gap('LoadPackage("QPA");')

import tempfile as _tf, os as _os
_gap_code = r"""
DeclareOperation("NthRadical",[IsList]);
InstallMethod(NthRadical, "for a representation of a quiver", [IsList], 0, function(LIST)
    local M, N, f, h, i, n;
    M := LIST[1];
    n := LIST[2];
    if n = 0 then
        return(IdentityMapping(M));
    else
        f := RadicalOfModuleInclusion(M);
        N := Source(f);
        for i in [1..n-1] do
            h := RadicalOfModuleInclusion(N);
            N := Source(h);
            f := \*(h,f);
        od;
        return(f);
    fi;
end);

DeclareOperation("ARQuiverNak",[IsList]);
InstallMethod(ARQuiverNak, "for a representation of a quiver", [IsList], 0, function(LIST)
    local A, UU, i, injA, j;
    A := LIST[1];
    injA := IndecInjectiveModules(A);
    UU := [];
    for i in injA do
        for j in [0..Dimension(i)-1] do
            Append(UU,[Source(NthRadical([i,j]))]);
        od;
    od;
    return(UU);
end);

DeclareOperation("TiltingModulesnosim",[IsList]);

InstallMethod(TiltingModulesnosim, "for a representation of a quiver", [IsList],0,function(LIST)
    local A, L, LL, W, WW, g, i, priA, prinjA, projA, r, subsets1, subsets2;
    A := LIST[1];
    g := GlobalDimensionOfAlgebra(A,30);
    L := Filtered(ARQuiverNak([A]),x->Dimension(x)>1);
    LL := Filtered(L,x->(IsProjectiveModule(x)=false or IsInjectiveModule(x)=false));
    r := Size(SimpleModules(A))-(Size(L)-Size(LL));
    subsets1 := Combinations([1..Length(LL)],r);
    subsets2 := List(subsets1,x->LL{x});
    W := Filtered(subsets2,x->N_RigidModule(DirectSumOfQPAModules(x),g)=true);
    projA := IndecProjectiveModules(A);
    prinjA := Filtered(projA,x->IsInjectiveModule(x)=true);
    priA := DirectSumOfQPAModules(prinjA);
    WW := [];
    for i in W do Append(WW,[DirectSumOfQPAModules([priA,DirectSumOfQPAModules(i)])]);
    od;

    return(Size(WW));
end);
"""
with _tf.NamedTemporaryFile(mode="w", suffix=".g", delete=False, dir="/tmp") as _f:
    _f.write('LoadPackage("QPA");;\n')
    _f.write(_gap_code)
    _tmp = _f.name
gap.eval('Read("' + _tmp + '");')
_os.unlink(_tmp)

def kupisch(D):
    DR = D.reverse()
    H = DR.heights()
    return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]

def statistic(D):
    K = kupisch(D)
    A = gap.NakayamaAlgebra(gap.GF(3), K)
    return ZZ(gap.TiltingModulesnosim([A]))