGroupPPowerPoly( ParPres, m );
end);
###############################################################################
##
## GetPcpGroupPPowerPoly( SchurExtParPres, x )
##
## Input: a record SchurExtParPres, presententing p-power-poly-pcp-groups,
## and an integer x
##
## Ouput: a pcp-group which corresponds to SchurExtParPres evaluated at x
##
InstallMethod( GetPcpGroupPPowerPoly,
"take rels of Schur extension and get a pcp-presentation for this",
[ IsRecord, IsInt ],
function( SchurExtParPres, x )
local p, n, d, m, rel, expo, expo_vec, coll, Zero0, One1, word,
rel_pcp, help, i, j, k, G, rel_ordC, rel_ord;
if not IsPrime( SchurExtParPres!.prime ) then Error("Wrong input." ); fi;
p := SchurExtParPres!.prime;
n := SchurExtParPres!.n;
d := SchurExtParPres!.d;
m := SchurExtParPres!.m;
rel := SchurExtParPres!.rel;
expo := SchurExtParPres!.expo;
expo_vec := SchurExtParPres!.expo_vec;
Zero0 := Int2PPowerPoly( p, 0 );
One1 := Int2PPowerPoly( p, 1 );
## initalize collector
coll := FromTheLeftCollector( n+d+m );
## set relative orders
for i in [1..n] do
SetRelativeOrder( coll, i, p );
od;
word := EvaluatePPowerPoly( expo, x );
rel_ord := word;
for i in [1..d] do
SetRelativeOrder( coll, n+i, word );
od;
rel_ordC := [];
for i in [1..m] do
if expo_vec[i] <> Zero0 then
word := EvaluatePPowerPoly( expo_vec[i], x );
rel_ordC[i] := word;
SetRelativeOrder( coll, n+d+i, word );
else rel_ordC[i] := 0;
fi;
od;
## get powers
for i in [1..n] do
if rel[i][i] <> [[i,0]] then
rel_pcp := [];
for j in [1..Length(rel[i][i])] do
help := Length( rel_pcp );
if rel[i][i][j][1] <= n then
rel_pcp[help+1] := rel[i][i][j][1];
rel_pcp[help+2] := rel[i][i][j][2];
else word := EvaluatePPowerPoly( rel[i][i][j][2], x );
if rel[i][i][j][1] <= n+d then
word := word mod rel_ord;
if word <> 0 then
rel_pcp[help+1] := rel[i][i][j][1];
rel_pcp[help+2] := word;
fi;
else word := word mod rel_ordC[rel[i][i][j][1]-n-d];
if word <> 0 then
rel_pcp[help+1] := rel[i][i][j][1];
rel_pcp[help+2] := word;
fi;
fi;
fi;
od;
SetPower( coll, i, rel_pcp );
fi;
od;
for i in [1..d] do
if rel[n+i][n+i] <> [[n+i,Zero0]] then
rel_pcp := [];
for j in [1..Length(rel[n+i][n+i])] do
help := Length( rel_pcp );
if rel[n+i][n+i][j][1] <= n then
rel_pcp[help+1] := rel[n+i][n+i][j][1];
rel_pcp[help+2] := rel[n+i][n+i][j][2];
else word := EvaluatePPowerPoly( rel[n+i][n+i][j][2], x );
if rel[n+i][n+i][j][1] <= n+d then
word := word mod rel_ord;
if word <> 0 then
rel_pcp[help+1] := rel[n+i][n+i][j][1];
rel_pcp[help+2] := word;
fi;
else word := word mod rel_ordC[rel[n+i][n+i][j][1]-n-d];
if word <> 0 then
rel_pcp[help+1] := rel[n+i][n+i][j][1];
rel_pcp[help+2] := word;
fi;
fi;
fi;
od;
SetPower( coll, n+i, rel_pcp );
fi;
od;
## get conjugates
for i in [2..n] do
for j in [1..i-1] do
if rel[i][j] <> [[i,1]] then
rel_pcp := [];
for k in [1..Length(rel[i][j])] do
help := Length( rel_pcp );
if rel[i][j][k][1] <= n then
rel_pcp[help+1] := rel[i][j][k][1];
rel_pcp[help+2] := rel[i][j][k][2];
else word := EvaluatePPowerPoly( rel[i][j][k][2], x );
if rel[i][j][k][1] <= n+d then
word := word mod rel_ord;
if word <> 0 then
rel_pcp[help+1] := rel[i][j][k][1];
rel_pcp[help+2] := word;
fi;
else word := word mod rel_ordC[rel[i][j][k][1]-n-d];
if word <> 0 then
rel_pcp[help+1] := rel[i][j][k][1];
rel_pcp[help+2] := word;
fi;
fi;
fi;
od;
SetConjugate( coll, i, j, rel_pcp );
fi;
od;
od;
for i in [1..d] do
for j in [1..n+i-1] do
if rel[n+i][j] <> [[n+i,Zero0]] then
rel_pcp := [];
for k in [1..Length(rel[n+i][j])] do
help := Length( rel_pcp );
if rel[n+i][j][k][1] <= n then
rel_pcp[help+1] := rel[n+i][j][k][1];
rel_pcp[help+2] := rel[n+i][j][k][2];
else word := EvaluatePPowerPoly( rel[n+i][j][k][2], x );
if rel[n+i][j][k][1] <= n+d then
word := word mod rel_ord;
if word <> 0 then
rel_pcp[help+1] := rel[n+i][j][k][1];
rel_pcp[help+2] := word;
fi;
else word := word mod rel_ordC[rel[n+i][j][k][1]-n-d];
if word <> 0 then
rel_pcp[help+1] := rel[n+i][j][k][1];
rel_pcp[help+2] := word;
fi;
fi;
fi;
od;
SetConjugate( coll, n+i, j, rel_pcp );
fi;
od;
od;
UpdatePolycyclicCollector( coll );
G := PcpGroupByCollector( coll );
return G;
end);
###############################################################################
##
## GetPcpGroupPPowerPoly( H, x )
##
## Input: p-power-poly-pcp-groups H and an integer x
##
## Ouput: a pcp-group which corresponds to H evaluated at x
##
InstallMethod( GetPcpGroupPPowerPoly,
"take rels of Schur extension and get a pcp-presentation for this",
[ IsPPPPcpGroups, IsInt ],
function( H, x )
local ParPres;
ParPres := rec( prime := H!.prime );
ParPres!.rel := H!.rel;
ParPres!.n := H!.n;
ParPres!.d := H!.d;
ParPres!.m := H!.m;
ParPres!.expo := H!.expo;
ParPres!.expo_vec := H!.expo_vec;
ParPres!.cc := H!.cc;
ParPres!.name := H!.name;
return GetPcpGroupPPowerPoly( ParPres, x );
end);
#E RelGroups.gi . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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