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#######################################################################
#0
#F SL2ZResolution
## Input: A pair of positive integers (m,n)
##
## Output: The first n+1 terms of a free ZG-resolution
## where G is SL2Z(1/m)
##
InstallGlobalFunction(SL2ZResolution,
function(m,n)
local l,p,k,
C,R,T,RH,RK,RGamma,H,K,Gamma,D,G,F,RF;
l:=Factors(m);
p:=l[Length(l)];
k:=m/p;
R:=ResolutionSL2Z(1,n);
if m=1 then
return R;
else
RH:=SL2ZResolution(k,n);
H:=RH!.group;
## Create resolution for K
RK:=ConjugatedResolution(RH,[[1,0],[0,p]]);
RK!.group:=ConjugateSL2ZGroup(H,[[1,0],[0,p]]);
## Create resolution for Gamma
Gamma:=CongruenceSubgroup(k,p);
RGamma:=ResolutionFiniteSubgroup(RH,Gamma);
SetName(Gamma,"Gamma");
## Create tree of groups
D:=[RH,RK,RGamma];
G:=SL2Z(1/m);
## Compute a non-free complex for SL(2,Z[1/p])
F:=TreeOfResolutionsToSL2Zcomplex(D,G);
RF:=ResolutionGTree(F,n);
return RF;
fi;
end);
################### end of SL2ZResolution ############################
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