Magma

// Linear algebra!

import "helper.m" : MVM;

function Decompose(T, t)
	// The characteristic polynomial of this matrix.
	chi := CharacteristicPolynomial(T);

	// Factorization of the characteristic polynomial.
	fs := Factorization(chi);

	// The eigenspaces arising from this matrix.
	spaces := [* *];

	for data in fs do
		// Number field associated to one of the irreducible factors.
		// TODO: Fix this. Sometimes crashes.
		//K := NumberField(ChangeRing(data[1], Rationals()));
		K := NumberField(data[1]);
		// TODO: Keep an eye out for this, make sure it works.

		// The eigenvalue associated to this factor.
		if Degree(data[1]) eq 1 then
			eig := -Evaluate(data[1], 0);
		else
			eig := K.1;
		end if;

		// If the field K is not the rationals, try to optimize it as
		//  long as the degree of the field isn't too large.
		if Category(K) ne FldRat and Degree(K) le 8 then
			// Optimize the number field.
			K, map := OptimizedRepresentation(K);

			// The eigenvalue in the new field.
			eig := map(eig);
		end if;

		// The identity matrix of the appropriate dimension.
		id := Id(MatrixRing(K, Nrows(t)));

		// Promote the ambient matrix to the current number field.
		tt := ChangeRing(t, K);

		// Add eigenspace to the list of spaces and flag it depending
		//  on whether this eigenspace is irreducible.
		Append(~spaces,
			< Nullspace(Transpose(tt)-eig*id), data[2] eq 1 >);
	end for;

	return spaces;
end function;

intrinsic EigenspaceDecomposition(array::Assoc : Warning := true)
	-> List, SeqEnum
{ Decompose an array of mutually commuting matrices into their eigenspaces. }
	// Make sure that the associative array is non-empty.
	require #array ne 0: "Associative array must not be empty.";

	// Extract the keys associated to the associative array.
	keys := Keys(array);

	// Put keys into an enumerative array.
	keys := [ x : x in keys ];

	// Extract the full list of matrices.
	Ts := [ array[x] : x in keys ];

	// Verify that all matrices mutually commute.
	require &and[ A*B eq B*A : A,B in Ts ]:
		"Matrices in array do not mutually commute.";

	// List of eigenspaces for the first matrix.
	sp := Decompose(Ts[1], Ts[1]);

	for idx in [2..#Ts] do
		// If all eigenspaces are irreducible, we're done.
		if &and[ data[2] : data in sp ] then break; end if;

		// The number of eigenspaces we are starting with.
		num := #sp;

		// Keep track of the eigenspaces we'll need to delete.
		delList := [];

		for i in [1..num] do
			// Skip this eigenspace if it is irreducible.
			if sp[i][2] then continue; end if;

			// Add the current eigenspace to the delete list.
			Append(~delList, i);

			// The current subspace.
			space := sp[i][1];

			// Dimension of this space.
			dim := Dimension(space);

			// The basis of this space.
			basis := Basis(space);

			// The pivots for this space.
			pivots := [ 0 : v in basis ];
			for j in [1..#basis] do
				repeat pivots[j] +:= 1;
				until basis[j][pivots[j]] ne 0;
			end for;

			// Modify the base ring in preparation for matrix-
			//  vector multiplication.
			tempT := ChangeRing(Ts[idx], BaseRing(space));

			// Form a "tall" matrix which corresponds to the column
			//  vectors AFTER we act tempT upon the eigenbasis.
			T := Transpose(Matrix([ Eltseq(MVM(tempT, v))
				: v in basis ]));

			// Extract the submatrix associated to this subspace.
			T := Submatrix(T, pivots, [1..dim]);

			// Compute the eigenspaces associated to T.
			newSpaces := Decompose(T, Ts[idx]);

			for newSp in newSpaces do
				// The field over which both spaces live.
				F := Compositum(
					BaseRing(newSp[1]), BaseRing(space));

				// Compute the intersection of these two spaces
				//  and add it to the list.
				Append(~sp, < ChangeRing(newSp[1], F)
					meet ChangeRing(space, F), newSp[2] >);
			end for;
		end for;

		// Remove the outdated subspaces from last to first.
		sp := [* sp[i] : i in [1..#sp] | not i in delList *];

		assert &+[ Dimension(s[1]) * Degree(BaseRing(s[1])) : s in sp ]
			eq Nrows(Ts[1]);
	end for;

	// Determine whether this decomposition is stll decomposable.
	decomposable := [ i : i in [1..#sp] | not sp[i][2] ];

	// Return the eigenspaces.
	sp := [* data[1] : data in sp *];

	// Display a warning if the decomposition is reducible.
	if Warning and #decomposable ne 0 then
		print "WARNING: Eigenspaces not completely decomposed!";
	end if;

	return sp, decomposable;
end intrinsic;

s := SolvablePassportDBInitialize();

/*
Magma printing
*/

s`Filename := "64S12-8,8,2-g9.m";
s`GaloisOrbits := [ Strings() | "64S12-8,8,2-g9-path23.m", "64S12-8,8,2-g9-path8.m", "64S12-8,8,2-g9-path43.m", "64S12-8,8,2-g9-path19.m", "64S12-8,8,2-g9-path37.m", "64S12-8,8,2-g9-path20.m", "64S12-8,8,2-g9-path30.m", "64S12-8,8,2-g9-path44.m", "64S12-8,8,2-g9-path17.m", "64S12-8,8,2-g9-path31.m", "64S12-8,8,2-g9-path7.m", "64S12-8,8,2-g9-path6.m", "64S12-8,8,2-g9-path36.m", "64S12-8,8,2-g9-path11.m", "64S12-8,8,2-g9-path25.m", "64S12-8,8,2-g9-path35.m", "64S12-8,8,2-g9-path39.m", "64S12-8,8,2-g9-path22.m", "64S12-8,8,2-g9-path12.m", "64S12-8,8,2-g9-path1.m", "64S12-8,8,2-g9-path18.m", "64S12-8,8,2-g9-path24.m", "64S12-8,8,2-g9-path14.m", "64S12-8,8,2-g9-path21.m", "64S12-8,8,2-g9-path26.m", "64S12-8,8,2-g9-path5.m", "64S12-8,8,2-g9-path10.m", "64S12-8,8,2-g9-path28.m", "64S12-8,8,2-g9-path40.m", "64S12-8,8,2-g9-path2.m", "64S12-8,8,2-g9-path4.m", "64S12-8,8,2-g9-path45.m", "64S12-8,8,2-g9-path33.m", "64S12-8,8,2-g9-path41.m", "64S12-8,8,2-g9-path34.m", "64S12-8,8,2-g9-path13.m", "64S12-8,8,2-g9-path38.m", "64S12-8,8,2-g9-path27.m", "64S12-8,8,2-g9-path9.m", "64S12-8,8,2-g9-path32.m", "64S12-8,8,2-g9-path15.m", "64S12-8,8,2-g9-path42.m", "64S12-8,8,2-g9-path29.m", "64S12-8,8,2-g9-path3.m", "64S12-8,8,2-g9-path16.m" ];
s`Name := "64S12-8,8,2-g9";
s`Passport := [ PowerSequence(PermutationGroup<64 |  
\[ 2, 8, 4, 15, 10, 1, 20, 18, 7, 22, 3, 13, 33, 16, 29, 24, 12, 5, 38, 21, 28, 6, 26, 11, 9, 27, 45, 19, 14, 31, 50, 34, 37, 36, 30, 17, 32, 25, 44, 23, 40, 56, 42, 41, 39, 43, 48, 58, 51, 54, 53, 47, 35, 49, 60, 57, 59, 64, 55, 46, 62, 63, 52, 61 ],
\[ 3, 9, 12, 6, 14, 20, 1, 24, 26, 28, 2, 30, 11, 32, 36, 18, 4, 38, 5, 40, 22, 15, 7, 33, 8, 43, 25, 44, 10, 47, 17, 49, 53, 29, 13, 50, 16, 45, 19, 56, 21, 23, 48, 59, 60, 27, 42, 35, 61, 63, 37, 31, 58, 34, 39, 52, 41, 46, 62, 64, 55, 54, 57, 51 ],
\[ 4, 7, 13, 1, 16, 21, 2, 11, 27, 19, 8, 31, 3, 34, 17, 5, 15, 25, 10, 23, 6, 29, 20, 37, 18, 42, 9, 41, 22, 48, 12, 51, 35, 14, 33, 54, 24, 39, 38, 57, 28, 26, 58, 55, 46, 45, 56, 30, 62, 52, 32, 50, 64, 36, 44, 47, 40, 43, 63, 61, 60, 49, 59, 53 ]:
 Order := 64 >) |
[ PermutationGroup<64 |  
\[ 2, 8, 4, 15, 10, 1, 20, 18, 7, 22, 3, 13, 33, 16, 29, 24, 12, 5, 38, 21, 28, 6, 26, 11, 9, 27, 45, 19, 14, 31, 50, 34, 37, 36, 30, 17, 32, 25, 44, 23, 40, 56, 42, 41, 39, 43, 48, 58, 51, 54, 53, 47, 35, 49, 60, 57, 59, 64, 55, 46, 62, 63, 52, 61 ],
\[ 3, 9, 12, 6, 14, 20, 1, 24, 26, 28, 2, 30, 11, 32, 36, 18, 4, 38, 5, 40, 22, 15, 7, 33, 8, 43, 25, 44, 10, 47, 17, 49, 53, 29, 13, 50, 16, 45, 19, 56, 21, 23, 48, 59, 60, 27, 42, 35, 61, 63, 37, 31, 58, 34, 39, 52, 41, 46, 62, 64, 55, 54, 57, 51 ],
\[ 4, 7, 13, 1, 16, 21, 2, 11, 27, 19, 8, 31, 3, 34, 17, 5, 15, 25, 10, 23, 6, 29, 20, 37, 18, 42, 9, 41, 22, 48, 12, 51, 35, 14, 33, 54, 24, 39, 38, 57, 28, 26, 58, 55, 46, 45, 56, 30, 62, 52, 32, 50, 64, 36, 44, 47, 40, 43, 63, 61, 60, 49, 59, 53 ]:
 Order := 64 > |
[ 2, 8, 4, 15, 10, 1, 20, 18, 7, 22, 3, 13, 33, 16, 29, 24, 12, 5, 38, 21, 28, 6, 26, 11, 9, 27, 45, 19, 14, 31, 50, 34, 37, 36, 30, 17, 32, 25, 44, 23, 40, 56, 42, 41, 39, 43, 48, 58, 51, 54, 53, 47, 35, 49, 60, 57, 59, 64, 55, 46, 62, 63, 52, 61 ],
[ 3, 9, 12, 6, 14, 20, 1, 24, 26, 28, 2, 30, 11, 32, 36, 18, 4, 38, 5, 40, 22, 15, 7, 33, 8, 43, 25, 44, 10, 47, 17, 49, 53, 29, 13, 50, 16, 45, 19, 56, 21, 23, 48, 59, 60, 27, 42, 35, 61, 63, 37, 31, 58, 34, 39, 52, 41, 46, 62, 64, 55, 54, 57, 51 ],
[ 4, 7, 13, 1, 16, 21, 2, 11, 27, 19, 8, 31, 3, 34, 17, 5, 15, 25, 10, 23, 6, 29, 20, 37, 18, 42, 9, 41, 22, 48, 12, 51, 35, 14, 33, 54, 24, 39, 38, 57, 28, 26, 58, 55, 46, 45, 56, 30, 62, 52, 32, 50, 64, 36, 44, 47, 40, 43, 63, 61, 60, 49, 59, 53 ]
]
];

/*
Return for eval
*/

return s;

/******************************************************************************
 *
 *    bn.m      BN-pair code for Suzuki groups
 *
 *    File      : $HeadURL:: https://subversion.sfac.auckland.ac.nz/svn/prj_#$:
 *    Author    : Henrik B��rnhielm
 *    Dev start : 2007-11-26
 *
 *    Version   : $Revision:: 1605                                           $:
 *    Date      : $Date:: 2008-12-15 20:05:48 +1100 (Mon, 15 Dec 2008)       $:
 *    Last edit : $Author:: jbaa004                                          $:
 *
 *    $Id:: bn.m 1605 2008-12-15 09:05:48Z jbaa004                         $:
 *
 *****************************************************************************/

freeze;
 
/*****************************************************************************/
/* DECLARATIONS                                                              */
/*****************************************************************************/

declare verbose SuzukiBN, 10;

declare attributes GrpMat : SuzukiBNData;

// Information about Suzuki maximal subgroups
SuzukiBNInfo := recformat<
    BNGroups : SeqEnum,
    slps : SeqEnum>;

/*****************************************************************************/
/* MAIN INTRINSICS                                                           */
/*****************************************************************************/

function SuzukiStandardBNpair(G)

    F := CoefficientRing(G);
    m := (Degree(F) - 1) div 2;
    _, gens := SuzukiStandardGeneratorsNaturalRep(m);
    q := #F;
    
    // Borel
    B := sub<Generic(G) | gens[2], gens[3]>;
    B`Order := q^2 * (q - 1);
    
    // Torus
    T := sub<Generic(G) | gens[2]>;
    T`Order := q - 1;
    
    // Monomial (torus-normaliser)
    N := sub<Generic(G) | gens[1], gens[2]>;
    N`Order := 2 * (q - 1);
    
    // Weyl 
    W := sub<Generic(G) | gens[1]>;
    W`Order := 2;
    
    // Unipotent
    U := sub<Generic(G) | [gens[3]^(gens[2]^i) : i in [1 .. Degree(F)]]>;
    U`Order := q^2;
    
    assert assigned G`RandomProcess;
    groups := [B, N, U, T, W];
    slps := [[slp where _, slp is
	SuzukiStandardConstructiveMembership(G, g : CheckInput := false,
	Randomiser := G`RandomProcess) :
	g in UserGenerators(H)] : H in groups];

    return groups, slps;
end function;

intrinsic SuzukiBNpair(G :: GrpMat) -> [], []
    { If G has been constructively recognised as a Suzuki group,
    return B,N,U,T,W of G.

    Also returns lists of SLPs of the generators of the subgroups, in
    the generators of G. }
    local maximals, slps;
    
    if not assigned G`SuzukiReductionData then
	error "G must be a recognised Suzuki group";
    end if;

    if assigned G`SuzukiBNData then
	return G`SuzukiBNData`BNGroups, G`SuzukiBNData`slps;
    end if;

    assert assigned G`SuzukiReductionData`stdCopy;
    if not assigned G`SuzukiReductionData`stdCopy`SuzukiBNData then
	vprint SuzukiBN, 1:
	    "Construct BN groups of standard copy";
	
	bnGroups, slps :=
	    SuzukiStandardBNpair(G`SuzukiReductionData`stdCopy);
	G`SuzukiReductionData`stdCopy`SuzukiBNData :=
	    rec<SuzukiBNInfo |
	    BNGroups := bnGroups, slps := slps>;
    end if;

    // Use explicit isomorphism to obtain maximals in input copy
    bnGroups := [sub<Generic(G) | G`SuzukiReductionData`slpHomo(slps)> :
	slps in G`SuzukiReductionData`stdCopy`SuzukiBNData`slps];

    // Take orders from standard copies
    for i in [1 .. #bnGroups] do
	bnGroups[i]`Order :=
	    G`SuzukiReductionData`stdCopy`SuzukiBNData`BNGroups[i]`Order;
    end for;
    
    G`SuzukiBNData := rec<SuzukiBNInfo |
	BNGroups := bnGroups,
	slps := G`SuzukiReductionData`stdCopy`SuzukiBNData`slps>;

    return G`SuzukiBNData`BNGroups, G`SuzukiBNData`slps;
end intrinsic;

s := SolvableDBInitialize();

/*
Magma printing
*/

s`SolvableDBName := "64S20-4,4,8-g13-path35";
s`SolvableDBFilename := "64S20-4,4,8-g13-path35.m";
s`SolvableDBPassportName := "64S20-4,4,8-g13";
s`SolvableDBPathNumber := 35;
s`SolvableDBDegree := 64;
s`SolvableDBOrders := \[ 4, 4, 8 ];
s`SolvableDBType := "Hyperbolic";
s`SolvableDBGenus := 13;
s`SolvableDBGaloisOrbitSize := 1;
s`SolvableDBPassportSize := 2;
s`SolvableDBPointedPassportSize := 2;
s`SolvableDBLevel := 6;
s`SolvableDBBlocks := {@ PowerSet(IntegerRing()) |
{ IntegerRing() | 1, 5 },
{ IntegerRing() | 2, 12 },
{ IntegerRing() | 3, 18 },
{ IntegerRing() | 4, 24 },
{ IntegerRing() | 6, 22 },
{ IntegerRing() | 7, 11 },
{ IntegerRing() | 8, 15 },
{ IntegerRing() | 9, 39 },
{ IntegerRing() | 10, 45 },
{ IntegerRing() | 13, 38 },
{ IntegerRing() | 14, 42 },
{ IntegerRing() | 16, 49 },
{ IntegerRing() | 17, 59 },
{ IntegerRing() | 19, 41 },
{ IntegerRing() | 20, 26 },
{ IntegerRing() | 21, 51 },
{ IntegerRing() | 23, 62 },
{ IntegerRing() | 25, 50 },
{ IntegerRing() | 27, 52 },
{ IntegerRing() | 28, 40 },
{ IntegerRing() | 29, 46 },
{ IntegerRing() | 30, 47 },
{ IntegerRing() | 31, 34 },
{ IntegerRing() | 32, 48 },
{ IntegerRing() | 33, 37 },
{ IntegerRing() | 35, 56 },
{ IntegerRing() | 36, 53 },
{ IntegerRing() | 43, 57 },
{ IntegerRing() | 44, 60 },
{ IntegerRing() | 54, 58 },
{ IntegerRing() | 55, 63 },
{ IntegerRing() | 61, 64 }
@};
s`SolvableDBIsRamifiedAtEveryLevel := false;
s`SolvableDBGaloisOrbit := [ PowerSequence(PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 >) |
[ PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 > |
[ 12, 39, 8, 51, 2, 5, 47, 37, 22, 14, 30, 9, 25, 27, 33, 20, 54, 15, 18, 64, 13, 1, 31, 21, 24, 61, 29, 32, 10, 28, 53, 11, 19, 36, 44, 63, 41, 50, 6, 48, 3, 52, 16, 17, 42, 45, 40, 7, 26, 4, 38, 46, 55, 35, 23, 60, 49, 56, 58, 59, 57, 34, 62, 43 ],
[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
[ 4, 11, 17, 23, 24, 28, 31, 1, 38, 44, 34, 7, 36, 2, 5, 10, 50, 59, 39, 3, 20, 40, 19, 62, 43, 18, 54, 63, 6, 49, 29, 61, 56, 46, 51, 8, 35, 53, 13, 55, 9, 12, 37, 32, 60, 22, 16, 64, 45, 57, 26, 58, 15, 30, 14, 21, 33, 47, 25, 48, 52, 41, 42, 27 ]
]
];
s`SolvableDBPassport := [ PowerSequence(PermutationGroup<64 |  
\[ 12, 39, 8, 51, 2, 5, 47, 37, 22, 14, 30, 9, 25, 27, 33, 20, 54, 15, 18, 64, 13, 1, 31, 21, 24, 61, 29, 32, 10, 28, 53, 11, 19, 36, 44, 63, 41, 50, 6, 48, 3, 52, 16, 17, 42, 45, 40, 7, 26, 4, 38, 46, 55, 35, 23, 60, 49, 56, 58, 59, 57, 34, 62, 43 ],
\[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
\[ 4, 11, 17, 23, 24, 28, 31, 1, 38, 44, 34, 7, 36, 2, 5, 10, 50, 59, 39, 3, 20, 40, 19, 62, 43, 18, 54, 63, 6, 49, 29, 61, 56, 46, 51, 8, 35, 53, 13, 55, 9, 12, 37, 32, 60, 22, 16, 64, 45, 57, 26, 58, 15, 30, 14, 21, 33, 47, 25, 48, 52, 41, 42, 27 ]:
 Order := 64 >) |
[ PermutationGroup<64 |  
\[ 12, 39, 8, 51, 2, 5, 47, 37, 22, 14, 30, 9, 25, 27, 33, 20, 54, 15, 18, 64, 13, 1, 31, 21, 24, 61, 29, 32, 10, 28, 53, 11, 19, 36, 44, 63, 41, 50, 6, 48, 3, 52, 16, 17, 42, 45, 40, 7, 26, 4, 38, 46, 55, 35, 23, 60, 49, 56, 58, 59, 57, 34, 62, 43 ],
\[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
\[ 4, 11, 17, 23, 24, 28, 31, 1, 38, 44, 34, 7, 36, 2, 5, 10, 50, 59, 39, 3, 20, 40, 19, 62, 43, 18, 54, 63, 6, 49, 29, 61, 56, 46, 51, 8, 35, 53, 13, 55, 9, 12, 37, 32, 60, 22, 16, 64, 45, 57, 26, 58, 15, 30, 14, 21, 33, 47, 25, 48, 52, 41, 42, 27 ]:
 Order := 64 > |
[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
[ 35, 54, 27, 7, 56, 44, 38, 42, 17, 3, 13, 58, 28, 19, 14, 55, 1, 52, 29, 36, 48, 60, 26, 11, 47, 53, 37, 24, 15, 51, 16, 50, 45, 49, 9, 43, 10, 40, 59, 4, 46, 41, 62, 2, 18, 8, 21, 25, 63, 30, 32, 33, 57, 6, 64, 39, 23, 22, 5, 12, 34, 20, 61, 31 ],
[ 4, 11, 17, 23, 24, 28, 31, 1, 38, 44, 34, 7, 36, 2, 5, 10, 50, 59, 39, 3, 20, 40, 19, 62, 43, 18, 54, 63, 6, 49, 29, 61, 56, 46, 51, 8, 35, 53, 13, 55, 9, 12, 37, 32, 60, 22, 16, 64, 45, 57, 26, 58, 15, 30, 14, 21, 33, 47, 25, 48, 52, 41, 42, 27 ]
],
[ PermutationGroup<64 |  
\[ 12, 39, 8, 51, 2, 5, 47, 37, 22, 14, 30, 9, 25, 27, 33, 20, 54, 15, 18, 64, 13, 1, 31, 21, 24, 61, 29, 32, 10, 28, 53, 11, 19, 36, 44, 63, 41, 50, 6, 48, 3, 52, 16, 17, 42, 45, 40, 7, 26, 4, 38, 46, 55, 35, 23, 60, 49, 56, 58, 59, 57, 34, 62, 43 ],
\[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
\[ 4, 11, 17, 23, 24, 28, 31, 1, 38, 44, 34, 7, 36, 2, 5, 10, 50, 59, 39, 3, 20, 40, 19, 62, 43, 18, 54, 63, 6, 49, 29, 61, 56, 46, 51, 8, 35, 53, 13, 55, 9, 12, 37, 32, 60, 22, 16, 64, 45, 57, 26, 58, 15, 30, 14, 21, 33, 47, 25, 48, 52, 41, 42, 27 ]:
 Order := 64 > |
[ 12, 39, 8, 51, 2, 5, 47, 37, 22, 14, 30, 9, 25, 27, 33, 20, 54, 15, 18, 64, 13, 1, 31, 21, 24, 61, 29, 32, 10, 28, 53, 11, 19, 36, 44, 63, 41, 50, 6, 48, 3, 52, 16, 17, 42, 45, 40, 7, 26, 4, 38, 46, 55, 35, 23, 60, 49, 56, 58, 59, 57, 34, 62, 43 ],
[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
[ 4, 11, 17, 23, 24, 28, 31, 1, 38, 44, 34, 7, 36, 2, 5, 10, 50, 59, 39, 3, 20, 40, 19, 62, 43, 18, 54, 63, 6, 49, 29, 61, 56, 46, 51, 8, 35, 53, 13, 55, 9, 12, 37, 32, 60, 22, 16, 64, 45, 57, 26, 58, 15, 30, 14, 21, 33, 47, 25, 48, 52, 41, 42, 27 ]
]
];
s`SolvableDBPointedPassport := [ PowerSequence(PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 >) |
[ PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 > |
[ 46, 15, 62, 17, 29, 19, 60, 20, 42, 31, 44, 8, 56, 16, 26, 25, 10, 23, 57, 47, 5, 41, 40, 59, 39, 30, 55, 54, 64, 2, 4, 6, 53, 24, 27, 11, 36, 35, 14, 58, 43, 49, 48, 37, 34, 61, 12, 22, 50, 9, 1, 63, 7, 3, 38, 52, 32, 18, 45, 33, 51, 28, 13, 21 ],
[ 59, 60, 45, 28, 17, 58, 24, 29, 56, 33, 4, 44, 7, 8, 46, 34, 39, 10, 42, 23, 30, 54, 43, 40, 32, 62, 18, 38, 41, 25, 61, 21, 27, 64, 5, 26, 52, 11, 35, 13, 14, 15, 53, 22, 37, 19, 50, 51, 31, 48, 47, 3, 20, 12, 49, 1, 36, 2, 9, 6, 55, 57, 16, 63 ],
[ 48, 21, 22, 49, 32, 25, 43, 54, 47, 5, 57, 51, 64, 17, 58, 41, 11, 6, 60, 14, 34, 50, 27, 16, 63, 42, 39, 26, 35, 36, 18, 62, 2, 3, 28, 45, 12, 61, 30, 20, 44, 59, 29, 38, 1, 56, 53, 23, 19, 55, 31, 9, 10, 4, 33, 40, 46, 24, 7, 13, 15, 52, 37, 8 ]
],
[ PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 > |
[ 59, 60, 45, 28, 17, 58, 24, 29, 56, 33, 4, 44, 7, 8, 46, 34, 39, 10, 42, 23, 30, 54, 43, 40, 32, 62, 18, 38, 41, 25, 61, 21, 27, 64, 5, 26, 52, 11, 35, 13, 14, 15, 53, 22, 37, 19, 50, 51, 31, 48, 47, 3, 20, 12, 49, 1, 36, 2, 9, 6, 55, 57, 16, 63 ],
[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
[ 48, 21, 22, 49, 32, 25, 43, 54, 47, 5, 57, 51, 64, 17, 58, 41, 11, 6, 60, 14, 34, 50, 27, 16, 63, 42, 39, 26, 35, 36, 18, 62, 2, 3, 28, 45, 12, 61, 30, 20, 44, 59, 29, 38, 1, 56, 53, 23, 19, 55, 31, 9, 10, 4, 33, 40, 46, 24, 7, 13, 15, 52, 37, 8 ]
]
];
s`SolvableDBMonodromyGroup := PermutationGroup<64 |  
\[ 12, 39, 8, 51, 2, 5, 47, 37, 22, 14, 30, 9, 25, 27, 33, 20, 54, 15, 18, 64, 13, 1, 31, 21, 24, 61, 29, 32, 10, 28, 53, 11, 19, 36, 44, 63, 41, 50, 6, 48, 3, 52, 16, 17, 42, 45, 40, 7, 26, 4, 38, 46, 55, 35, 23, 60, 49, 56, 58, 59, 57, 34, 62, 43 ],
\[ 3, 10, 16, 22, 18, 27, 1, 34, 37, 43, 5, 45, 2, 53, 31, 7, 41, 49, 55, 24, 58, 52, 50, 6, 60, 4, 20, 39, 23, 17, 48, 35, 61, 32, 8, 21, 64, 12, 33, 9, 63, 36, 13, 29, 57, 62, 59, 56, 11, 44, 54, 26, 51, 14, 47, 15, 38, 42, 19, 46, 28, 25, 30, 40 ],
\[ 4, 11, 17, 23, 24, 28, 31, 1, 38, 44, 34, 7, 36, 2, 5, 10, 50, 59, 39, 3, 20, 40, 19, 62, 43, 18, 54, 63, 6, 49, 29, 61, 56, 46, 51, 8, 35, 53, 13, 55, 9, 12, 37, 32, 60, 22, 16, 64, 45, 57, 26, 58, 15, 30, 14, 21, 33, 47, 25, 48, 52, 41, 42, 27 ] >;
s`SolvableDBAutomorphismGroup := PermutationGroup<64 |  
\[ 22, 5, 52, 40, 6, 39, 4, 46, 12, 18, 24, 1, 11, 15, 29, 26, 58, 27, 14, 61, 32, 9, 55, 28, 30, 64, 33, 13, 19, 21, 23, 25, 10, 62, 60, 34, 45, 7, 2, 38, 42, 8, 49, 59, 3, 41, 51, 50, 20, 47, 48, 37, 31, 56, 53, 44, 16, 35, 54, 17, 43, 63, 36, 57 ],
\[ 64, 57, 40, 27, 61, 26, 37, 48, 16, 38, 33, 43, 45, 50, 32, 9, 55, 28, 30, 22, 46, 20, 54, 52, 42, 6, 4, 18, 51, 19, 35, 15, 11, 56, 31, 60, 7, 10, 49, 3, 47, 25, 12, 53, 13, 21, 41, 8, 39, 14, 29, 24, 44, 23, 17, 34, 2, 62, 63, 36, 5, 58, 59, 1 ],
\[ 52, 29, 26, 58, 27, 14, 22, 61, 45, 23, 6, 46, 44, 31, 64, 4, 18, 20, 16, 51, 35, 42, 47, 54, 17, 21, 53, 2, 55, 5, 40, 39, 43, 28, 33, 32, 57, 60, 10, 12, 49, 34, 50, 19, 62, 63, 1, 9, 24, 59, 56, 36, 48, 15, 7, 37, 25, 8, 3, 41, 13, 30, 11, 38 ]:
 Order := 64 >;
s`SolvableDBPointedAutomorphismGroup := PermutationGroup<64 |  
\[ 12, 39, 45, 7, 2, 5, 38, 42, 22, 33, 13, 9, 28, 19, 14, 57, 60, 10, 29, 49, 30, 1, 31, 11, 32, 16, 18, 24, 15, 25, 53, 21, 27, 36, 58, 63, 52, 40, 6, 4, 46, 41, 61, 56, 37, 8, 50, 51, 43, 48, 47, 3, 55, 59, 23, 54, 64, 17, 44, 35, 20, 34, 62, 26 ]:
 Order := 4 >;
s`SolvableDBPathToPP1 := [ Strings() | "PP1", "2T1-2,2,1-g0-path1", "4T2-2,2,2-g0-path3", "8T2-2,4,4-g1-path5", "16T10-2,4,4-g1-path3", "32S11-4,4,8-g7-path5", "64S20-4,4,8-g13-path35" ];
s`SolvableDBParents := [ Strings() | "128S8-8,4,8-g33-path278", "128S11-4,8,8-g33-path505", "128S10-8,8,8-g41-path1458", "128S35-8,4,8-g33-path51", "128S32-4,8,8-g33-path96", "128S31-8,8,8-g41-path96", "128S32-8,4,8-g33-path96", "128S27-4,8,8-g33-path183", "128S34-8,8,8-g41-path96", "128S17-8,4,8-g33-path213", "128S20-4,8,8-g33-path213", "128S23-8,8,8-g41-path582", "128S29-4,4,8-g25-path96", "128S26-4,4,8-g25-path96", "128S16-4,4,8-g25-path258" ];
s`SolvableDBChild := "32S11-4,4,8-g7-path5";

/*
Return for eval
*/

return s;

s := SolvableDBInitialize();

/*
Magma printing
*/

s`SolvableDBName := "64S14-4,8,8-g17-path7-notcomputed";
s`SolvableDBFilename := "64S14-4,8,8-g17-path7-notcomputed.m";
s`SolvableDBPassportName := "64S14-4,8,8-g17";
s`SolvableDBPathNumber := 7;
s`SolvableDBDegree := 64;
s`SolvableDBOrders := \[ 4, 8, 8 ];
s`SolvableDBType := "Hyperbolic";
s`SolvableDBGenus := 17;
s`SolvableDBGaloisOrbitSize := 1;
s`SolvableDBPassportSize := 1;
s`SolvableDBPointedPassportSize := 1;
s`SolvableDBLevel := 6;
s`SolvableDBBlocks := {@ PowerSet(IntegerRing()) |
{ IntegerRing() | 1, 5 },
{ IntegerRing() | 2, 6 },
{ IntegerRing() | 3, 15 },
{ IntegerRing() | 4, 19 },
{ IntegerRing() | 7, 10 },
{ IntegerRing() | 8, 12 },
{ IntegerRing() | 9, 22 },
{ IntegerRing() | 11, 23 },
{ IntegerRing() | 13, 40 },
{ IntegerRing() | 14, 29 },
{ IntegerRing() | 16, 21 },
{ IntegerRing() | 17, 20 },
{ IntegerRing() | 18, 34 },
{ IntegerRing() | 24, 26 },
{ IntegerRing() | 25, 28 },
{ IntegerRing() | 27, 33 },
{ IntegerRing() | 30, 37 },
{ IntegerRing() | 31, 51 },
{ IntegerRing() | 32, 35 },
{ IntegerRing() | 36, 48 },
{ IntegerRing() | 38, 61 },
{ IntegerRing() | 39, 44 },
{ IntegerRing() | 41, 43 },
{ IntegerRing() | 42, 55 },
{ IntegerRing() | 45, 49 },
{ IntegerRing() | 46, 50 },
{ IntegerRing() | 47, 59 },
{ IntegerRing() | 52, 54 },
{ IntegerRing() | 53, 58 },
{ IntegerRing() | 56, 57 },
{ IntegerRing() | 60, 64 },
{ IntegerRing() | 62, 63 }
@};
s`SolvableDBIsRamifiedAtEveryLevel := true;
s`SolvableDBGaloisOrbit := [ PowerSequence(PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 >) |
[ PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 > |
[ 6, 1, 8, 20, 2, 5, 26, 15, 11, 24, 22, 3, 16, 32, 12, 40, 4, 48, 17, 19, 13, 23, 9, 7, 37, 10, 51, 30, 35, 25, 27, 29, 31, 36, 14, 18, 28, 41, 52, 21, 61, 56, 38, 54, 46, 49, 53, 34, 50, 45, 33, 44, 59, 39, 57, 55, 42, 47, 58, 62, 43, 64, 60, 63 ],
[ 3, 9, 13, 2, 15, 22, 1, 28, 31, 5, 34, 25, 38, 12, 40, 19, 45, 17, 6, 49, 4, 51, 18, 50, 24, 46, 7, 26, 8, 42, 57, 23, 10, 20, 11, 43, 55, 60, 21, 61, 29, 35, 14, 16, 54, 59, 36, 41, 52, 47, 56, 30, 27, 37, 32, 62, 63, 33, 48, 53, 64, 44, 39, 58 ],
[ 4, 10, 14, 18, 19, 7, 25, 1, 32, 28, 2, 5, 39, 42, 29, 3, 16, 47, 34, 21, 15, 35, 6, 33, 52, 27, 9, 54, 55, 8, 58, 43, 22, 59, 41, 11, 12, 36, 45, 44, 13, 31, 40, 49, 24, 17, 64, 23, 26, 20, 53, 63, 50, 62, 51, 30, 37, 46, 60, 57, 48, 38, 61, 56 ]
]
];
s`SolvableDBPassport := [ PowerSequence(PermutationGroup<64 |  
\[ 6, 1, 8, 20, 2, 5, 26, 15, 11, 24, 22, 3, 16, 32, 12, 40, 4, 48, 17, 19, 13, 23, 9, 7, 37, 10, 51, 30, 35, 25, 27, 29, 31, 36, 14, 18, 28, 41, 52, 21, 61, 56, 38, 54, 46, 49, 53, 34, 50, 45, 33, 44, 59, 39, 57, 55, 42, 47, 58, 62, 43, 64, 60, 63 ],
\[ 3, 9, 13, 2, 15, 22, 1, 28, 31, 5, 34, 25, 38, 12, 40, 19, 45, 17, 6, 49, 4, 51, 18, 50, 24, 46, 7, 26, 8, 42, 57, 23, 10, 20, 11, 43, 55, 60, 21, 61, 29, 35, 14, 16, 54, 59, 36, 41, 52, 47, 56, 30, 27, 37, 32, 62, 63, 33, 48, 53, 64, 44, 39, 58 ],
\[ 4, 10, 14, 18, 19, 7, 25, 1, 32, 28, 2, 5, 39, 42, 29, 3, 16, 47, 34, 21, 15, 35, 6, 33, 52, 27, 9, 54, 55, 8, 58, 43, 22, 59, 41, 11, 12, 36, 45, 44, 13, 31, 40, 49, 24, 17, 64, 23, 26, 20, 53, 63, 50, 62, 51, 30, 37, 46, 60, 57, 48, 38, 61, 56 ]:
 Order := 64 >) |
[ PermutationGroup<64 |  
\[ 6, 1, 8, 20, 2, 5, 26, 15, 11, 24, 22, 3, 16, 32, 12, 40, 4, 48, 17, 19, 13, 23, 9, 7, 37, 10, 51, 30, 35, 25, 27, 29, 31, 36, 14, 18, 28, 41, 52, 21, 61, 56, 38, 54, 46, 49, 53, 34, 50, 45, 33, 44, 59, 39, 57, 55, 42, 47, 58, 62, 43, 64, 60, 63 ],
\[ 3, 9, 13, 2, 15, 22, 1, 28, 31, 5, 34, 25, 38, 12, 40, 19, 45, 17, 6, 49, 4, 51, 18, 50, 24, 46, 7, 26, 8, 42, 57, 23, 10, 20, 11, 43, 55, 60, 21, 61, 29, 35, 14, 16, 54, 59, 36, 41, 52, 47, 56, 30, 27, 37, 32, 62, 63, 33, 48, 53, 64, 44, 39, 58 ],
\[ 4, 10, 14, 18, 19, 7, 25, 1, 32, 28, 2, 5, 39, 42, 29, 3, 16, 47, 34, 21, 15, 35, 6, 33, 52, 27, 9, 54, 55, 8, 58, 43, 22, 59, 41, 11, 12, 36, 45, 44, 13, 31, 40, 49, 24, 17, 64, 23, 26, 20, 53, 63, 50, 62, 51, 30, 37, 46, 60, 57, 48, 38, 61, 56 ]:
 Order := 64 > |
[ 25, 18, 4, 15, 28, 34, 9, 55, 10, 22, 41, 42, 14, 40, 19, 49, 47, 6, 3, 59, 45, 7, 43, 52, 5, 54, 50, 1, 13, 63, 32, 51, 46, 2, 31, 64, 62, 39, 61, 29, 23, 8, 11, 38, 16, 27, 20, 60, 21, 33, 35, 26, 57, 24, 12, 53, 58, 56, 17, 36, 44, 30, 37, 48 ],
[ 3, 9, 13, 2, 15, 22, 1, 28, 31, 5, 34, 25, 38, 12, 40, 19, 45, 17, 6, 49, 4, 51, 18, 50, 24, 46, 7, 26, 8, 42, 57, 23, 10, 20, 11, 43, 55, 60, 21, 61, 29, 35, 14, 16, 54, 59, 36, 41, 52, 47, 56, 30, 27, 37, 32, 62, 63, 33, 48, 53, 64, 44, 39, 58 ],
[ 8, 11, 16, 1, 12, 23, 6, 30, 27, 2, 36, 37, 41, 3, 21, 17, 46, 4, 5, 50, 20, 33, 48, 45, 7, 49, 26, 10, 15, 56, 42, 9, 24, 19, 22, 38, 57, 62, 13, 43, 35, 14, 32, 40, 39, 58, 18, 61, 44, 53, 55, 25, 51, 28, 29, 64, 60, 31, 34, 59, 63, 54, 52, 47 ]
]
];
s`SolvableDBPointedPassport := [ PowerSequence(PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 >) |
[ PermutationGroup<64 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 ]:
 Order := 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 > |
[ 21, 33, 43, 23, 16, 27, 12, 7, 55, 8, 4, 10, 63, 30, 41, 1, 44, 50, 11, 39, 5, 42, 19, 58, 49, 53, 2, 45, 37, 29, 64, 36, 6, 46, 48, 35, 14, 47, 17, 62, 3, 9, 15, 20, 25, 18, 61, 32, 28, 34, 60, 57, 24, 56, 22, 52, 54, 26, 38, 31, 59, 13, 40, 51 ],
[ 11, 12, 37, 46, 23, 8, 45, 16, 48, 49, 27, 21, 20, 22, 30, 41, 5, 38, 50, 1, 43, 36, 33, 2, 56, 6, 42, 57, 9, 10, 24, 3, 55, 61, 15, 19, 7, 32, 28, 17, 62, 60, 63, 25, 53, 39, 31, 4, 58, 44, 26, 13, 18, 40, 64, 14, 29, 34, 51, 52, 35, 59, 47, 54 ],
[ 8, 11, 16, 1, 12, 23, 6, 30, 27, 2, 36, 37, 41, 3, 21, 17, 46, 4, 5, 50, 20, 33, 48, 45, 7, 49, 26, 10, 15, 56, 42, 9, 24, 19, 22, 38, 57, 62, 13, 43, 35, 14, 32, 40, 39, 58, 18, 61, 44, 53, 55, 25, 51, 28, 29, 64, 60, 31, 34, 59, 63, 54, 52, 47 ]
]
];
s`SolvableDBMonodromyGroup := PermutationGroup<64 |  
\[ 6, 1, 8, 20, 2, 5, 26, 15, 11, 24, 22, 3, 16, 32, 12, 40, 4, 48, 17, 19, 13, 23, 9, 7, 37, 10, 51, 30, 35, 25, 27, 29, 31, 36, 14, 18, 28, 41, 52, 21, 61, 56, 38, 54, 46, 49, 53, 34, 50, 45, 33, 44, 59, 39, 57, 55, 42, 47, 58, 62, 43, 64, 60, 63 ],
\[ 3, 9, 13, 2, 15, 22, 1, 28, 31, 5, 34, 25, 38, 12, 40, 19, 45, 17, 6, 49, 4, 51, 18, 50, 24, 46, 7, 26, 8, 42, 57, 23, 10, 20, 11, 43, 55, 60, 21, 61, 29, 35, 14, 16, 54, 59, 36, 41, 52, 47, 56, 30, 27, 37, 32, 62, 63, 33, 48, 53, 64, 44, 39, 58 ],
\[ 4, 10, 14, 18, 19, 7, 25, 1, 32, 28, 2, 5, 39, 42, 29, 3, 16, 47, 34, 21, 15, 35, 6, 33, 52, 27, 9, 54, 55, 8, 58, 43, 22, 59, 41, 11, 12, 36, 45, 44, 13, 31, 40, 49, 24, 17, 64, 23, 26, 20, 53, 63, 50, 62, 51, 30, 37, 46, 60, 57, 48, 38, 61, 56 ] >;
s`SolvableDBAutomorphismGroup := PermutationGroup<64 |  
\[ 60, 63, 53, 57, 64, 62, 38, 59, 39, 61, 52, 47, 27, 50, 58, 51, 55, 37, 56, 42, 31, 44, 54, 43, 36, 41, 13, 48, 46, 34, 21, 45, 40, 30, 49, 25, 18, 7, 9, 33, 26, 20, 24, 22, 32, 29, 12, 28, 35, 14, 16, 11, 3, 23, 17, 19, 4, 15, 8, 1, 10, 6, 2, 5 ],
\[ 53, 47, 27, 50, 58, 59, 60, 51, 36, 64, 18, 31, 7, 9, 33, 26, 49, 20, 46, 45, 24, 48, 34, 63, 57, 62, 38, 56, 22, 55, 43, 11, 61, 17, 23, 4, 42, 1, 25, 10, 6, 32, 2, 28, 52, 44, 21, 19, 54, 39, 41, 37, 13, 30, 35, 29, 14, 40, 16, 3, 5, 8, 12, 15 ],
\[ 64, 62, 58, 56, 60, 63, 61, 47, 44, 38, 54, 59, 33, 46, 53, 31, 42, 30, 57, 55, 51, 39, 52, 41, 48, 43, 40, 36, 50, 18, 16, 49, 13, 37, 45, 28, 34, 10, 22, 27, 24, 17, 26, 9, 35, 14, 8, 25, 32, 29, 21, 23, 15, 11, 20, 4, 19, 3, 12, 5, 7, 2, 6, 1 ],
\[ 2, 5, 9, 10, 6, 1, 4, 11, 15, 19, 12, 23, 31, 32, 22, 27, 26, 28, 7, 24, 33, 3, 8, 17, 18, 20, 21, 34, 35, 36, 40, 29, 16, 25, 14, 37, 48, 57, 58, 51, 42, 43, 55, 53, 46, 49, 54, 30, 50, 45, 13, 47, 39, 59, 41, 38, 61, 44, 52, 63, 56, 60, 64, 62 ]:
 Order := 64 >;
s`SolvableDBPointedAutomorphismGroup := PermutationGroup<64 |  
\[ 6, 1, 22, 7, 2, 5, 19, 23, 3, 4, 8, 11, 51, 35, 9, 33, 24, 25, 10, 26, 27, 15, 12, 20, 34, 17, 16, 18, 32, 48, 13, 14, 21, 28, 29, 30, 36, 56, 53, 31, 55, 41, 42, 58, 50, 45, 52, 37, 46, 49, 40, 59, 44, 47, 43, 61, 38, 39, 54, 62, 57, 64, 60, 63 ]:
 Order := 4 >;
s`SolvableDBPathToPP1 := [ Strings() | "PP1", "2T1-1,2,2-g0-path1-computed", "4T2-2,2,2-g0-path1-notcomputed", "8T4-2,2,4-g0-path1-notcomputed", "16T10-2,4,4-g1-path4-notcomputed", "32S7-2,8,8-g5-path2-notcomputed", "64S14-4,8,8-g17-path7-notcomputed" ];
s`SolvableDBParents := [ Strings() | "128S98-4,16,16-g41-path9-notcomputed", "128S98-4,16,16-g41-path10-notcomputed", "128S98-4,16,16-g41-path11-notcomputed", "128S98-4,16,16-g41-path12-notcomputed", "128S4-4,8,8-g33-path11-notcomputed", "128S28-4,8,8-g33-path12-notcomputed", "128S4-4,8,8-g33-path12-notcomputed" ];
s`SolvableDBChild := "32S7-2,8,8-g5-path2-notcomputed";

/*
Return for eval
*/

return s;

s := SolvableDBInitialize();

/*
Magma printing
*/

s`SolvableDBName := "128S124-8,8,8-g41-path194";
s`SolvableDBFilename := "128S124-8,8,8-g41-path194.m";
s`SolvableDBPassportName := "128S124-8,8,8-g41";
s`SolvableDBPathNumber := 194;
s`SolvableDBDegree := 128;
s`SolvableDBOrders := \[ 8, 8, 8 ];
s`SolvableDBType := "Hyperbolic";
s`SolvableDBGenus := 41;
s`SolvableDBGaloisOrbitSize := 1;
s`SolvableDBPassportSize := 6;
s`SolvableDBPointedPassportSize := 6;
s`SolvableDBLevel := 7;
s`SolvableDBBlocks := {@ PowerSet(IntegerRing()) |
{ IntegerRing() | 1, 5 },
{ IntegerRing() | 2, 12 },
{ IntegerRing() | 3, 18 },
{ IntegerRing() | 4, 24 },
{ IntegerRing() | 6, 22 },
{ IntegerRing() | 7, 11 },
{ IntegerRing() | 8, 15 },
{ IntegerRing() | 9, 29 },
{ IntegerRing() | 10, 45 },
{ IntegerRing() | 13, 40 },
{ IntegerRing() | 14, 42 },
{ IntegerRing() | 16, 34 },
{ IntegerRing() | 17, 65 },
{ IntegerRing() | 19, 64 },
{ IntegerRing() | 20, 60 },
{ IntegerRing() | 21, 77 },
{ IntegerRing() | 23, 38 },
{ IntegerRing() | 25, 73 },
{ IntegerRing() | 26, 76 },
{ IntegerRing() | 27, 78 },
{ IntegerRing() | 28, 79 },
{ IntegerRing() | 30, 80 },
{ IntegerRing() | 31, 48 },
{ IntegerRing() | 32, 49 },
{ IntegerRing() | 33, 50 },
{ IntegerRing() | 35, 57 },
{ IntegerRing() | 36, 58 },
{ IntegerRing() | 37, 59 },
{ IntegerRing() | 39, 90 },
{ IntegerRing() | 41, 91 },
{ IntegerRing() | 43, 54 },
{ IntegerRing() | 44, 75 },
{ IntegerRing() | 46, 107 },
{ IntegerRing() | 47, 83 },
{ IntegerRing() | 51, 103 },
{ IntegerRing() | 52, 93 },
{ IntegerRing() | 53, 104 },
{ IntegerRing() | 55, 61 },
{ IntegerRing() | 56, 81 },
{ IntegerRing() | 62, 99 },
{ IntegerRing() | 63, 116 },
{ IntegerRing() | 66, 87 },
{ IntegerRing() | 67, 119 },
{ IntegerRing() | 68, 100 },
{ IntegerRing() | 69, 108 },
{ IntegerRing() | 70, 89 },
{ IntegerRing() | 71, 74 },
{ IntegerRing() | 72, 92 },
{ IntegerRing() | 82, 86 },
{ IntegerRing() | 84, 114 },
{ IntegerRing() | 85, 121 },
{ IntegerRing() | 88, 101 },
{ IntegerRing() | 94, 98 },
{ IntegerRing() | 95, 111 },
{ IntegerRing() | 96, 110 },
{ IntegerRing() | 97, 112 },
{ IntegerRing() | 102, 126 },
{ IntegerRing() | 105, 106 },
{ IntegerRing() | 109, 118 },
{ IntegerRing() | 113, 117 },
{ IntegerRing() | 115, 122 },
{ IntegerRing() | 120, 123 },
{ IntegerRing() | 124, 125 },
{ IntegerRing() | 127, 128 }
@};
s`SolvableDBIsRamifiedAtEveryLevel := false;
s`SolvableDBGaloisOrbit := [ PowerSequence(PermutationGroup<128 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128 ]:
 Order := 385620482362580421735677065923463640617493109590223590278828403276373402575165543560686168588507361534030051833058916347592172932262498857766114955245039357760034644709279247692495585280000000000000000000000000000000 >) |
[ PermutationGroup<128 |  
\[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 1 ],
\[ 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128 ]:
 Order := 385620482362580421735677065923463640617493109590223590278828403276373402575165543560686168588507361534030051833058916347592172932262498857766114955245039357760034644709279247692495585280000000000000000000000000000000 > |
[ 12, 29, 8, 77, 2, 5, 48, 57, 6, 14, 31, 9, 103, 61, 35, 20, 116, 15, 18, 89, 71, 1, 49, 21, 24, 86, 30, 66, 22, 72, 98, 52, 11, 60, 64, 38, 114, 32, 41, 51, 106, 55, 47, 59, 42, 45, 26, 94, 93, 7, 117, 58, 40, 83, 107, 65, 19, 23, 84, 70, 46, 34, 95, 3, 63, 123, 69, 109, 96, 99, 73, 85, 4, 25, 37, 82, 74, 80, 87, 92, 17, 43, 76, 97, 78, 54, 120, 79, 62, 91, 105, 121, 36, 33, 81, 122, 75, 50, 16, 118, 28, 90, 113, 13, 126, 102, 10, 110, 127, 115, 56, 44, 53, 112, 67, 111, 104, 128, 108, 101, 27, 119, 88, 100, 68, 39, 124, 125 ],
[ 3, 10, 16, 22, 18, 27, 1, 36, 39, 43, 5, 45, 2, 38, 58, 11, 64, 34, 67, 71, 75, 78, 73, 6, 81, 4, 26, 9, 90, 93, 95, 50, 97, 7, 83, 88, 8, 25, 70, 12, 32, 23, 40, 107, 54, 108, 94, 111, 33, 112, 114, 104, 116, 13, 62, 14, 47, 101, 15, 74, 99, 117, 30, 119, 19, 17, 66, 57, 21, 79, 124, 20, 56, 125, 46, 24, 44, 76, 29, 52, 42, 123, 98, 121, 122, 120, 65, 59, 28, 89, 49, 60, 53, 100, 126, 31, 41, 68, 113, 35, 37, 96, 84, 63, 86, 82, 69, 77, 61, 48, 102, 91, 118, 85, 51, 80, 109, 55, 87, 127, 115, 103, 128, 92, 72, 110, 106, 105 ],
[ 4, 11, 17, 23, 24, 28, 32, 1, 40, 44, 49, 7, 52, 2, 5, 61, 25, 65, 68, 3, 76, 79, 15, 38, 60, 57, 84, 58, 13, 6, 16, 14, 47, 55, 59, 30, 21, 8, 95, 93, 9, 12, 106, 50, 75, 109, 10, 34, 42, 83, 43, 41, 99, 105, 81, 48, 37, 80, 77, 18, 56, 90, 87, 100, 73, 89, 121, 74, 19, 92, 69, 63, 20, 108, 33, 35, 26, 114, 36, 22, 31, 78, 45, 88, 125, 27, 70, 82, 72, 111, 29, 116, 91, 110, 104, 107, 103, 96, 39, 71, 86, 127, 54, 62, 112, 97, 118, 64, 98, 46, 53, 51, 122, 101, 126, 66, 115, 94, 85, 119, 124, 102, 67, 120, 123, 128, 117, 113 ]
]
];
s`SolvableDBPassport := [ PowerSequence(PermutationGroup<128 |  
\[ 12, 29, 8, 77, 2, 5, 48, 57, 6, 14, 31, 9, 103, 61, 35, 20, 116, 15, 18, 89, 71, 1, 49, 21, 24, 86, 30, 66, 22, 72, 98, 52, 11, 60, 64, 38, 114, 32, 41, 51, 106, 55, 47, 59, 42, 45, 26, 94, 93, 7, 117, 58, 40, 83, 107, 65, 19, 23, 84, 70, 46, 34, 95, 3, 63, 123, 69, 109, 96, 99, 73, 85, 4, 25, 37, 82, 74, 80, 87, 92, 17, 43, 76, 97, 78, 54, 120, 79, 62, 91, 105, 121, 36, 33, 81, 122, 75, 50, 16, 118, 28, 90, 113, 13, 126, 102, 10, 110, 127, 115, 56, 44, 53, 112, 67, 111, 104, 128, 108, 101, 27, 119, 88, 100, 68, 39, 124, 125 ],
\[ 3, 10, 16, 22, 18, 27, 1, 36, 39, 43, 5, 45, 2, 38, 58, 11, 64, 34, 67, 71, 75, 78, 73, 6, 81, 4, 26, 9, 90, 93, 95, 50, 97, 7, 83, 88, 8, 25, 70, 12, 32, 23, 40, 107, 54, 108, 94, 111, 33, 112, 114, 104, 116, 13, 62, 14, 47, 101, 15, 74, 99, 117, 30, 119, 19, 17, 66, 57, 21, 79, 124, 20, 56, 125, 46, 24, 44, 76, 29, 52, 42, 123, 98, 121, 122, 120, 65, 59, 28, 89, 49, 60, 53, 100, 126, 31, 41, 68, 113, 35, 37, 96, 84, 63, 86, 82, 69, 77, 61, 48, 102, 91, 118, 85, 51, 80, 109, 55, 87, 127, 115, 103, 128, 92, 72, 110, 106, 105 ],
\[ 4, 11, 17, 23, 24, 28, 32, 1, 40, 44, 49, 7, 52, 2, 5, 61, 25, 65, 68, 3, 76, 79, 15, 38, 60, 57, 84, 58, 13, 6, 16, 14, 47, 55, 59, 30, 21, 8, 95, 93, 9, 12, 106, 50, 75, 109, 10, 34, 42, 83, 43, 41, 99, 105, 81, 48, 37, 80, 77, 18, 56, 90, 87, 100, 73, 89, 121, 74, 19, 92, 69, 63, 20, 108, 33, 35, 26, 114, 36, 22, 31, 78, 45, 88, 125, 27, 70, 82, 72, 111, 29, 116, 91, 110, 104, 107, 103, 96, 39, 71, 86, 127, 54, 62, 112, 97, 118, 64, 98, 46, 53, 51, 122, 101, 126, 66, 115, 94, 85, 119, 124, 102, 67, 120, 123, 128, 117, 113 ]:
 Order := 128 >) |
[ PermutationGroup<128 |  
\[ 12, 29, 8, 77, 2, 5, 48, 57, 6, 14, 31, 9, 103, 61, 35, 20, 116, 15, 18, 89, 71, 1, 49, 21, 24, 86, 30, 66, 22, 72, 98, 52, 11, 60, 64, 38, 114, 32, 41, 51, 106, 55, 47, 59, 42, 45, 26, 94, 93, 7, 117, 58, 40, 83, 107, 65, 19, 23, 84, 70, 46, 34, 95, 3, 63, 123, 69, 109, 96, 99, 73, 85, 4, 25, 37, 82, 74, 80, 87, 92, 17, 43, 76, 97, 78, 54, 120, 79, 62, 91, 105, 121, 36, 33, 81, 122, 75, 50, 16, 118, 28, 90, 113, 13, 126, 102, 10, 110, 127, 115, 56, 44, 53, 112, 67, 111, 104, 128, 108, 101, 27, 119, 88, 100, 68, 39, 124, 125 ],
\[ 3, 10, 16, 22, 18, 27, 1, 36, 39, 43, 5, 45, 2, 38, 58, 11, 64, 34, 67, 71, 75, 78, 73, 6, 81, 4, 26, 9, 90, 93, 95, 50, 97, 7, 83, 88, 8, 25, 70, 12, 32, 23, 40, 107, 54, 108, 94, 111, 33, 112, 114, 104, 116, 13, 62, 14, 47, 101, 15, 74, 99, 117, 30, 119, 19, 17, 66, 57, 21, 79, 124, 20, 56, 125, 46, 24, 44, 76, 29, 52, 42, 123, 98, 121, 122, 120, 65, 59, 28, 89, 49, 60, 53, 100, 126, 31, 41, 68, 113, 35, 37, 96, 84, 63, 86, 82, 69, 77, 61, 48, 102, 91, 118, 85, 51, 80, 109, 55, 87, 127, 115, 103, 128, 92, 72, 110, 106, 105 ],
\[ 4, 11, 17, 23, 24, 28, 32, 1, 40, 44, 49, 7, 52, 2, 5, 61, 25, 65, 68, 3, 76, 79, 15, 38, 60, 57, 84, 58, 13, 6, 16, 14, 47, 55, 59, 30, 21, 8, 95, 93, 9, 12, 106, 50, 75, 109, 10, 34, 42, 83, 43, 41, 99, 105, 81, 48, 37, 80, 77, 18, 56, 90, 87, 100, 73, 89, 121, 74, 19, 92, 69, 63, 20, 108, 33, 35, 26, 114, 36, 22, 31, 78, 45, 88, 125, 27, 70, 82, 72, 111, 29, 116, 91, 110, 104, 107, 103, 96, 39, 71, 86, 127, 54, 62, 112, 97, 118, 64, 98, 46, 53, 51, 122, 101, 126, 66, 115, 94, 85, 119, 124, 102, 67, 120, 123, 128, 117, 113 ]:
 Order := 128 > |
[ 40, 79, 37, 108, 13, 11, 110, 68, 24, 56, 96, 28, 122, 109, 100, 72, 53, 59, 5, 90, 20, 7, 91, 69, 76, 105, 63, 67, 4, 125, 83, 80, 16, 92, 17, 14, 51, 41, 97, 115, 127, 118, 57, 88, 81, 12, 27, 47, 30, 34, 62, 15, 43, 35, 44, 87, 65, 42, 103, 39, 75, 18, 31, 1, 104, 82, 107, 117, 102, 61, 23, 114, 26, 38, 101, 106, 60, 116, 119, 124, 66, 10, 78, 33, 22, 45, 86, 70, 55, 112, 128, 84, 8, 49, 25, 85, 21, 32, 3, 113, 89, 29, 99, 54, 95, 111, 2, 126, 120, 121, 73, 77, 93, 50, 19, 48, 52, 123, 46, 58, 6, 64, 36, 94, 98, 9, 71, 74 ],
[ 12, 29, 8, 77, 2, 5, 48, 57, 6, 14, 31, 9, 103, 61, 35, 20, 116, 15, 18, 89, 71, 1, 49, 21, 24, 86, 30, 66, 22, 72, 98, 52, 11, 60, 64, 38, 114, 32, 41, 51, 106, 55, 47, 59, 42, 45, 26, 94, 93, 7, 117, 58, 40, 83, 107, 65, 19, 23, 84, 70, 46, 34, 95, 3, 63, 123, 69, 109, 96, 99, 73, 85, 4, 25, 37, 82, 74, 80, 87, 92, 17, 43, 76, 97, 78, 54, 120, 79, 62, 91, 105, 121, 36, 33, 81, 122, 75, 50, 16, 118, 28, 90, 113, 13, 126, 102, 10, 110, 127, 115, 56, 44, 53, 112, 67, 111, 104, 128, 108, 101, 27, 119, 88, 100, 68, 39, 124, 125 ],
[ 35, 55, 70, 2, 57, 92, 29, 49, 105, 76, 9, 61, 6, 93, 32, 94, 15, 89, 110, 24, 84, 72, 21, 12, 63, 71, 43, 1, 106, 23, 65, 31, 59, 98, 86, 66, 64, 77, 34, 22, 36, 52, 113, 42, 26, 122, 7, 17, 48, 37, 75, 51, 81, 117, 20, 107, 82, 87, 19, 4, 60, 40, 121, 96, 8, 95, 101, 3, 25, 123, 109, 99, 116, 118, 14, 74, 114, 54, 5, 38, 46, 28, 11, 80, 69, 79, 111, 112, 120, 16, 58, 62, 103, 127, 91, 33, 126, 128, 13, 18, 97, 67, 44, 56, 47, 83, 115, 73, 10, 50, 41, 102, 124, 30, 53, 85, 125, 45, 88, 68, 108, 104, 100, 78, 27, 119, 39, 90 ]
],
[ PermutationGroup<128 |  
\[ 12, 29, 8, 77, 2, 5, 48, 57, 6, 14, 31, 9, 103, 61, 35, 20, 116, 15, 18, 89, 71, 1, 49, 21, 24, 86, 30, 66, 22, 72, 98, 52, 11, 60, 64, 38, 114, 32, 41, 51, 106, 55, 47, 59, 42, 45, 26, 94, 93, 7, 117, 58, 40, 83, 107, 65, 19, 23, 84, 70, 46, 34, 95, 3, 63, 123, 69, 109, 96, 99, 73, 85, 4, 25, 37, 82, 74, 80, 87, 92, 17, 43, 76, 97, 78, 54, 120, 79, 62, 91, 105, 121, 36, 33, 81, 122, 75, 50, 16, 118, 28, 90, 113, 13, 126, 102, 10, 110, 127, 115, 56, 44, 53, 112, 67, 111, 104, 128, 108, 101, 27, 119, 88, 100, 68, 39, 124, 125 ],
\[ 3, 10, 16, 22, 18, 27, 1, 36, 39, 43, 5, 45, 2, 38, 58, 11, 64, 34, 67, 71, 75, 78, 73, 6, 81, 4, 26, 9, 90, 93, 95, 50, 97, 7, 83, 88, 8, 25, 70, 12, 32, 23, 40, 107, 54, 108, 94, 111, 33, 112, 114, 104, 116, 13, 62, 14, 47, 101, 15, 74, 99, 117, 30, 119, 19, 17, 66, 57, 21, 79, 124, 20, 56, 125, 46, 24, 44, 76, 29, 52, 42, 123, 98, 121, 122, 120, 65, 59, 28, 89, 49, 60, 53, 100, 126, 31, 41, 68, 113, 35, 37, 96, 84, 63, 86, 82, 69, 77, 61, 48, 102, 91, 118, 85, 51, 80, 109, 55, 87, 127, 115, 103, 128, 92, 72, 110, 106, 105 ],
\[ 4, 11, 17, 23, 24, 28, 32, 1, 40, 44, 49, 7, 52, 2, 5, 61, 25, 65, 68, 3, 76, 79, 15, 38, 60, 57, 84, 58, 13, 6, 16, 14, 47, 55, 59, 30, 21, 8, 95, 93, 9, 12, 106, 50, 75, 109, 10, 34, 42, 83, 43, 41, 99, 105, 81, 48, 37, 80, 77, 18, 56, 90, 87, 100, 73, 89, 121, 74, 19, 92, 69, 63, 20, 108, 33, 35, 26, 114, 36, 22, 31, 78, 45, 88, 125, 27, 70, 82, 72, 111, 29, 116, 91, 110, 104, 107, 103, 96, 39, 71, 86, 127, 54, 62, 112, 97, 118, 64, 98, 46, 53, 51, 122, 101, 126, 66, 115, 94, 85, 119, 124, 102, 67, 120, 123, 128, 117, 113 ]:
 Order := 128 > |
[ 12, 29, 8, 77, 2, 5, 48, 57, 6, 14, 31, 9, 103, 61, 35, 20, 116, 15, 18, 89, 71, 1, 49, 21, 24, 86, 30, 66, 22, 72, 98, 52, 11, 60, 64, 38, 114, 32, 41, 51, 106, 55, 47, 59, 42, 45, 26, 94, 93, 7, 117, 58, 40, 83, 107, 65, 19, 23, 84, 70, 46, 34, 95, 3, 63, 123, 69, 109, 96, 99, 73, 85, 4, 25, 37, 82, 74, 80, 87, 92, 17, 43, 76, 97, 78, 54, 120, 79, 62, 91, 105, 121, 36, 33, 81, 122, 75, 50, 16, 118, 28, 90, 113, 13, 126, 102, 10, 110, 127, 115, 56, 44, 53, 112, 67, 111, 104, 128, 108, 101, 27, 119, 88, 100, 68, 39, 124, 125 ],
[ 40, 79, 37, 108, 13, 11, 110, 68, 24, 56, 96, 28, 122, 109, 100, 72, 53, 59, 5, 90, 20, 7, 91, 69, 76, 105, 63, 67, 4, 125, 83, 80, 16, 92, 17, 14, 51, 41, 97, 115, 127, 118, 57, 88, 81, 12, 27, 47, 30, 34, 62, 15, 43, 35, 44, 87, 65, 42, 103, 39, 75, 18, 31, 1, 104, 82, 107, 117, 102, 61, 23, 114, 26, 38, 101, 106, 60, 116, 119, 124, 66, 10, 78, 33, 22, 45, 86, 70, 55, 112, 128, 84, 8, 49, 25, 85, 21, 32, 3, 113, 89, 29, 99, 54, 95, 111, 2, 126, 120, 121, 73, 77, 93, 50, 19, 48, 52, 123, 46, 58, 6, 64, 36, 94, 98, 9, 71, 74 ],
[ 85, 19, 122, 111, 121, 126, 114, 99, 46, 67, 84, 64, 65, 82, 62, 103, 45, 115, 43, 33, 9, 102, 120, 95, 128, 48, 110, 75, 107, 47, 6, 74, 124, 51, 52, 113, 61, 123, 108, 17, 60, 86, 66, 90, 119, 70, 53, 22, 71, 125, 1, 98, 100, 87, 58, 106, 93, 117, 55, 50, 36, 101, 57, 54, 10, 12, 40, 30, 28, 77, 97, 49, 127, 112, 39, 31, 29, 96, 44, 83, 105, 25, 104, 18, 16, 73, 2, 118, 21, 69, 20, 32, 94, 116, 27, 24, 92, 63, 88, 80, 109, 76, 5, 68, 23, 38, 89, 79, 8, 4, 78, 72, 59, 3, 7, 35, 37, 15, 13, 56, 34, 11, 81, 41, 91, 26, 14, 42 ]
],
[ PermutationGroup<128 |  
\[ 12, 29, 8, 77, 2, 5, 48, 57, 6, 14, 31, 9, 103, 61, 35, 20, 116, 15, 18, 89, 71, 1, 49, 21, 24, 86, 30, 66, 22, 72, 98, 52, 11, 60, 64, 38, 114, 32, 41, 51, 106, 55, 47, 59, 42, 45, 26, 94, 93, 7, 117, 58, 40, 83, 107, 65, 19, 23, 84, 70, 46, 34, 95, 3, 63, 123, 69, 109, 96, 99, 73, 85, 4, 25, 37, 82, 74, 80, 87, 92, 17, 43, 76, 97, 78, 54, 120, 79, 62, 91, 105, 121, 36, 33, 81, 122, 75, 50, 16, 118, 28, 90, 113, 13, 126, 102, 10, 110, 127, 115, 56, 44, 53, 112, 67, 111, 104, 128, 108, 101, 27, 119, 88, 100, 68, 39, 124, 125 ],
\[ 3, 10, 16, 22, 18, 27, 1, 36, 39, 43, 5, 45, 2, 38, 58, 11, 64, 34, 67, 71, 75, 78, 73, 6, 81, 4, 26, 9, 90, 93, 95, 50, 97, 7, 83, 88, 8, 25, 70, 12, 32, 23, 40, 107, 54, 108, 94, 111, 33, 112, 114, 104, 116, 13, 62, 14, 47, 101, 15, 74, 99, 117, 30, 119, 19, 17, 66, 57, 21, 79, 124, 20, 56, 125, 46, 24, 44, 76, 29, 52, 42, 123, 98, 121, 122, 120, 65, 59, 28, 89, 49, 60, 53, 100, 126, 31, 41, 68, 113, 35, 37, 96, 84, 63, 86, 82, 69, 77, 61, 48, 102, 91, 118, 85, 51, 80, 109, 55, 87, 127
…(truncated)…

/***
 *  Produces benchmarks
 *
 *  Distributed under the terms of the GNU Lesser General Public License (L-GPL)
 *                  http://www.gnu.org/licenses/
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU Lesser General Public License as published by
 *  the Free Software Foundation; either version 2.1 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 *
 *  Copyright 2016 R. Lercier, C. Ritzenthaler & J.R. Sijsling
 */

AttachSpec("../package/spec");
AttachSpec("../g3twists_v2-0/spec");
filename := "Implementation-Benchmarks.dat";

n_max := 4;
exp_max := 4;
N := 2^6;

Fs := [* *];
Fs cat:= [*
GF(p, exp) : exp in [1] cat [ 25*n : n in [1..n_max] ], p in [19, 31, 41]
*];
Fs cat:= [*
GF(NextPrime(10^(50*N)), exp) : exp in [1..exp_max] cat [10], N in [1..4]
*];

for F in Fs do
    print "Proceeding to field", F;
    Write(filename, F);
    Domain := F;
    R<x,y,z> := PolynomialRing(F, 3);
    Mons := MonomialsOfDegree(R, 4);
    TotalTimeRec := 0;
    n := 0;
    while n ne N do
        f := &+[ Random(Domain)*Mons[i] : i in [1..#Mons] ];
        I, WI := DixmierOhnoInvariants(f);
        Time := Cputime();
        g := TernaryQuarticFromDixmierOhnoInvariants(I);
        delta := Cputime(Time);
        J, WJ := DixmierOhnoInvariants(g);
        if WPSNormalize(WI, I) eq WPSNormalize(WJ, J) then
            n +:= 1;
            TotalTimeRec +:= delta;
        else
            print F;
            print f;
        end if;
    end while;
    Write(filename, TotalTimeRec/N);
end for;

exit;