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# All the functions in this file are intended to
# improve the readability of the rest of the programs.
InstallGlobalFunction(ExtractColumn,function(M,n)
# Returns column n of M as a list.
return List(M,x->x[n]);
end
);
InstallGlobalFunction(FirstLift,function(C,v)
# Returns a list containing a |v| by |G| matrix
# having the transpose of v in the first column.
local N,j;
N:=NullMat(Size(v),Size(C!.G),C!.K);
for j in [1..Size(v)] do N[j][1]:=v[j];od;
return [N];
end
);
InstallGlobalFunction(LiftChainMap,function(C,L,d,n)
# Lifts the chain map L of degree d several times.
# There will be a total of n lifts afterwards,
# not including the first map P_d -> P_0 in position 1.
# Thus, the last map in position n+1 will be P_{n+d} -> P_n.
local j,c;
ProjectiveResolution(C,d+n);
for j in [Size(L)..n] do
c:=C!.R[d+j]*LiftHom(C!.L[1],L[j],C!.p);
Append(L,[List(c,x->SolutionMat(C!.d[j],x))]);
od;
end
);
InstallGlobalFunction(LiftChainMapAlternating,function(C,L,d,n)
# Same as the previous function, but with a sign change.
# Read the documentation for an explanation of the (-1)^n.
local j,c;
ProjectiveResolution(C,d+n);
for j in [Size(L)..n] do
c:=C!.R[d+j]*LiftHom(C!.L[1],L[j],C!.p);
Append(L,[List((-1)^d*c,x->SolutionMat(C!.d[j],x))]);
od;
end
);
InstallMethod(SubgroupInclusion,"Inclusion of a subgroup",
[IsGroup,IsGroup], function(H,G)
return GroupHomomorphismByImages(H,G,
GeneratorsOfGroup(H),GeneratorsOfGroup(H));
end
);
InstallGlobalFunction(ActDiagonally,function(N,g)
# Applies g to each block of the vectors in N
local n,m;
m:=Size(g);
n:=Size(N[1])/m; # n is the number of block columns
return List(N,x->Concatenation(List([1..n],i->x{[(i-1)*m+1..i*m]}*g)));
end
);
[ Dauer der Verarbeitung: 0.5 Sekunden
(vorverarbeitet)
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