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

import tempfile as _tf, os as _os
_gap_code = r"""
DeclareOperation("ARQuiver", [IsList]);

InstallMethod(ARQuiver, "for an algebra and bound", [IsList], 0, function(LIST)
    local A, L, N, PI, bound, dim, f, h, inj, injA, j;
    A := LIST[1];
    bound := LIST[2];
    injA := IndecInjectiveModules(A);
    L := [];
    for inj in injA do
        dim := Dimension(inj);
        for j in [0..dim-1] do
            if j = 0 then
                f := IdentityMapping(inj);
            else
                f := RadicalOfModuleInclusion(inj);
                N := Source(f);
                h := 1;
                while h < j do
                    f := RadicalOfModuleInclusion(N);
                    N := Source(f);
                    h := h + 1;
                od;
            fi;
            Add(L, Source(f));
        od;
    od;
    PI := Filtered(L, x -> IsProjectiveModule(x) and IsInjectiveModule(x));
    return [PI, L];
end);

DeclareOperation("numbersprojinjdimg", [IsList]);

InstallMethod(numbersprojinjdimg, "for a representation of a quiver", [IsList],0,function(LIST)
    local A, L, LL, g, list;
    list := LIST[1];
    g := LIST[2];
    A := NakayamaAlgebra(GF(3),list);
    L := ARQuiver([A,1000])[2];
    LL := Filtered(L,x->ProjDimensionOfModule(x,g)=g and InjDimensionOfModule(x,g)=g);
    return(Size(LL));
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 gldim_from_kupisch(L):
    n = len(L)
    def f(x, y):
        c = (x + y) % n
        if c == 0: c = n
        z = (x + 1) % n
        if z == 0: z = n
        return (c, L[z - 1] - y)
    temp = [[(i, 1)] for i in range(n)]
    for i in range(n):
        for _ in range(2 * n + 2):
            temp[i].append(f(temp[i][-1][0], temp[i][-1][1]))
    temp3 = []
    for i in range(n):
        zeros = [j + 1 for j in range(len(temp[i])) if temp[i][j][1] == 0]
        if zeros:
            temp3.append(min(zeros))
        else:
            return "inf"
    return max(temp3) - 2

def statistic(D):
    K = kupisch(D)
    g = gldim_from_kupisch(K)
    return ZZ(gap.numbersprojinjdimg([K, g]))