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The Riemann tensor, Class. Quantum Grav., ", StyleBox["9", FontWeight->"Bold"], ", 1992, 1151 - 1197.\n\n[2] Fiedler, Bernd, A characterization of the \ dependence of the Riemannian metric on the curvature tensor by Young \ symmetrizers, Z. Anal. Anw., ", StyleBox["17", FontWeight->"Bold"], " (1) 1998, 135 -- 157." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The problem", "Section"], Cell[TextData[{ "A result of [1] says that the symmetry class of the first covariant \ derivative \[Del]R of the Riemannian curvature tensorR is generated by ", Cell[BoxData[ \(TraditionalForm\`\(y\^\[Star]\)\)]], ", where ", Cell[BoxData[ \(TraditionalForm\`y\)]], " is the normalized Young symmetrizer of the standard tableau ", Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"1", "3", "5"}, {"2", \(\ 4\), " "} }], ")"}], TraditionalForm]]], ". A prove of this fact is given in [2], too.\n\nWe verify this result by a \ calculation, which uses the packages PERMS, Ricci and RicciPerms." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The calculation", "Section"], Cell[CellGroupData[{ Cell["< Default Output Format Type -> OutputForm ------------------------------------------------------------ PERMS, Version 2.2, (05.07.2000), for Mathematica 2.x-4.0 Copyright (c) 1994-2000 Bernd Fiedler A.-Rosch-Str. 13, Leipzig, Germany email: Bernd.Fiedler.RoschStr.Leipzig@t-online.de ------------------------------------------------------------ -- For formatted output in a Version 3 or 4 notebook: Cell menu -> Default Intput Format Type -> InputForm -> Default Output Format Type -> OutputForm Enter the PERMS configuration which is intended to load. ------------------------------------------------------------- (m) Minimal configuration with character tables of S1...S10 (v) Full version with character tables of S1...S17 The evaluation of CHARTAB.M is running. Please wait.\ \>", "Print"], Cell["\<\ Type::shdw: Symbol Type appears in multiple contexts {Perms`, Ricci`}; \ definitions in context Perms` may shadow or be shadowed by other definitions.\ \>", "Message"] }, Open ]], Cell["First we define a differentable Riemannian manifold.", "Text"], Cell[CellGroupData[{ Cell["\<\ DefineBundle[TM,n,g,{i,j,k,l,r,s,t}, MetricType -> Riemannian]\ \>", "Input"], Cell["\<\ Constant n defined. Conjugate[n] = n. Index i associated with TM Index j associated with TM Index k associated with TM Index l associated with TM Index r associated with TM Index s associated with TM Index t associated with TM Tensor g defined. Rank = 2 Symmetries = Symmetric Type = {Real} Bundle = TM Variance = Covariant Tensor Rm defined. Rank = 4 Symmetries = RiemannSymmetries Type = {Real} Bundle = TM Variance = Covariant Tensor Rc defined. Rank = 2 Symmetries = Symmetric Type = {Real} Bundle = TM Variance = Covariant Tensor Sc defined. Rank = 0 Symmetries = NoSymmetries Type = {Real} Bundle = TM Variance = Covariant Bundle TM defined. Metric = g Dimension = n Indices = {i, j, k, l, r, s, t} Bundle Type = Real Metric Type = Riemannian Tangent Bundle = {TM} Connection is torsion free.\ \>", "Print"], Cell[OutputFormData["\<\ TM\ \>", "\<\ TM\ \>"], "Output"] }, Open ]], Cell[TextData[{ "Next we define a pure function that yields the coordinates ", Cell[BoxData[ \(TraditionalForm\`R\_\(i\ j\ k\ l\ ; \ s\)\)]], " of the first covariant derivative of the Riemannian curvarure tensor, if \ the names ", StyleBox["i, j, k, l, s ", FontSlant->"Italic"], "of indizes", StyleBox[" ", FontSlant->"Italic"], "are given", StyleBox[".", FontSlant->"Italic"] }], "Text"], Cell[CellGroupData[{ Cell["\<\ driemfunc = Function[{i,j,k,l,s},Del[Rm][L[i],L[j],L[k],L[l],L[s]]]\ \>", "Input"], Cell[OutputFormData["\<\ Function[{i, j, k, l, s}, (\\[Del]Rm)[L[i], L[j], L[k], L[l], L[s]]]\ \>", "\<\ Function[{i, j, k, l, s}, (\[Del]Rm)[L[i], L[j], L[k], L[l], L[s]]]\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["driemfunc[s,i,j,k,l]", "Input"], Cell[OutputFormData["\<\ -Rm[L[i], L[s], L[j], L[k]] [L[l]]\ \>", "\<\ -Rm i s j k ;l\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["driemfunc[s,i,j,k,l] //CovDExpand", "Input"], Cell[OutputFormData["\<\ -Del[Basis[L[l]], Rm[L[i], L[s], L[j], L[k]]] + Conn[L[k], U[t4], L[l]]*Rm[L[i], L[s], L[j], L[t4]] - Conn[L[j], U[t3], L[l]]*Rm[L[i], L[s], L[k], L[t3]] + Conn[L[s], U[t2], L[l]]*Rm[L[i], L[t2], L[j], L[k]] - Conn[L[i], U[t1], L[l]]*Rm[L[j], L[k], L[s], L[t1]]\ \>", "\<\ t4 t3 -Del [Rm ] + Conn Rm - Conn Rm + l i s j k k l i s j t4 j l i s k t3 t2 t1 Conn Rm - Conn Rm s l i t2 j k i l j k s t1\ \>"], "Output"] }, Open ]], Cell["We determine all partitions of 5.", "Text"], Cell[CellGroupData[{ Cell["allparts = AllPartitions[5]", "Input"], Cell[OutputFormData["\<\ HoldList[Parti[1, 1, 1, 1, 1], Parti[2, 1, 1, 1], Parti[2, 2, 1], Parti[3, 1, \ 1], Parti[3, 2], Parti[4, 1], Parti[5]]\ \>", "\<\ {{1, 1, 1, 1, 1}, {2, 1, 1, 1}, {2, 2, 1}, {3, 1, 1}, {3, 2}, {4, 1}, {5}}\ \>"], "Output"] }, Open ]], Cell["We generate all standard tableaux of all these partitions.", "Text"], Cell[CellGroupData[{ Cell["alltabls = StandardTableaux[#]& /@ allparts", "Input"], Cell[OutputFormData["\<\ HoldList[HoldList[Tableau[TabRow[1], TabRow[2], TabRow[3], TabRow[4], \ TabRow[5]]], HoldList[Tableau[TabRow[1, 2], TabRow[3], TabRow[4], TabRow[5]], Tableau[TabRow[1, 3], TabRow[2], TabRow[4], TabRow[5]], Tableau[TabRow[1, 4], TabRow[2], TabRow[3], TabRow[5]], Tableau[TabRow[1, 5], TabRow[2], TabRow[3], TabRow[4]]], HoldList[Tableau[TabRow[1, 2], TabRow[3, 4], TabRow[5]], Tableau[TabRow[1, 2], TabRow[3, 5], TabRow[4]], Tableau[TabRow[1, 3], TabRow[2, 4], TabRow[5]], Tableau[TabRow[1, 3], TabRow[2, 5], TabRow[4]], Tableau[TabRow[1, 4], TabRow[2, 5], TabRow[3]]], HoldList[Tableau[TabRow[1, 2, 3], TabRow[4], TabRow[5]], Tableau[TabRow[1, 2, 4], TabRow[3], TabRow[5]], Tableau[TabRow[1, 2, 5], TabRow[3], TabRow[4]], Tableau[TabRow[1, 3, 4], TabRow[2], TabRow[5]], Tableau[TabRow[1, 3, 5], TabRow[2], TabRow[4]], Tableau[TabRow[1, 4, 5], TabRow[2], TabRow[3]]], HoldList[Tableau[TabRow[1, 2, 3], TabRow[4, 5]], Tableau[TabRow[1, 2, 4], \ TabRow[3, 5]], Tableau[TabRow[1, 2, 5], TabRow[3, 4]], Tableau[TabRow[1, 3, 4], TabRow[2, \ 5]], Tableau[TabRow[1, 3, 5], TabRow[2, 4]]], HoldList[Tableau[TabRow[1, 2, 3, 4], TabRow[5]], Tableau[TabRow[1, 2, 3, \ 5], TabRow[4]], Tableau[TabRow[1, 2, 4, 5], TabRow[3]], Tableau[TabRow[1, 3, 4, 5], \ TabRow[2]]], HoldList[Tableau[TabRow[1, 2, 3, 4, 5]]]]\ \>", "\<\ {{{1}}, {{1, 2}, {1, 3}, {1, 4}, {1, 5}}, {{1, 2}, {1, 2}, {1, 3}, {1, 3}, \ {1, 4}}, {2} {3} {2} {2} {2} {3, 4} {3, 5} {2, 4} {2, 5} \ {2, 5} {3} {4} {4} {3} {3} {5} {4} {5} {4} \ {3} {4} {5} {5} {5} {4} {5} {{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5}}, {4} {3} {3} {2} {2} {2} {5} {5} {4} {5} {4} {3} {{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}}, {4, 5} {3, 5} {3, 4} {2, 5} {2, 4} {{1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}}, {{1, 2, 3, 4, \ 5}}} {5} {4} {3} {2}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["alltabls = Flatten[alltabls]", "Input"], Cell[OutputFormData["\<\ HoldList[Tableau[TabRow[1], TabRow[2], TabRow[3], TabRow[4], TabRow[5]], Tableau[TabRow[1, 2], TabRow[3], TabRow[4], TabRow[5]], Tableau[TabRow[1, 3], TabRow[2], TabRow[4], TabRow[5]], Tableau[TabRow[1, 4], TabRow[2], TabRow[3], TabRow[5]], Tableau[TabRow[1, 5], TabRow[2], TabRow[3], TabRow[4]], Tableau[TabRow[1, 2], TabRow[3, 4], TabRow[5]], Tableau[TabRow[1, 2], TabRow[3, 5], TabRow[4]], Tableau[TabRow[1, 3], TabRow[2, 4], TabRow[5]], Tableau[TabRow[1, 3], TabRow[2, 5], TabRow[4]], Tableau[TabRow[1, 4], TabRow[2, 5], TabRow[3]], Tableau[TabRow[1, 2, 3], TabRow[4], TabRow[5]], Tableau[TabRow[1, 2, 4], TabRow[3], TabRow[5]], Tableau[TabRow[1, 2, 5], TabRow[3], TabRow[4]], Tableau[TabRow[1, 3, 4], TabRow[2], TabRow[5]], Tableau[TabRow[1, 3, 5], TabRow[2], TabRow[4]], Tableau[TabRow[1, 4, 5], TabRow[2], TabRow[3]], Tableau[TabRow[1, 2, 3], \ TabRow[4, 5]], Tableau[TabRow[1, 2, 4], TabRow[3, 5]], Tableau[TabRow[1, 2, 5], TabRow[3, \ 4]], Tableau[TabRow[1, 3, 4], TabRow[2, 5]], Tableau[TabRow[1, 3, 5], TabRow[2, \ 4]], Tableau[TabRow[1, 2, 3, 4], TabRow[5]], Tableau[TabRow[1, 2, 3, 5], \ TabRow[4]], Tableau[TabRow[1, 2, 4, 5], TabRow[3]], Tableau[TabRow[1, 3, 4, 5], \ TabRow[2]], Tableau[TabRow[1, 2, 3, 4, 5]]]\ \>", "\<\ {{1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 2}, {1, 2}, {1, 3}, {1, 3}, {1, 4}, \ {1, 2, 3}, {2} {3} {2} {2} {2} {3, 4} {3, 5} {2, 4} {2, 5} {2, 5} \ {4} {3} {4} {4} {3} {3} {5} {4} {5} {4} {3} \ {5} {4} {5} {5} {5} {4} {5} {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, {1, 2, 3}, {1, 2, \ 4}, {1, 2, 5}, {3} {3} {2} {2} {2} {4, 5} {3, 5} \ {3, 4} {5} {4} {5} {4} {3} {1, 3, 4}, {1, 3, 5}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, \ 5}, {2, 5} {2, 4} {5} {4} {3} {2} {1, 2, 3, 4, 5}}\ \>"], "Output"] }, Open ]], Cell[TextData[{ "Now we generate all Young symmetrizers of all these standard tableaux. \ These Young symmetrizers ", StyleBox["y ", FontSlant->"Italic"], "are not normalized, i.e. they are essentially idempotent elements." }], "Text"], Cell[CellGroupData[{ Cell["allys = YoungSymmetrizer[#]& /@ alltabls", "Input"], Cell[OutputFormData["\<\ HoldList[Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] - Perm[1, 2, 5, 4, 3] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] + Perm[1, 3, 4, 2, 5] - Perm[1, 3, 4, 5, 2] - Perm[1, \ 3, 5, 2, 4] + Perm[1, 3, 5, 4, 2] + Perm[1, 4, 2, 3, 5] - Perm[1, 4, 2, 5, 3] - Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 4, 5, 2, 3] - Perm[1, 4, 5, 3, 2] - Perm[1, \ 5, 2, 3, 4] + Perm[1, 5, 2, 4, 3] + Perm[1, 5, 3, 2, 4] - Perm[1, 5, 3, 4, 2] - Perm[1, \ 5, 4, 2, 3] + Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 1, 4, 3, 5] - Perm[2, 1, 4, 5, 3] - Perm[2, 1, 5, 3, 4] + Perm[2, 1, 5, 4, 3] + Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] - Perm[2, 3, 4, 1, 5] + Perm[2, 3, 4, 5, 1] + Perm[2, \ 3, 5, 1, 4] - Perm[2, 3, 5, 4, 1] - Perm[2, 4, 1, 3, 5] + Perm[2, 4, 1, 5, 3] + Perm[2, \ 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] - Perm[2, 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] + Perm[2, \ 5, 1, 3, 4] - Perm[2, 5, 1, 4, 3] - Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] - Perm[2, 5, 4, 3, 1] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] - Perm[3, \ 1, 4, 2, 5] + Perm[3, 1, 4, 5, 2] + Perm[3, 1, 5, 2, 4] - Perm[3, 1, 5, 4, 2] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] - Perm[3, 2, 4, 5, 1] - Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] - Perm[3, 4, 1, 5, 2] - Perm[3, \ 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, 4, 5, 1, 2] - Perm[3, 4, 5, 2, 1] - Perm[3, \ 5, 1, 2, 4] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 1, 4] - Perm[3, 5, 2, 4, 1] - Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] - Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] + Perm[4, \ 1, 3, 2, 5] - Perm[4, 1, 3, 5, 2] - Perm[4, 1, 5, 2, 3] + Perm[4, 1, 5, 3, 2] + Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] - Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, \ 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] + Perm[4, \ 3, 2, 1, 5] - Perm[4, 3, 2, 5, 1] - Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 1, 2, 3] - Perm[4, 5, 1, 3, 2] - Perm[4, 5, 2, 1, 3] + Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] + Perm[5, 1, 2, 3, 4] - Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] + Perm[5, 1, 4, 2, 3] - Perm[5, 1, 4, 3, 2] - Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1] + Perm[5, 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] - Perm[5, \ 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] + Perm[5, 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1] - Perm[5, \ 4, 1, 2, 3] + Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] - Perm[5, 4, 2, 3, 1] - Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, \ 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] - Perm[1, 2, 5, 4, 3] + Perm[2, \ 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] - Perm[2, 1, 4, 3, 5] + Perm[2, 1, 4, 5, 3] + Perm[2, \ 1, 5, 3, 4] - Perm[2, 1, 5, 4, 3] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] + Perm[3, \ 1, 4, 2, 5] - Perm[3, 1, 4, 5, 2] - Perm[3, 1, 5, 2, 4] + Perm[3, 1, 5, 4, 2] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] - Perm[3, 2, 4, 5, 1] - Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[4, 1, 2, 3, 5] - Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] + Perm[4, 1, 3, 5, 2] + Perm[4, 1, 5, 2, 3] - Perm[4, 1, 5, 3, 2] + Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] - Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, \ 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] - Perm[5, 1, 2, 3, 4] + Perm[5, 1, 2, 4, 3] + Perm[5, \ 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] - Perm[5, 1, 4, 2, 3] + Perm[5, 1, 4, 3, 2] - Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 5, 3, 2, 4] - Perm[1, 5, 3, 4, 2] - Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] - Perm[2, 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] + Perm[2, \ 4, 1, 3, 5] - Perm[2, 4, 1, 5, 3] + Perm[2, 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] - Perm[2, \ 5, 1, 3, 4] + Perm[2, 5, 1, 4, 3] - Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] + Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] - Perm[3, 4, 1, 2, 5] + Perm[3, 4, 1, 5, 2] + Perm[3, \ 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] + Perm[4, 1, 3, 2, 5] - Perm[4, 1, 3, 5, 2] - Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] - Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, \ 3, 1, 2, 5] - Perm[4, 3, 1, 5, 2] - Perm[4, 5, 1, 2, 3] + Perm[4, 5, 1, 3, 2] + Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] - Perm[5, 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] + Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] + Perm[5, 4, 1, 2, 3] - Perm[5, 4, 1, 3, 2] - Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 5, 4, 3] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 5, 4, 2] + Perm[1, 5, 2, 4, 3] - Perm[1, 5, 3, 4, 2] - Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] + Perm[2, 3, 1, 4, 5] + Perm[2, 3, 4, 1, 5] - Perm[2, \ 3, 5, 1, 4] - Perm[2, 3, 5, 4, 1] - Perm[2, 4, 3, 1, 5] + Perm[2, 4, 5, 1, 3] - Perm[2, \ 5, 1, 4, 3] + Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] - Perm[2, 5, 4, 1, 3] + Perm[3, \ 1, 2, 4, 5] - Perm[3, 1, 5, 4, 2] - Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] + Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 2, 1, 5] - Perm[3, 4, 5, 1, 2] + Perm[3, \ 5, 1, 4, 2] - Perm[3, 5, 2, 1, 4] - Perm[3, 5, 2, 4, 1] + Perm[3, 5, 4, 1, 2] + Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 5, 1, 3] - Perm[4, 3, 2, 1, 5] + Perm[4, 3, 5, 1, 2] + Perm[4, \ 5, 2, 1, 3] - Perm[4, 5, 3, 1, 2] - Perm[5, 1, 2, 4, 3] + Perm[5, 1, 3, 4, 2] + Perm[5, \ 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] + Perm[5, 2, 4, 1, 3] - Perm[5, \ 3, 1, 4, 2] + Perm[5, 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] - Perm[5, 3, 4, 1, 2] - Perm[5, \ 4, 2, 1, 3] + Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 4, 2, 5] + Perm[1, 4, 2, 3, 5] - Perm[1, 4, 3, 2, 5] - Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] + Perm[2, 3, 1, 4, 5] - Perm[2, 3, 4, 1, 5] - Perm[2, \ 3, 4, 5, 1] + Perm[2, 3, 5, 4, 1] - Perm[2, 4, 1, 3, 5] + Perm[2, 4, 3, 1, 5] + Perm[2, \ 4, 3, 5, 1] - Perm[2, 4, 5, 3, 1] - Perm[2, 5, 3, 4, 1] + Perm[2, 5, 4, 3, 1] + Perm[3, \ 1, 2, 4, 5] - Perm[3, 1, 4, 2, 5] - Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] + Perm[3, \ 2, 4, 5, 1] - Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] - Perm[3, 4, 2, 1, 5] - Perm[3, \ 4, 2, 5, 1] + Perm[3, 4, 5, 2, 1] + Perm[3, 5, 2, 4, 1] - Perm[3, 5, 4, 2, 1] - Perm[4, \ 1, 2, 3, 5] + Perm[4, 1, 3, 2, 5] + Perm[4, 2, 1, 3, 5] - Perm[4, 2, 3, 1, 5] - Perm[4, \ 2, 3, 5, 1] + Perm[4, 2, 5, 3, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] + Perm[4, \ 3, 2, 5, 1] - Perm[4, 3, 5, 2, 1] - Perm[4, 5, 2, 3, 1] + Perm[4, 5, 3, 2, 1] + Perm[5, \ 2, 3, 4, 1] - Perm[5, 2, 4, 3, 1] - Perm[5, 3, 2, 4, 1] + Perm[5, 3, 4, 2, 1] + Perm[5, \ 4, 2, 3, 1] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 5, 3, 4] - Perm[1, 2, 5, 4, 3] - Perm[1, 3, 4, 2, 5] + Perm[1, 3, 5, 2, 4] - Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 5, 2, 3] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] - Perm[2, \ 1, 5, 3, 4] - Perm[2, 1, 5, 4, 3] - Perm[2, 3, 4, 1, 5] + Perm[2, 3, 5, 1, 4] - Perm[2, \ 4, 3, 1, 5] + Perm[2, 4, 5, 1, 3] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 5, 4, 2] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] + Perm[3, 4, 2, 1, 5] - Perm[3, \ 4, 5, 1, 2] - Perm[3, 4, 5, 2, 1] - Perm[4, 1, 2, 3, 5] + Perm[4, 1, 5, 3, 2] - Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 5, 3, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] - Perm[4, \ 3, 5, 1, 2] - Perm[4, 3, 5, 2, 1] + Perm[5, 1, 2, 3, 4] + Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 4, 2] - Perm[5, 1, 4, 3, 2] + Perm[5, 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] - Perm[5, \ 2, 3, 4, 1] - Perm[5, 2, 4, 3, 1] - Perm[5, 3, 1, 2, 4] - Perm[5, 3, 2, 1, 4] + Perm[5, \ 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1] - Perm[5, 4, 1, 2, 3] - Perm[5, 4, 2, 1, 3] + Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 4, 5, 3] + Perm[1, 2, 5, 4, 3] + Perm[1, 3, 4, 5, 2] - Perm[1, 3, 5, 4, 2] - Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] - Perm[2, \ 1, 4, 5, 3] + Perm[2, 1, 5, 4, 3] + Perm[2, 3, 4, 5, 1] - Perm[2, 3, 5, 4, 1] - Perm[2, \ 5, 3, 4, 1] + Perm[2, 5, 4, 3, 1] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 4, 2, 5] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 4, 1] - Perm[3, \ 5, 4, 1, 2] - Perm[3, 5, 4, 2, 1] + Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] - Perm[4, 1, 5, 2, 3] + Perm[4, 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] - Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 5, 1, 3] - Perm[4, 3, 1, 5, 2] - Perm[4, 3, 2, 5, 1] + Perm[4, \ 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] - Perm[4, 5, 1, 3, 2] - Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] - Perm[5, 1, 2, 4, 3] + Perm[5, 1, 4, 2, 3] - Perm[5, \ 2, 1, 4, 3] + Perm[5, 2, 4, 1, 3] + Perm[5, 3, 1, 4, 2] + Perm[5, 3, 2, 4, 1] - Perm[5, \ 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 4, 2, 3, 5] + Perm[1, 4, 3, 2, 5] + Perm[1, 5, 2, 3, 4] - Perm[1, 5, 3, 2, 4] - Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] - Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 4, 1, 5] + Perm[2, 5, 1, 4, 3] + Perm[2, 5, 3, 4, 1] - Perm[2, \ 5, 4, 1, 3] - Perm[2, 5, 4, 3, 1] + Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] + Perm[3, \ 4, 1, 2, 5] - Perm[3, 4, 2, 1, 5] - Perm[3, 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] + Perm[3, \ 5, 2, 1, 4] + Perm[3, 5, 4, 1, 2] + Perm[4, 1, 2, 3, 5] - Perm[4, 1, 3, 2, 5] - Perm[4, \ 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] + Perm[4, 5, 1, 2, 3] - Perm[4, 5, 2, 1, 3] - Perm[4, \ 5, 2, 3, 1] + Perm[4, 5, 3, 2, 1] - Perm[5, 1, 2, 3, 4] + Perm[5, 1, 3, 2, 4] + Perm[5, \ 1, 3, 4, 2] - Perm[5, 1, 4, 3, 2] - Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1] + Perm[5, 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] - Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 4, 1, 2] - Perm[5, 4, 1, 2, 3] + Perm[5, 4, 2, 1, 3] + Perm[5, \ 4, 2, 3, 1] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 5, 4, 3] + Perm[1, \ 4, 2, 5, 3] - Perm[1, 4, 3, 2, 5] - Perm[1, 4, 3, 5, 2] + Perm[1, 4, 5, 2, 3] - Perm[1, \ 5, 2, 4, 3] + Perm[1, 5, 3, 4, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] - Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 5, 4, 1] + Perm[2, 4, 1, 3, 5] + Perm[2, 4, 3, 1, 5] - Perm[2, \ 4, 5, 1, 3] - Perm[2, 4, 5, 3, 1] + Perm[3, 2, 1, 4, 5] - Perm[3, 2, 5, 4, 1] - Perm[3, \ 4, 1, 2, 5] - Perm[3, 4, 1, 5, 2] + Perm[3, 4, 2, 5, 1] + Perm[3, 4, 5, 2, 1] + Perm[3, \ 5, 1, 4, 2] - Perm[3, 5, 2, 4, 1] - Perm[4, 1, 2, 5, 3] + Perm[4, 1, 3, 2, 5] + Perm[4, \ 1, 3, 5, 2] - Perm[4, 1, 5, 2, 3] - Perm[4, 2, 1, 3, 5] - Perm[4, 2, 3, 1, 5] + Perm[4, \ 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] - Perm[4, \ 3, 2, 5, 1] - Perm[4, 3, 5, 2, 1] - Perm[4, 5, 1, 3, 2] + Perm[4, 5, 2, 1, 3] + Perm[4, \ 5, 2, 3, 1] - Perm[4, 5, 3, 1, 2] + Perm[5, 1, 2, 4, 3] - Perm[5, 1, 3, 4, 2] - Perm[5, \ 3, 1, 4, 2] + Perm[5, 3, 2, 4, 1] + Perm[5, 4, 1, 3, 2] - Perm[5, 4, 2, 1, 3] - Perm[5, \ 4, 2, 3, 1] + Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] + Perm[1, 3, 5, 2, 4] - Perm[1, 3, 5, 4, 2] - Perm[1, \ 5, 3, 2, 4] + Perm[1, 5, 3, 4, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] + Perm[2, 3, 4, 1, 5] - Perm[2, 3, 4, 5, 1] - Perm[2, \ 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] - Perm[3, \ 1, 5, 2, 4] + Perm[3, 1, 5, 4, 2] - Perm[3, 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] - Perm[3, \ 2, 4, 1, 5] + Perm[3, 2, 4, 5, 1] + Perm[3, 4, 2, 1, 5] - Perm[3, 4, 2, 5, 1] + Perm[3, \ 4, 5, 1, 2] - Perm[3, 4, 5, 2, 1] + Perm[3, 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] - Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] + Perm[4, 2, 3, 1, 5] - Perm[4, 2, 3, 5, 1] - Perm[4, \ 3, 2, 1, 5] + Perm[4, 3, 2, 5, 1] - Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] + Perm[5, 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] - Perm[5, \ 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] + Perm[5, 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1] - Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] + Perm[1, \ 3, 2, 4, 5] - Perm[1, 3, 2, 5, 4] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] + Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] - Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] + Perm[4, 1, 3, 5, 2] - Perm[4, 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] - Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] - Perm[4, \ 3, 2, 1, 5] + Perm[4, 3, 2, 5, 1] + Perm[5, 1, 2, 3, 4] - Perm[5, 1, 2, 4, 3] + Perm[5, \ 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] + Perm[5, 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] + Perm[5, \ 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] + Perm[5, 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] + Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 2, 4, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 5, 4, 3] + Perm[1, \ 4, 3, 2, 5] - Perm[1, 4, 5, 2, 3] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 5, 4, 3] + Perm[2, \ 4, 3, 1, 5] - Perm[2, 4, 5, 1, 3] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 4, 2, 5] + Perm[3, \ 1, 5, 2, 4] + Perm[3, 1, 5, 4, 2] - Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] + Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] - Perm[3, 4, 1, 2, 5] - Perm[3, 4, 2, 1, 5] + Perm[3, \ 4, 5, 1, 2] + Perm[3, 4, 5, 2, 1] + Perm[4, 1, 3, 2, 5] - Perm[4, 1, 5, 2, 3] + Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 5, 1, 3] + Perm[5, 1, 2, 4, 3] - Perm[5, 1, 3, 2, 4] - Perm[5, \ 1, 3, 4, 2] + Perm[5, 1, 4, 2, 3] + Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] - Perm[5, \ 2, 3, 4, 1] + Perm[5, 2, 4, 1, 3] + Perm[5, 4, 1, 2, 3] + Perm[5, 4, 2, 1, 3] - Perm[5, \ 4, 3, 1, 2] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] + Perm[1, \ 5, 3, 4, 2] - Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] + Perm[2, \ 5, 3, 4, 1] - Perm[2, 5, 4, 3, 1] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 4, 2, 5] + Perm[3, \ 1, 4, 5, 2] - Perm[3, 1, 5, 4, 2] - Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] + Perm[3, \ 2, 4, 5, 1] - Perm[3, 2, 5, 4, 1] - Perm[3, 5, 1, 4, 2] - Perm[3, 5, 2, 4, 1] + Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] + Perm[4, 1, 2, 3, 5] - Perm[4, 1, 3, 2, 5] - Perm[4, \ 1, 3, 5, 2] + Perm[4, 1, 5, 3, 2] + Perm[4, 2, 1, 3, 5] - Perm[4, 2, 3, 1, 5] - Perm[4, \ 2, 3, 5, 1] + Perm[4, 2, 5, 3, 1] + Perm[4, 5, 1, 3, 2] + Perm[4, 5, 2, 3, 1] - Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] + Perm[5, 1, 3, 4, 2] - Perm[5, 1, 4, 3, 2] + Perm[5, \ 2, 3, 4, 1] - Perm[5, 2, 4, 3, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 5, 3, 4, 2] - Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] - Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 4, 1, 5] - Perm[2, 4, 1, 3, 5] - Perm[2, 4, 3, 1, 5] + Perm[2, \ 5, 1, 3, 4] + Perm[2, 5, 1, 4, 3] + Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] + Perm[2, 5, 4, 3, 1] + Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] - Perm[3, \ 5, 1, 4, 2] - Perm[3, 5, 4, 1, 2] + Perm[4, 2, 1, 3, 5] + Perm[4, 2, 3, 1, 5] - Perm[4, \ 5, 1, 3, 2] - Perm[4, 5, 3, 1, 2] + Perm[5, 1, 3, 4, 2] + Perm[5, 1, 4, 3, 2] - Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] - Perm[5, 2, 4, 3, 1] + Perm[5, 3, 1, 4, 2] + Perm[5, 3, 4, 1, 2] + Perm[5, \ 4, 1, 3, 2] + Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 5, 4, 3] - Perm[1, \ 4, 3, 2, 5] - Perm[1, 4, 5, 2, 3] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 5, 4, 3] - Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 5, 4, 1] + Perm[2, 4, 1, 3, 5] + Perm[2, 4, 1, 5, 3] + Perm[2, \ 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[2, 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] - Perm[2, \ 5, 1, 4, 3] - Perm[2, 5, 3, 4, 1] + Perm[3, 2, 1, 4, 5] + Perm[3, 2, 5, 4, 1] - Perm[3, \ 4, 1, 2, 5] - Perm[3, 4, 5, 2, 1] + Perm[4, 1, 3, 2, 5] + Perm[4, 1, 5, 2, 3] - Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] - Perm[4, 2, 3, 1, 5] - Perm[4, 2, 3, 5, 1] - Perm[4, \ 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 1, 2, 3] + Perm[4, 5, 3, 2, 1] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 4, 1] - Perm[5, \ 4, 1, 2, 3] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] - Perm[1, \ 3, 2, 4, 5] - Perm[1, 3, 2, 5, 4] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] + Perm[2, 3, 4, 1, 5] + Perm[2, 3, 4, 5, 1] + Perm[2, \ 3, 5, 1, 4] + Perm[2, 3, 5, 4, 1] - Perm[2, 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] - Perm[2, \ 5, 3, 1, 4] - Perm[2, 5, 3, 4, 1] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] - Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] - Perm[3, 2, 4, 1, 5] - Perm[3, 2, 4, 5, 1] - Perm[3, \ 2, 5, 1, 4] - Perm[3, 2, 5, 4, 1] + Perm[3, 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, \ 5, 2, 1, 4] + Perm[3, 5, 2, 4, 1] + Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] - Perm[4, \ 3, 2, 1, 5] - Perm[4, 3, 2, 5, 1] + Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] - Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 2, 4, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] - Perm[1, 4, 2, 5, 3] - Perm[1, 4, 3, 5, 2] - Perm[1, \ 5, 2, 4, 3] - Perm[1, 5, 3, 4, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] - Perm[2, 4, 1, 5, 3] - Perm[2, 4, 3, 5, 1] - Perm[2, \ 5, 1, 4, 3] - Perm[2, 5, 3, 4, 1] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] - Perm[3, 4, 1, 5, 2] - Perm[3, 4, 2, 5, 1] - Perm[3, \ 5, 1, 4, 2] - Perm[3, 5, 2, 4, 1] - Perm[4, 1, 2, 3, 5] - Perm[4, 1, 3, 2, 5] - Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 3, 1, 5] - Perm[4, 3, 1, 2, 5] - Perm[4, 3, 2, 1, 5] + Perm[4, \ 5, 1, 2, 3] + Perm[4, 5, 1, 3, 2] + Perm[4, 5, 2, 1, 3] + Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] - Perm[5, 1, 2, 3, 4] - Perm[5, 1, 3, 2, 4] - Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 3, 1, 4] - Perm[5, 3, 1, 2, 4] - Perm[5, 3, 2, 1, 4] + Perm[5, \ 4, 1, 2, 3] + Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] + Perm[5, 4, 2, 3, 1] + Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 5, 4, 3] - Perm[1, \ 3, 5, 2, 4] - Perm[1, 3, 5, 4, 2] + Perm[1, 4, 3, 2, 5] + Perm[1, 4, 5, 2, 3] - Perm[1, \ 5, 3, 2, 4] - Perm[1, 5, 3, 4, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] - Perm[2, \ 3, 5, 1, 4] - Perm[2, 3, 5, 4, 1] + Perm[2, 4, 3, 1, 5] + Perm[2, 4, 5, 1, 3] - Perm[2, \ 5, 3, 1, 4] - Perm[2, 5, 3, 4, 1] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 4, 2, 5] - Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] - Perm[3, 4, 1, 2, 5] - Perm[3, 4, 2, 1, 5] + Perm[3, \ 5, 1, 2, 4] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 1, 4] + Perm[3, 5, 2, 4, 1] + Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] + Perm[4, 1, 3, 2, 5] + Perm[4, 1, 5, 2, 3] + Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 5, 1, 3] - Perm[4, 3, 5, 1, 2] - Perm[4, 3, 5, 2, 1] - Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] - Perm[5, 1, 2, 4, 3] - Perm[5, 1, 4, 2, 3] - Perm[5, \ 2, 1, 4, 3] - Perm[5, 2, 4, 1, 3] + Perm[5, 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] + Perm[5, \ 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] + Perm[5, 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1] - Perm[5, \ 4, 1, 2, 3] - Perm[5, 4, 2, 1, 3], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 3, 4, 2, 5] - Perm[1, 3, 4, 5, 2] - Perm[1, 4, 3, 2, 5] - Perm[1, 4, 3, 5, 2] + Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] - Perm[2, \ 3, 4, 1, 5] - Perm[2, 3, 4, 5, 1] - Perm[2, 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] + Perm[2, \ 5, 3, 4, 1] + Perm[2, 5, 4, 3, 1] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 5, 4, 2] - Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] + Perm[3, 4, 1, 5, 2] + Perm[3, \ 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, 4, 5, 1, 2] + Perm[3, 4, 5, 2, 1] - Perm[3, \ 5, 1, 4, 2] - Perm[3, 5, 2, 4, 1] - Perm[4, 1, 2, 3, 5] - Perm[4, 1, 5, 3, 2] - Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 5, 3, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] + Perm[4, \ 3, 2, 1, 5] + Perm[4, 3, 2, 5, 1] + Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] - Perm[4, \ 5, 1, 3, 2] - Perm[4, 5, 2, 3, 1] + Perm[5, 1, 3, 4, 2] + Perm[5, 1, 4, 3, 2] + Perm[5, \ 2, 3, 4, 1] + Perm[5, 2, 4, 3, 1] - Perm[5, 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1] - Perm[5, \ 4, 3, 1, 2] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 5, 3, 4] - Perm[1, 2, 5, 4, 3] - Perm[1, 5, 2, 3, 4] - Perm[1, 5, 2, 4, 3] + Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] + Perm[2, \ 1, 5, 3, 4] + Perm[2, 1, 5, 4, 3] - Perm[2, 3, 1, 4, 5] - Perm[2, 3, 4, 1, 5] + Perm[2, \ 3, 5, 1, 4] + Perm[2, 3, 5, 4, 1] - Perm[2, 4, 1, 3, 5] - Perm[2, 4, 3, 1, 5] + Perm[2, \ 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] + Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] - Perm[3, \ 2, 5, 1, 4] - Perm[3, 2, 5, 4, 1] + Perm[3, 5, 1, 4, 2] - Perm[3, 5, 2, 1, 4] - Perm[3, \ 5, 2, 4, 1] + Perm[3, 5, 4, 1, 2] + Perm[4, 2, 1, 3, 5] + Perm[4, 2, 3, 1, 5] - Perm[4, \ 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] + Perm[4, 5, 1, 3, 2] - Perm[4, 5, 2, 1, 3] - Perm[4, \ 5, 2, 3, 1] + Perm[4, 5, 3, 1, 2] + Perm[5, 1, 2, 3, 4] + Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 4, 2] - Perm[5, 1, 4, 3, 2] - Perm[5, 3, 1, 4, 2] + Perm[5, 3, 2, 1, 4] + Perm[5, \ 3, 2, 4, 1] - Perm[5, 3, 4, 1, 2] - Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] + Perm[5, \ 4, 2, 3, 1] - Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 4, 5, 3] + Perm[1, 2, 5, 4, 3] - Perm[1, 4, 2, 3, 5] - Perm[1, 4, 2, 5, 3] + Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 5, 2, 3] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] + Perm[2, \ 1, 4, 5, 3] - Perm[2, 1, 5, 4, 3] - Perm[2, 3, 1, 4, 5] + Perm[2, 3, 4, 1, 5] + Perm[2, \ 3, 4, 5, 1] - Perm[2, 3, 5, 4, 1] - Perm[2, 5, 1, 4, 3] - Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] + Perm[2, 5, 4, 3, 1] + Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] - Perm[3, \ 2, 4, 5, 1] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] - Perm[3, 4, 2, 1, 5] - Perm[3, \ 4, 2, 5, 1] + Perm[3, 4, 5, 2, 1] + Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] - Perm[4, 1, 5, 2, 3] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] + Perm[4, \ 3, 2, 5, 1] - Perm[4, 3, 5, 2, 1] - Perm[4, 5, 1, 2, 3] + Perm[4, 5, 2, 1, 3] + Perm[4, \ 5, 2, 3, 1] - Perm[4, 5, 3, 2, 1] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] - Perm[5, 2, 4, 3, 1] + Perm[5, 4, 1, 2, 3] - Perm[5, 4, 2, 1, 3] - Perm[5, \ 4, 2, 3, 1] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 4, 2, 5] + Perm[1, 4, 2, 3, 5] + Perm[1, 4, 3, 2, 5] + Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] + Perm[2, 3, 1, 4, 5] + Perm[2, 3, 4, 1, 5] + Perm[2, \ 4, 1, 3, 5] + Perm[2, 4, 3, 1, 5] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 4, 2, 5] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] + Perm[3, 4, 1, 2, 5] + Perm[3, 4, 2, 1, 5] + Perm[4, \ 1, 2, 3, 5] + Perm[4, 1, 3, 2, 5] + Perm[4, 2, 1, 3, 5] + Perm[4, 2, 3, 1, 5] + Perm[4, \ 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] - Perm[5, 1, 2, 3, 4] - Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] - Perm[5, 1, 4, 2, 3] - Perm[5, 1, 4, 3, 2] - Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] - Perm[5, 2, 4, 3, 1] - Perm[5, 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] - Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 2, 4, 1] - Perm[5, 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1] - Perm[5, \ 4, 1, 2, 3] - Perm[5, 4, 1, 3, 2] - Perm[5, 4, 2, 1, 3] - Perm[5, 4, 2, 3, 1] - Perm[5, \ 4, 3, 1, 2] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 5, 4, 3] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 5, 4, 2] + Perm[1, 5, 2, 4, 3] + Perm[1, 5, 3, 4, 2] + Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] + Perm[2, 3, 1, 4, 5] + Perm[2, 3, 5, 4, 1] + Perm[2, \ 5, 1, 4, 3] + Perm[2, 5, 3, 4, 1] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 5, 4, 2] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 5, 4, 1] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 4, 1] - Perm[4, \ 1, 2, 3, 5] - Perm[4, 1, 2, 5, 3] - Perm[4, 1, 3, 2, 5] - Perm[4, 1, 3, 5, 2] - Perm[4, \ 1, 5, 2, 3] - Perm[4, 1, 5, 3, 2] - Perm[4, 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] - Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 3, 5, 1] - Perm[4, 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] - Perm[4, \ 3, 1, 2, 5] - Perm[4, 3, 1, 5, 2] - Perm[4, 3, 2, 1, 5] - Perm[4, 3, 2, 5, 1] - Perm[4, \ 3, 5, 1, 2] - Perm[4, 3, 5, 2, 1] - Perm[4, 5, 1, 2, 3] - Perm[4, 5, 1, 3, 2] - Perm[4, \ 5, 2, 1, 3] - Perm[4, 5, 2, 3, 1] - Perm[4, 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] + Perm[5, \ 1, 2, 4, 3] + Perm[5, 1, 3, 4, 2] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 3, 1, 4, 2] + Perm[5, 3, 2, 4, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 5, 3, 2, 4] + Perm[1, 5, 3, 4, 2] + Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[2, \ 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] - Perm[3, \ 1, 4, 2, 5] - Perm[3, 1, 4, 5, 2] - Perm[3, 1, 5, 2, 4] - Perm[3, 1, 5, 4, 2] - Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] - Perm[3, 2, 4, 1, 5] - Perm[3, 2, 4, 5, 1] - Perm[3, \ 2, 5, 1, 4] - Perm[3, 2, 5, 4, 1] - Perm[3, 4, 1, 2, 5] - Perm[3, 4, 1, 5, 2] - Perm[3, \ 4, 2, 1, 5] - Perm[3, 4, 2, 5, 1] - Perm[3, 4, 5, 1, 2] - Perm[3, 4, 5, 2, 1] - Perm[3, \ 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] - Perm[3, 5, 2, 1, 4] - Perm[3, 5, 2, 4, 1] - Perm[3, \ 5, 4, 1, 2] - Perm[3, 5, 4, 2, 1] + Perm[4, 1, 3, 2, 5] + Perm[4, 1, 3, 5, 2] + Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] + Perm[5, \ 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] + Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] + Perm[1, 2, 5, 4, 3] - Perm[2, \ 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] - Perm[2, 1, 4, 3, 5] - Perm[2, 1, 4, 5, 3] - Perm[2, \ 1, 5, 3, 4] - Perm[2, 1, 5, 4, 3] - Perm[2, 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] - Perm[2, \ 3, 4, 1, 5] - Perm[2, 3, 4, 5, 1] - Perm[2, 3, 5, 1, 4] - Perm[2, 3, 5, 4, 1] - Perm[2, \ 4, 1, 3, 5] - Perm[2, 4, 1, 5, 3] - Perm[2, 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] - Perm[2, \ 4, 5, 1, 3] - Perm[2, 4, 5, 3, 1] - Perm[2, 5, 1, 3, 4] - Perm[2, 5, 1, 4, 3] - Perm[2, \ 5, 3, 1, 4] - Perm[2, 5, 3, 4, 1] - Perm[2, 5, 4, 1, 3] - Perm[2, 5, 4, 3, 1] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] + Perm[3, 2, 4, 5, 1] + Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[4, 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] + Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] + Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] + Perm[1, 2, 5, 4, 3] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] + Perm[1, 3, 4, 2, 5] + Perm[1, 3, 4, 5, 2] + Perm[1, \ 3, 5, 2, 4] + Perm[1, 3, 5, 4, 2] + Perm[1, 4, 2, 3, 5] + Perm[1, 4, 2, 5, 3] + Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 4, 5, 2, 3] + Perm[1, 4, 5, 3, 2] + Perm[1, \ 5, 2, 3, 4] + Perm[1, 5, 2, 4, 3] + Perm[1, 5, 3, 2, 4] + Perm[1, 5, 3, 4, 2] + Perm[1, \ 5, 4, 2, 3] + Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 1, 4, 3, 5] + Perm[2, 1, 4, 5, 3] + Perm[2, 1, 5, 3, 4] + Perm[2, 1, 5, 4, 3] + Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] + Perm[2, 3, 4, 1, 5] + Perm[2, 3, 4, 5, 1] + Perm[2, \ 3, 5, 1, 4] + Perm[2, 3, 5, 4, 1] + Perm[2, 4, 1, 3, 5] + Perm[2, 4, 1, 5, 3] + Perm[2, \ 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[2, 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] + Perm[2, \ 5, 1, 3, 4] + Perm[2, 5, 1, 4, 3] + Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] + Perm[2, 5, 4, 3, 1] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] + Perm[3, \ 1, 4, 2, 5] + Perm[3, 1, 4, 5, 2] + Perm[3, 1, 5, 2, 4] + Perm[3, 1, 5, 4, 2] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] + Perm[3, 2, 4, 5, 1] + Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] + Perm[3, 4, 1, 5, 2] + Perm[3, \ 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, 4, 5, 1, 2] + Perm[3, 4, 5, 2, 1] + Perm[3, \ 5, 1, 2, 4] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 1, 4] + Perm[3, 5, 2, 4, 1] + Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] + Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] + Perm[4, \ 1, 3, 2, 5] + Perm[4, 1, 3, 5, 2] + Perm[4, 1, 5, 2, 3] + Perm[4, 1, 5, 3, 2] + Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] + Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, \ 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] + Perm[4, \ 3, 2, 1, 5] + Perm[4, 3, 2, 5, 1] + Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 1, 2, 3] + Perm[4, 5, 1, 3, 2] + Perm[4, 5, 2, 1, 3] + Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] + Perm[5, 1, 2, 3, 4] + Perm[5, 1, 2, 4, 3] + Perm[5, \ 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] + Perm[5, 1, 4, 2, 3] + Perm[5, 1, 4, 3, 2] + Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1] + Perm[5, 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] + Perm[5, \ 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] + Perm[5, 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1] + Perm[5, \ 4, 1, 2, 3] + Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] + Perm[5, 4, 2, 3, 1] + Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1]]\ \>", "\<\ {( 1 2 3 4 5 ) - 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( 3 5 2 1 4 ) - ( 3 5 2 4 1 ) - ( 3 5 4 1 \ 2 ) - ( 3 5 4 2 1 ) + ( 4 1 3 2 5 ) + ( 4 1 3 5 2 ) + ( 4 2 3 1 5 ) + ( 4 2 3 5 \ 1 ) + ( 4 5 3 1 2 ) + ( 4 5 3 2 1 ) + ( 5 1 3 2 4 ) + ( 5 1 3 4 2 ) + ( 5 2 3 1 \ 4 ) + ( 5 2 3 4 1 ) + ( 5 4 3 1 2 ) + ( 5 4 3 2 1 ), ( 1 2 3 4 5 ) + ( 1 2 3 5 4 ) + ( 1 2 4 3 5 ) + ( 1 2 4 5 3 ) + ( 1 2 5 3 4 \ ) + ( 1 2 5 4 3 ) - ( 2 1 3 4 5 ) - ( 2 1 3 5 4 ) - ( 2 1 4 3 5 ) - ( 2 1 4 5 \ 3 ) - ( 2 1 5 3 4 ) - ( 2 1 5 4 3 ) - ( 2 3 1 4 5 ) - ( 2 3 1 5 4 ) - ( 2 3 4 1 \ 5 ) - ( 2 3 4 5 1 ) - ( 2 3 5 1 4 ) - ( 2 3 5 4 1 ) - ( 2 4 1 3 5 ) - ( 2 4 1 5 \ 3 ) - ( 2 4 3 1 5 ) - ( 2 4 3 5 1 ) - ( 2 4 5 1 3 ) - ( 2 4 5 3 1 ) - ( 2 5 1 3 \ 4 ) - ( 2 5 1 4 3 ) - ( 2 5 3 1 4 ) - ( 2 5 3 4 1 ) - ( 2 5 4 1 3 ) - ( 2 5 4 3 \ 1 ) + ( 3 2 1 4 5 ) + ( 3 2 1 5 4 ) + ( 3 2 4 1 5 ) + ( 3 2 4 5 1 ) + ( 3 2 5 1 \ 4 ) + ( 3 2 5 4 1 ) + ( 4 2 1 3 5 ) + ( 4 2 1 5 3 ) + ( 4 2 3 1 5 ) + ( 4 2 3 5 \ 1 ) + ( 4 2 5 1 3 ) + ( 4 2 5 3 1 ) + ( 5 2 1 3 4 ) + ( 5 2 1 4 3 ) + ( 5 2 3 1 \ 4 ) + ( 5 2 3 4 1 ) + ( 5 2 4 1 3 ) + ( 5 2 4 3 1 ), ( 1 2 3 4 5 ) + ( 1 2 3 5 4 ) + ( 1 2 4 3 5 ) + ( 1 2 4 5 3 ) + ( 1 2 5 3 4 \ ) + ( 1 2 5 4 3 ) + ( 1 3 2 4 5 ) + ( 1 3 2 5 4 ) + ( 1 3 4 2 5 ) + ( 1 3 4 5 \ 2 ) + ( 1 3 5 2 4 ) + ( 1 3 5 4 2 ) + ( 1 4 2 3 5 ) + ( 1 4 2 5 3 ) + ( 1 4 3 2 \ 5 ) + ( 1 4 3 5 2 ) + ( 1 4 5 2 3 ) + ( 1 4 5 3 2 ) + ( 1 5 2 3 4 ) + ( 1 5 2 4 \ 3 ) + ( 1 5 3 2 4 ) + ( 1 5 3 4 2 ) + ( 1 5 4 2 3 ) + ( 1 5 4 3 2 ) + ( 2 1 3 4 \ 5 ) + ( 2 1 3 5 4 ) + ( 2 1 4 3 5 ) + ( 2 1 4 5 3 ) + ( 2 1 5 3 4 ) + ( 2 1 5 4 \ 3 ) + ( 2 3 1 4 5 ) + ( 2 3 1 5 4 ) + ( 2 3 4 1 5 ) + ( 2 3 4 5 1 ) + ( 2 3 5 1 \ 4 ) + ( 2 3 5 4 1 ) + ( 2 4 1 3 5 ) + ( 2 4 1 5 3 ) + ( 2 4 3 1 5 ) + ( 2 4 3 5 \ 1 ) + ( 2 4 5 1 3 ) + ( 2 4 5 3 1 ) + ( 2 5 1 3 4 ) + ( 2 5 1 4 3 ) + ( 2 5 3 1 \ 4 ) + ( 2 5 3 4 1 ) + ( 2 5 4 1 3 ) + ( 2 5 4 3 1 ) + ( 3 1 2 4 5 ) + ( 3 1 2 5 \ 4 ) + ( 3 1 4 2 5 ) + ( 3 1 4 5 2 ) + ( 3 1 5 2 4 ) + ( 3 1 5 4 2 ) + ( 3 2 1 4 \ 5 ) + ( 3 2 1 5 4 ) + ( 3 2 4 1 5 ) + ( 3 2 4 5 1 ) + ( 3 2 5 1 4 ) + ( 3 2 5 4 \ 1 ) + ( 3 4 1 2 5 ) + ( 3 4 1 5 2 ) + ( 3 4 2 1 5 ) + ( 3 4 2 5 1 ) + ( 3 4 5 1 \ 2 ) + ( 3 4 5 2 1 ) + ( 3 5 1 2 4 ) + ( 3 5 1 4 2 ) + ( 3 5 2 1 4 ) + ( 3 5 2 4 \ 1 ) + ( 3 5 4 1 2 ) + ( 3 5 4 2 1 ) + ( 4 1 2 3 5 ) + ( 4 1 2 5 3 ) + ( 4 1 3 2 \ 5 ) + ( 4 1 3 5 2 ) + ( 4 1 5 2 3 ) + ( 4 1 5 3 2 ) + ( 4 2 1 3 5 ) + ( 4 2 1 5 \ 3 ) + ( 4 2 3 1 5 ) + ( 4 2 3 5 1 ) + ( 4 2 5 1 3 ) + ( 4 2 5 3 1 ) + ( 4 3 1 2 \ 5 ) + ( 4 3 1 5 2 ) + ( 4 3 2 1 5 ) + ( 4 3 2 5 1 ) + ( 4 3 5 1 2 ) + ( 4 3 5 2 \ 1 ) + ( 4 5 1 2 3 ) + ( 4 5 1 3 2 ) + ( 4 5 2 1 3 ) + ( 4 5 2 3 1 ) + ( 4 5 3 1 \ 2 ) + ( 4 5 3 2 1 ) + ( 5 1 2 3 4 ) + ( 5 1 2 4 3 ) + ( 5 1 3 2 4 ) + ( 5 1 3 4 \ 2 ) + ( 5 1 4 2 3 ) + ( 5 1 4 3 2 ) + ( 5 2 1 3 4 ) + ( 5 2 1 4 3 ) + ( 5 2 3 1 \ 4 ) + ( 5 2 3 4 1 ) + ( 5 2 4 1 3 ) + ( 5 2 4 3 1 ) + ( 5 3 1 2 4 ) + ( 5 3 1 4 \ 2 ) + ( 5 3 2 1 4 ) + ( 5 3 2 4 1 ) + ( 5 3 4 1 2 ) + ( 5 3 4 2 1 ) + ( 5 4 1 2 \ 3 ) + ( 5 4 1 3 2 ) + ( 5 4 2 1 3 ) + ( 5 4 2 3 1 ) + ( 5 4 3 1 2 ) + ( 5 4 3 2 \ 1 )}\ \>"], "Output"] }, Open ]], Cell[TextData[{ "We form ", Cell[BoxData[ \(TraditionalForm\`\(y\^\[Star]\)\)]], " for all Young symmetrizers ", StyleBox["y", FontSlant->"Italic"], "." }], "Text"], Cell[CellGroupData[{ Cell["allyy = Star[#]& /@ allys", "Input"], Cell["\<\ General::spell1: Possible spelling error: new symbol name \"allyy\" is similar to existing symbol \"allys\".\ \>", "Message"], Cell[OutputFormData["\<\ HoldList[Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] - Perm[1, 2, 5, 4, 3] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] + Perm[1, 3, 4, 2, 5] - Perm[1, 3, 4, 5, 2] - Perm[1, \ 3, 5, 2, 4] + Perm[1, 3, 5, 4, 2] + Perm[1, 4, 2, 3, 5] - Perm[1, 4, 2, 5, 3] - Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 4, 5, 2, 3] - Perm[1, 4, 5, 3, 2] - Perm[1, \ 5, 2, 3, 4] + Perm[1, 5, 2, 4, 3] + Perm[1, 5, 3, 2, 4] - Perm[1, 5, 3, 4, 2] - Perm[1, \ 5, 4, 2, 3] + Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 1, 4, 3, 5] - Perm[2, 1, 4, 5, 3] - Perm[2, 1, 5, 3, 4] + Perm[2, 1, 5, 4, 3] + Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] - Perm[2, 3, 4, 1, 5] + Perm[2, 3, 4, 5, 1] + Perm[2, \ 3, 5, 1, 4] - Perm[2, 3, 5, 4, 1] - Perm[2, 4, 1, 3, 5] + Perm[2, 4, 1, 5, 3] + Perm[2, \ 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] - Perm[2, 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] + Perm[2, \ 5, 1, 3, 4] - Perm[2, 5, 1, 4, 3] - Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] - Perm[2, 5, 4, 3, 1] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] - Perm[3, \ 1, 4, 2, 5] + Perm[3, 1, 4, 5, 2] + Perm[3, 1, 5, 2, 4] - Perm[3, 1, 5, 4, 2] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] - Perm[3, 2, 4, 5, 1] - Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] - Perm[3, 4, 1, 5, 2] - Perm[3, \ 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, 4, 5, 1, 2] - Perm[3, 4, 5, 2, 1] - Perm[3, \ 5, 1, 2, 4] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 1, 4] - Perm[3, 5, 2, 4, 1] - Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] - Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] + Perm[4, \ 1, 3, 2, 5] - Perm[4, 1, 3, 5, 2] - Perm[4, 1, 5, 2, 3] + Perm[4, 1, 5, 3, 2] + Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] - Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, \ 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] + Perm[4, \ 3, 2, 1, 5] - Perm[4, 3, 2, 5, 1] - Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 1, 2, 3] - Perm[4, 5, 1, 3, 2] - Perm[4, 5, 2, 1, 3] + Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] + Perm[5, 1, 2, 3, 4] - Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] + Perm[5, 1, 4, 2, 3] - Perm[5, 1, 4, 3, 2] - Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1] + Perm[5, 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] - Perm[5, \ 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] + Perm[5, 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1] - Perm[5, \ 4, 1, 2, 3] + Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] - Perm[5, 4, 2, 3, 1] - Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, \ 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] - Perm[1, 2, 5, 4, 3] + Perm[2, \ 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] - Perm[2, 1, 4, 3, 5] + Perm[2, 1, 4, 5, 3] + Perm[2, \ 1, 5, 3, 4] - Perm[2, 1, 5, 4, 3] - Perm[2, 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] + Perm[2, \ 3, 4, 1, 5] - Perm[2, 3, 4, 5, 1] - Perm[2, 3, 5, 1, 4] + Perm[2, 3, 5, 4, 1] + Perm[2, \ 4, 1, 3, 5] - Perm[2, 4, 1, 5, 3] - Perm[2, 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[2, \ 4, 5, 1, 3] - Perm[2, 4, 5, 3, 1] - Perm[2, 5, 1, 3, 4] + Perm[2, 5, 1, 4, 3] + Perm[2, \ 5, 3, 1, 4] - Perm[2, 5, 3, 4, 1] - Perm[2, 5, 4, 1, 3] + Perm[2, 5, 4, 3, 1] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] - Perm[3, 2, 4, 5, 1] - Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[4, 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] - Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] - Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 5, 3, 2, 4] - Perm[1, 5, 3, 4, 2] - Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] - Perm[2, \ 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] + Perm[3, \ 1, 4, 2, 5] - Perm[3, 1, 4, 5, 2] - Perm[3, 1, 5, 2, 4] + Perm[3, 1, 5, 4, 2] + Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] - Perm[3, 2, 4, 1, 5] + Perm[3, 2, 4, 5, 1] + Perm[3, \ 2, 5, 1, 4] - Perm[3, 2, 5, 4, 1] - Perm[3, 4, 1, 2, 5] + Perm[3, 4, 1, 5, 2] + Perm[3, \ 4, 2, 1, 5] - Perm[3, 4, 2, 5, 1] - Perm[3, 4, 5, 1, 2] + Perm[3, 4, 5, 2, 1] + Perm[3, \ 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] - Perm[3, 5, 2, 1, 4] + Perm[3, 5, 2, 4, 1] + Perm[3, \ 5, 4, 1, 2] - Perm[3, 5, 4, 2, 1] + Perm[4, 1, 3, 2, 5] - Perm[4, 1, 3, 5, 2] - Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] - Perm[5, \ 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] + Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 5, 4, 3] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 5, 4, 2] + Perm[1, 5, 2, 4, 3] - Perm[1, 5, 3, 4, 2] - Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] + Perm[2, 3, 1, 4, 5] - Perm[2, 3, 5, 4, 1] - Perm[2, \ 5, 1, 4, 3] + Perm[2, 5, 3, 4, 1] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 5, 4, 2] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 5, 4, 1] + Perm[3, 5, 1, 4, 2] - Perm[3, 5, 2, 4, 1] + Perm[4, \ 1, 2, 3, 5] - Perm[4, 1, 2, 5, 3] - Perm[4, 1, 3, 2, 5] + Perm[4, 1, 3, 5, 2] + Perm[4, \ 1, 5, 2, 3] - Perm[4, 1, 5, 3, 2] - Perm[4, 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] + Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 3, 5, 1] - Perm[4, 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] + Perm[4, \ 3, 1, 2, 5] - Perm[4, 3, 1, 5, 2] - Perm[4, 3, 2, 1, 5] + Perm[4, 3, 2, 5, 1] + Perm[4, \ 3, 5, 1, 2] - Perm[4, 3, 5, 2, 1] - Perm[4, 5, 1, 2, 3] + Perm[4, 5, 1, 3, 2] + Perm[4, \ 5, 2, 1, 3] - Perm[4, 5, 2, 3, 1] - Perm[4, 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] - Perm[5, \ 1, 2, 4, 3] + Perm[5, 1, 3, 4, 2] + Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 4, 1] - Perm[5, \ 3, 1, 4, 2] + Perm[5, 3, 2, 4, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 4, 2, 5] + Perm[1, 4, 2, 3, 5] - Perm[1, 4, 3, 2, 5] - Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] + Perm[2, 3, 1, 4, 5] - Perm[2, 3, 4, 1, 5] - Perm[2, \ 4, 1, 3, 5] + Perm[2, 4, 3, 1, 5] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 4, 2, 5] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] + Perm[3, 4, 1, 2, 5] - Perm[3, 4, 2, 1, 5] - Perm[4, \ 1, 2, 3, 5] + Perm[4, 1, 3, 2, 5] + Perm[4, 2, 1, 3, 5] - Perm[4, 2, 3, 1, 5] - Perm[4, \ 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] - Perm[5, 1, 2, 3, 4] + Perm[5, 1, 2, 4, 3] + Perm[5, \ 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] - Perm[5, 1, 4, 2, 3] + Perm[5, 1, 4, 3, 2] + Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] - Perm[5, 2, 4, 3, 1] - Perm[5, 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] + Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 2, 4, 1] - Perm[5, 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1] + Perm[5, \ 4, 1, 2, 3] - Perm[5, 4, 1, 3, 2] - Perm[5, 4, 2, 1, 3] + Perm[5, 4, 2, 3, 1] + Perm[5, \ 4, 3, 1, 2] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 4, 5, 3] - Perm[1, 2, 5, 4, 3] - Perm[1, 4, 2, 3, 5] + Perm[1, 4, 2, 5, 3] - Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 5, 2, 3] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] - Perm[2, \ 1, 4, 5, 3] - Perm[2, 1, 5, 4, 3] - Perm[2, 3, 1, 4, 5] - Perm[2, 3, 4, 1, 5] + Perm[2, \ 3, 4, 5, 1] + Perm[2, 3, 5, 4, 1] + Perm[2, 5, 1, 4, 3] - Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] - Perm[2, 5, 4, 3, 1] - Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] + Perm[3, \ 2, 4, 5, 1] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] + Perm[3, 4, 2, 1, 5] - Perm[3, \ 4, 2, 5, 1] - Perm[3, 4, 5, 2, 1] - Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] + Perm[4, 1, 5, 2, 3] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] - Perm[4, \ 3, 2, 5, 1] - Perm[4, 3, 5, 2, 1] - Perm[4, 5, 1, 2, 3] - Perm[4, 5, 2, 1, 3] + Perm[4, \ 5, 2, 3, 1] + Perm[4, 5, 3, 2, 1] + Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] - Perm[5, 2, 4, 3, 1] - Perm[5, 4, 1, 2, 3] - Perm[5, 4, 2, 1, 3] + Perm[5, \ 4, 2, 3, 1] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 5, 3, 4] + Perm[1, 2, 5, 4, 3] + Perm[1, 5, 2, 3, 4] - Perm[1, 5, 2, 4, 3] - Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] - Perm[2, \ 1, 5, 3, 4] + Perm[2, 1, 5, 4, 3] - Perm[2, 3, 1, 4, 5] + Perm[2, 3, 4, 1, 5] + Perm[2, \ 3, 5, 1, 4] - Perm[2, 3, 5, 4, 1] + Perm[2, 4, 1, 3, 5] - Perm[2, 4, 3, 1, 5] - Perm[2, \ 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] - Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] + Perm[3, \ 2, 5, 1, 4] - Perm[3, 2, 5, 4, 1] + Perm[3, 5, 1, 4, 2] - Perm[3, 5, 2, 1, 4] + Perm[3, \ 5, 2, 4, 1] - Perm[3, 5, 4, 1, 2] + Perm[4, 2, 1, 3, 5] - Perm[4, 2, 3, 1, 5] - Perm[4, \ 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] - Perm[4, 5, 1, 3, 2] + Perm[4, 5, 2, 1, 3] - Perm[4, \ 5, 2, 3, 1] + Perm[4, 5, 3, 1, 2] + Perm[5, 1, 2, 3, 4] - Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 4, 2] + Perm[5, 1, 4, 3, 2] + Perm[5, 3, 1, 4, 2] - Perm[5, 3, 2, 1, 4] + Perm[5, \ 3, 2, 4, 1] - Perm[5, 3, 4, 1, 2] - Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] - Perm[5, \ 4, 2, 3, 1] + Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 3, 4, 2, 5] + Perm[1, 3, 4, 5, 2] + Perm[1, 4, 3, 2, 5] - Perm[1, 4, 3, 5, 2] - Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] + Perm[2, \ 3, 4, 1, 5] - Perm[2, 3, 4, 5, 1] - Perm[2, 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[2, \ 5, 3, 4, 1] - Perm[2, 5, 4, 3, 1] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 5, 4, 2] + Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] - Perm[3, 4, 1, 5, 2] - Perm[3, \ 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, 4, 5, 1, 2] - Perm[3, 4, 5, 2, 1] - Perm[3, \ 5, 1, 4, 2] + Perm[3, 5, 2, 4, 1] + Perm[4, 1, 2, 3, 5] - Perm[4, 1, 5, 3, 2] - Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 5, 3, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] + Perm[4, \ 3, 2, 1, 5] - Perm[4, 3, 2, 5, 1] - Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 1, 3, 2] - Perm[4, 5, 2, 3, 1] + Perm[5, 1, 3, 4, 2] - Perm[5, 1, 4, 3, 2] - Perm[5, \ 2, 3, 4, 1] + Perm[5, 2, 4, 3, 1] - Perm[5, 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1] + Perm[5, \ 4, 3, 1, 2] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 5, 4, 3] + Perm[1, \ 3, 5, 2, 4] - Perm[1, 3, 5, 4, 2] - Perm[1, 4, 3, 2, 5] + Perm[1, 4, 5, 2, 3] - Perm[1, \ 5, 3, 2, 4] + Perm[1, 5, 3, 4, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] - Perm[2, \ 3, 5, 1, 4] + Perm[2, 3, 5, 4, 1] + Perm[2, 4, 3, 1, 5] - Perm[2, 4, 5, 1, 3] + Perm[2, \ 5, 3, 1, 4] - Perm[2, 5, 3, 4, 1] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 4, 2, 5] + Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] - Perm[3, 4, 1, 2, 5] + Perm[3, 4, 2, 1, 5] - Perm[3, \ 5, 1, 2, 4] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 1, 4] - Perm[3, 5, 2, 4, 1] - Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] + Perm[4, 1, 3, 2, 5] - Perm[4, 1, 5, 2, 3] - Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 5, 1, 3] + Perm[4, 3, 5, 1, 2] - Perm[4, 3, 5, 2, 1] - Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] + Perm[5, 1, 2, 4, 3] - Perm[5, 1, 4, 2, 3] - Perm[5, \ 2, 1, 4, 3] + Perm[5, 2, 4, 1, 3] + Perm[5, 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] - Perm[5, \ 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] + Perm[5, 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1] + Perm[5, \ 4, 1, 2, 3] - Perm[5, 4, 2, 1, 3], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] - Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] + Perm[1, 4, 2, 5, 3] - Perm[1, 4, 3, 5, 2] - Perm[1, \ 5, 2, 4, 3] + Perm[1, 5, 3, 4, 2] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] - Perm[2, 4, 1, 5, 3] + Perm[2, 4, 3, 5, 1] + Perm[2, \ 5, 1, 4, 3] - Perm[2, 5, 3, 4, 1] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] - Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 4, 1, 5, 2] - Perm[3, 4, 2, 5, 1] - Perm[3, \ 5, 1, 4, 2] + Perm[3, 5, 2, 4, 1] + Perm[4, 1, 2, 3, 5] - Perm[4, 1, 3, 2, 5] - Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 3, 1, 5] + Perm[4, 3, 1, 2, 5] - Perm[4, 3, 2, 1, 5] + Perm[4, \ 5, 1, 2, 3] - Perm[4, 5, 1, 3, 2] - Perm[4, 5, 2, 1, 3] + Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] - Perm[5, 1, 2, 3, 4] + Perm[5, 1, 3, 2, 4] + Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 3, 1, 4] - Perm[5, 3, 1, 2, 4] + Perm[5, 3, 2, 1, 4] - Perm[5, \ 4, 1, 2, 3] + Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] - Perm[5, 4, 2, 3, 1] - Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 3, 5, 4] + Perm[1, \ 3, 2, 4, 5] - Perm[1, 3, 2, 5, 4] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] - Perm[2, 3, 4, 1, 5] + Perm[2, 3, 4, 5, 1] + Perm[2, \ 3, 5, 1, 4] - Perm[2, 3, 5, 4, 1] - Perm[2, 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[2, \ 5, 3, 1, 4] - Perm[2, 5, 3, 4, 1] + Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] + Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] - Perm[3, 2, 4, 1, 5] + Perm[3, 2, 4, 5, 1] + Perm[3, \ 2, 5, 1, 4] - Perm[3, 2, 5, 4, 1] - Perm[3, 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, \ 5, 2, 1, 4] - Perm[3, 5, 2, 4, 1] - Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] - Perm[4, \ 3, 2, 1, 5] + Perm[4, 3, 2, 5, 1] + Perm[5, 2, 3, 1, 4] - Perm[5, 2, 3, 4, 1] + Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 2, 4, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 5, 4, 3] + Perm[1, \ 4, 3, 2, 5] - Perm[1, 4, 5, 2, 3] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 5, 4, 3] - Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 5, 4, 1] - Perm[2, 4, 1, 3, 5] + Perm[2, 4, 1, 5, 3] + Perm[2, \ 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] - Perm[2, 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] + Perm[2, \ 5, 1, 4, 3] - Perm[2, 5, 3, 4, 1] - Perm[3, 2, 1, 4, 5] + Perm[3, 2, 5, 4, 1] - Perm[3, \ 4, 1, 2, 5] + Perm[3, 4, 5, 2, 1] + Perm[4, 1, 3, 2, 5] - Perm[4, 1, 5, 2, 3] - Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] + Perm[4, 2, 3, 1, 5] - Perm[4, 2, 3, 5, 1] - Perm[4, \ 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 1, 2, 3] - Perm[4, 5, 3, 2, 1] + Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 4, 1] + Perm[5, \ 4, 1, 2, 3] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] + Perm[1, \ 5, 3, 4, 2] - Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] - Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 4, 1, 5] + Perm[2, 4, 1, 3, 5] - Perm[2, 4, 3, 1, 5] + Perm[2, \ 5, 1, 3, 4] - Perm[2, 5, 1, 4, 3] - Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] - Perm[2, 5, 4, 3, 1] - Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] - Perm[3, \ 5, 1, 4, 2] + Perm[3, 5, 4, 1, 2] + Perm[4, 2, 1, 3, 5] - Perm[4, 2, 3, 1, 5] + Perm[4, \ 5, 1, 3, 2] - Perm[4, 5, 3, 1, 2] + Perm[5, 1, 3, 4, 2] - Perm[5, 1, 4, 3, 2] + Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] - Perm[5, 2, 4, 3, 1] - Perm[5, 3, 1, 4, 2] + Perm[5, 3, 4, 1, 2] + Perm[5, \ 4, 1, 3, 2] - Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 5, 3, 4, 2] - Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] + Perm[2, \ 5, 3, 4, 1] + Perm[2, 5, 4, 3, 1] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 4, 2, 5] + Perm[3, \ 1, 4, 5, 2] + Perm[3, 1, 5, 4, 2] + Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] - Perm[3, \ 2, 4, 5, 1] - Perm[3, 2, 5, 4, 1] - Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 4, 1] - Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] - Perm[4, 1, 2, 3, 5] - Perm[4, 1, 3, 2, 5] + Perm[4, \ 1, 3, 5, 2] + Perm[4, 1, 5, 3, 2] + Perm[4, 2, 1, 3, 5] + Perm[4, 2, 3, 1, 5] - Perm[4, \ 2, 3, 5, 1] - Perm[4, 2, 5, 3, 1] - Perm[4, 5, 1, 3, 2] + Perm[4, 5, 2, 3, 1] - Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] + Perm[5, 1, 3, 4, 2] + Perm[5, 1, 4, 3, 2] - Perm[5, \ 2, 3, 4, 1] - Perm[5, 2, 4, 3, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 5, 4, 3] - Perm[1, \ 4, 3, 2, 5] - Perm[1, 4, 5, 2, 3] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 5, 4, 3] + Perm[2, \ 4, 3, 1, 5] + Perm[2, 4, 5, 1, 3] - Perm[3, 1, 2, 4, 5] + Perm[3, 1, 4, 2, 5] + Perm[3, \ 1, 5, 2, 4] - Perm[3, 1, 5, 4, 2] + Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] - Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] - Perm[3, 4, 1, 2, 5] + Perm[3, 4, 2, 1, 5] + Perm[3, \ 4, 5, 1, 2] - Perm[3, 4, 5, 2, 1] + Perm[4, 1, 3, 2, 5] + Perm[4, 1, 5, 2, 3] - Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 5, 1, 3] - Perm[5, 1, 2, 4, 3] + Perm[5, 1, 3, 2, 4] - Perm[5, \ 1, 3, 4, 2] + Perm[5, 1, 4, 2, 3] + Perm[5, 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] + Perm[5, \ 2, 3, 4, 1] - Perm[5, 2, 4, 1, 3] - Perm[5, 4, 1, 2, 3] + Perm[5, 4, 2, 1, 3] + Perm[5, \ 4, 3, 1, 2] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] - Perm[1, \ 3, 2, 4, 5] - Perm[1, 3, 2, 5, 4] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] - Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] + Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] - Perm[4, 1, 3, 5, 2] - Perm[4, 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] + Perm[4, \ 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] - Perm[4, \ 3, 2, 1, 5] - Perm[4, 3, 2, 5, 1] + Perm[5, 1, 2, 3, 4] + Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] - Perm[5, 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] + Perm[5, \ 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] - Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 2, 4, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] - Perm[1, 3, 5, 2, 4] - Perm[1, 3, 5, 4, 2] - Perm[1, \ 5, 3, 2, 4] - Perm[1, 5, 3, 4, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] - Perm[2, 3, 4, 1, 5] - Perm[2, 3, 4, 5, 1] - Perm[2, \ 4, 3, 1, 5] - Perm[2, 4, 3, 5, 1] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] - Perm[3, \ 1, 5, 2, 4] - Perm[3, 1, 5, 4, 2] + Perm[3, 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] - Perm[3, \ 2, 4, 1, 5] - Perm[3, 2, 4, 5, 1] - Perm[3, 4, 2, 1, 5] - Perm[3, 4, 2, 5, 1] + Perm[3, \ 4, 5, 1, 2] + Perm[3, 4, 5, 2, 1] - Perm[3, 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] + Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] - Perm[4, 2, 3, 1, 5] - Perm[4, 2, 3, 5, 1] - Perm[4, \ 3, 2, 1, 5] - Perm[4, 3, 2, 5, 1] + Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] - Perm[5, 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] - Perm[5, \ 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] + Perm[5, 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1] + Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 5, 4, 3] - Perm[1, \ 4, 2, 5, 3] + Perm[1, 4, 3, 2, 5] - Perm[1, 4, 3, 5, 2] + Perm[1, 4, 5, 2, 3] - Perm[1, \ 5, 2, 4, 3] - Perm[1, 5, 3, 4, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] - Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 5, 4, 1] - Perm[2, 4, 1, 3, 5] + Perm[2, 4, 3, 1, 5] + Perm[2, \ 4, 5, 1, 3] - Perm[2, 4, 5, 3, 1] - Perm[3, 2, 1, 4, 5] - Perm[3, 2, 5, 4, 1] - Perm[3, \ 4, 1, 2, 5] + Perm[3, 4, 1, 5, 2] + Perm[3, 4, 2, 5, 1] - Perm[3, 4, 5, 2, 1] + Perm[3, \ 5, 1, 4, 2] + Perm[3, 5, 2, 4, 1] - Perm[4, 1, 2, 5, 3] + Perm[4, 1, 3, 2, 5] - Perm[4, \ 1, 3, 5, 2] + Perm[4, 1, 5, 2, 3] - Perm[4, 2, 1, 3, 5] + Perm[4, 2, 3, 1, 5] + Perm[4, \ 2, 5, 1, 3] - Perm[4, 2, 5, 3, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] + Perm[4, \ 3, 2, 5, 1] - Perm[4, 3, 5, 2, 1] + Perm[4, 5, 1, 3, 2] - Perm[4, 5, 2, 1, 3] + Perm[4, \ 5, 2, 3, 1] - Perm[4, 5, 3, 1, 2] - Perm[5, 1, 2, 4, 3] - Perm[5, 1, 3, 4, 2] + Perm[5, \ 3, 1, 4, 2] + Perm[5, 3, 2, 4, 1] + Perm[5, 4, 1, 3, 2] - Perm[5, 4, 2, 1, 3] + Perm[5, \ 4, 2, 3, 1] - Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 4, 2, 3, 5] - Perm[1, 4, 3, 2, 5] - Perm[1, 5, 2, 3, 4] - Perm[1, 5, 3, 2, 4] + Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] - Perm[2, \ 3, 1, 4, 5] - Perm[2, 3, 4, 1, 5] - Perm[2, 5, 1, 4, 3] + Perm[2, 5, 3, 4, 1] - Perm[2, \ 5, 4, 1, 3] + Perm[2, 5, 4, 3, 1] - Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] + Perm[3, \ 4, 1, 2, 5] + Perm[3, 4, 2, 1, 5] + Perm[3, 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] + Perm[3, \ 5, 2, 1, 4] - Perm[3, 5, 4, 1, 2] - Perm[4, 1, 2, 3, 5] - Perm[4, 1, 3, 2, 5] + Perm[4, \ 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] + Perm[4, 5, 1, 2, 3] + Perm[4, 5, 2, 1, 3] - Perm[4, \ 5, 2, 3, 1] - Perm[4, 5, 3, 2, 1] - Perm[5, 1, 2, 3, 4] - Perm[5, 1, 3, 2, 4] + Perm[5, \ 1, 3, 4, 2] + Perm[5, 1, 4, 3, 2] - Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 4, 1] - Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1] + Perm[5, 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] + Perm[5, \ 3, 2, 1, 4] - Perm[5, 3, 4, 1, 2] + Perm[5, 4, 1, 2, 3] + Perm[5, 4, 2, 1, 3] - Perm[5, \ 4, 2, 3, 1] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 4, 5, 3] - Perm[1, 2, 5, 4, 3] - Perm[1, 3, 4, 5, 2] - Perm[1, 3, 5, 4, 2] + Perm[1, \ 5, 3, 4, 2] + Perm[1, 5, 4, 3, 2] - Perm[2, 1, 3, 4, 5] - Perm[2, 1, 4, 3, 5] + Perm[2, \ 1, 4, 5, 3] + Perm[2, 1, 5, 4, 3] + Perm[2, 3, 4, 5, 1] + Perm[2, 3, 5, 4, 1] - Perm[2, \ 5, 3, 4, 1] - Perm[2, 5, 4, 3, 1] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 4, 2, 5] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] + Perm[3, 5, 1, 4, 2] - Perm[3, 5, 2, 4, 1] + Perm[3, \ 5, 4, 1, 2] - Perm[3, 5, 4, 2, 1] - Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] + Perm[4, 1, 5, 2, 3] + Perm[4, 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] + Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 5, 1, 3] - Perm[4, 3, 1, 5, 2] + Perm[4, 3, 2, 5, 1] - Perm[4, \ 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, 5, 1, 3, 2] - Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] - Perm[4, 5, 3, 2, 1] + Perm[5, 1, 2, 4, 3] + Perm[5, 1, 4, 2, 3] - Perm[5, \ 2, 1, 4, 3] - Perm[5, 2, 4, 1, 3] - Perm[5, 3, 1, 4, 2] + Perm[5, 3, 2, 4, 1] - Perm[5, \ 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1], Perm[1, 2, 3, 4, 5] - Perm[1, 2, 4, 3, 5] - Perm[1, \ 2, 5, 3, 4] + Perm[1, 2, 5, 4, 3] - Perm[1, 3, 4, 2, 5] - Perm[1, 3, 5, 2, 4] + Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 5, 2, 3] - Perm[2, 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] + Perm[2, \ 1, 5, 3, 4] - Perm[2, 1, 5, 4, 3] + Perm[2, 3, 4, 1, 5] + Perm[2, 3, 5, 1, 4] - Perm[2, \ 4, 3, 1, 5] - Perm[2, 4, 5, 1, 3] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 5, 4, 2] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] - Perm[3, 4, 2, 1, 5] - Perm[3, \ 4, 5, 1, 2] + Perm[3, 4, 5, 2, 1] + Perm[4, 1, 2, 3, 5] + Perm[4, 1, 5, 3, 2] - Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 5, 3, 1] - Perm[4, 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] + Perm[4, \ 3, 5, 1, 2] - Perm[4, 3, 5, 2, 1] + Perm[5, 1, 2, 3, 4] - Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 4, 2] + Perm[5, 1, 4, 3, 2] - Perm[5, 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, \ 2, 3, 4, 1] - Perm[5, 2, 4, 3, 1] - Perm[5, 3, 1, 2, 4] + Perm[5, 3, 2, 1, 4] + Perm[5, \ 3, 4, 1, 2] - Perm[5, 3, 4, 2, 1] + Perm[5, 4, 1, 2, 3] - Perm[5, 4, 2, 1, 3] - Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 4, 3, 5] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 4, 2, 5] + Perm[1, 4, 2, 3, 5] + Perm[1, 4, 3, 2, 5] + Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 4, 3, 5] + Perm[2, 3, 1, 4, 5] + Perm[2, 3, 4, 1, 5] - Perm[2, \ 3, 4, 5, 1] - Perm[2, 3, 5, 4, 1] + Perm[2, 4, 1, 3, 5] + Perm[2, 4, 3, 1, 5] - Perm[2, \ 4, 3, 5, 1] - Perm[2, 4, 5, 3, 1] - Perm[2, 5, 3, 4, 1] - Perm[2, 5, 4, 3, 1] + Perm[3, \ 1, 2, 4, 5] + Perm[3, 1, 4, 2, 5] + Perm[3, 2, 1, 4, 5] + Perm[3, 2, 4, 1, 5] - Perm[3, \ 2, 4, 5, 1] - Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] + Perm[3, 4, 2, 1, 5] - Perm[3, \ 4, 2, 5, 1] - Perm[3, 4, 5, 2, 1] - Perm[3, 5, 2, 4, 1] - Perm[3, 5, 4, 2, 1] + Perm[4, \ 1, 2, 3, 5] + Perm[4, 1, 3, 2, 5] + Perm[4, 2, 1, 3, 5] + Perm[4, 2, 3, 1, 5] - Perm[4, \ 2, 3, 5, 1] - Perm[4, 2, 5, 3, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 2, 1, 5] - Perm[4, \ 3, 2, 5, 1] - Perm[4, 3, 5, 2, 1] - Perm[4, 5, 2, 3, 1] - Perm[4, 5, 3, 2, 1] - Perm[5, \ 2, 3, 4, 1] - Perm[5, 2, 4, 3, 1] - Perm[5, 3, 2, 4, 1] - Perm[5, 3, 4, 2, 1] - Perm[5, \ 4, 2, 3, 1] - Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 5, 4, 3] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 5, 4, 2] + Perm[1, 5, 2, 4, 3] + Perm[1, 5, 3, 4, 2] + Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 5, 4, 3] + Perm[2, 3, 1, 4, 5] - Perm[2, 3, 4, 1, 5] - Perm[2, \ 3, 5, 1, 4] + Perm[2, 3, 5, 4, 1] - Perm[2, 4, 3, 1, 5] - Perm[2, 4, 5, 1, 3] + Perm[2, \ 5, 1, 4, 3] - Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] - Perm[2, 5, 4, 1, 3] + Perm[3, \ 1, 2, 4, 5] + Perm[3, 1, 5, 4, 2] + Perm[3, 2, 1, 4, 5] - Perm[3, 2, 4, 1, 5] - Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] - Perm[3, 4, 2, 1, 5] - Perm[3, 4, 5, 1, 2] + Perm[3, \ 5, 1, 4, 2] - Perm[3, 5, 2, 1, 4] + Perm[3, 5, 2, 4, 1] - Perm[3, 5, 4, 1, 2] - Perm[4, \ 2, 3, 1, 5] - Perm[4, 2, 5, 1, 3] - Perm[4, 3, 2, 1, 5] - Perm[4, 3, 5, 1, 2] - Perm[4, \ 5, 2, 1, 3] - Perm[4, 5, 3, 1, 2] + Perm[5, 1, 2, 4, 3] + Perm[5, 1, 3, 4, 2] + Perm[5, \ 2, 1, 4, 3] - Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] - Perm[5, 2, 4, 1, 3] + Perm[5, \ 3, 1, 4, 2] - Perm[5, 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] - Perm[5, 3, 4, 1, 2] - Perm[5, \ 4, 2, 1, 3] - Perm[5, 4, 3, 1, 2], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 5, 3, 2, 4] + Perm[1, 5, 3, 4, 2] + Perm[2, \ 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] - Perm[2, 3, 1, 4, 5] - Perm[2, 3, 1, 5, 4] - Perm[2, \ 4, 1, 3, 5] - Perm[2, 4, 1, 5, 3] + Perm[2, 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] - Perm[2, \ 5, 1, 3, 4] - Perm[2, 5, 1, 4, 3] + Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] - Perm[3, \ 2, 1, 4, 5] - Perm[3, 2, 1, 5, 4] - Perm[3, 4, 1, 2, 5] - Perm[3, 4, 1, 5, 2] - Perm[3, \ 5, 1, 2, 4] - Perm[3, 5, 1, 4, 2] + Perm[4, 1, 3, 2, 5] + Perm[4, 1, 3, 5, 2] - Perm[4, \ 2, 1, 3, 5] - Perm[4, 2, 1, 5, 3] + Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] - Perm[4, \ 3, 1, 2, 5] - Perm[4, 3, 1, 5, 2] - Perm[4, 5, 1, 2, 3] - Perm[4, 5, 1, 3, 2] + Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] + Perm[5, 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] - Perm[5, \ 2, 1, 3, 4] - Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] - Perm[5, \ 3, 1, 2, 4] - Perm[5, 3, 1, 4, 2] - Perm[5, 4, 1, 2, 3] - Perm[5, 4, 1, 3, 2] + Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] + Perm[1, 2, 5, 4, 3] - Perm[2, \ 1, 3, 4, 5] - Perm[2, 1, 3, 5, 4] - Perm[2, 1, 4, 3, 5] - Perm[2, 1, 4, 5, 3] - Perm[2, \ 1, 5, 3, 4] - Perm[2, 1, 5, 4, 3] - Perm[3, 1, 2, 4, 5] - Perm[3, 1, 2, 5, 4] - Perm[3, \ 1, 4, 2, 5] - Perm[3, 1, 4, 5, 2] - Perm[3, 1, 5, 2, 4] - Perm[3, 1, 5, 4, 2] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] + Perm[3, 2, 4, 5, 1] + Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] - Perm[4, 1, 2, 3, 5] - Perm[4, 1, 2, 5, 3] - Perm[4, \ 1, 3, 2, 5] - Perm[4, 1, 3, 5, 2] - Perm[4, 1, 5, 2, 3] - Perm[4, 1, 5, 3, 2] + Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] + Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, \ 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] - Perm[5, 1, 2, 3, 4] - Perm[5, 1, 2, 4, 3] - Perm[5, \ 1, 3, 2, 4] - Perm[5, 1, 3, 4, 2] - Perm[5, 1, 4, 2, 3] - Perm[5, 1, 4, 3, 2] + Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1], Perm[1, 2, 3, 4, 5] + Perm[1, 2, 3, 5, 4] + Perm[1, \ 2, 4, 3, 5] + Perm[1, 2, 4, 5, 3] + Perm[1, 2, 5, 3, 4] + Perm[1, 2, 5, 4, 3] + Perm[1, \ 3, 2, 4, 5] + Perm[1, 3, 2, 5, 4] + Perm[1, 3, 4, 2, 5] + Perm[1, 3, 4, 5, 2] + Perm[1, \ 3, 5, 2, 4] + Perm[1, 3, 5, 4, 2] + Perm[1, 4, 2, 3, 5] + Perm[1, 4, 2, 5, 3] + Perm[1, \ 4, 3, 2, 5] + Perm[1, 4, 3, 5, 2] + Perm[1, 4, 5, 2, 3] + Perm[1, 4, 5, 3, 2] + Perm[1, \ 5, 2, 3, 4] + Perm[1, 5, 2, 4, 3] + Perm[1, 5, 3, 2, 4] + Perm[1, 5, 3, 4, 2] + Perm[1, \ 5, 4, 2, 3] + Perm[1, 5, 4, 3, 2] + Perm[2, 1, 3, 4, 5] + Perm[2, 1, 3, 5, 4] + Perm[2, \ 1, 4, 3, 5] + Perm[2, 1, 4, 5, 3] + Perm[2, 1, 5, 3, 4] + Perm[2, 1, 5, 4, 3] + Perm[2, \ 3, 1, 4, 5] + Perm[2, 3, 1, 5, 4] + Perm[2, 3, 4, 1, 5] + Perm[2, 3, 4, 5, 1] + Perm[2, \ 3, 5, 1, 4] + Perm[2, 3, 5, 4, 1] + Perm[2, 4, 1, 3, 5] + Perm[2, 4, 1, 5, 3] + Perm[2, \ 4, 3, 1, 5] + Perm[2, 4, 3, 5, 1] + Perm[2, 4, 5, 1, 3] + Perm[2, 4, 5, 3, 1] + Perm[2, \ 5, 1, 3, 4] + Perm[2, 5, 1, 4, 3] + Perm[2, 5, 3, 1, 4] + Perm[2, 5, 3, 4, 1] + Perm[2, \ 5, 4, 1, 3] + Perm[2, 5, 4, 3, 1] + Perm[3, 1, 2, 4, 5] + Perm[3, 1, 2, 5, 4] + Perm[3, \ 1, 4, 2, 5] + Perm[3, 1, 4, 5, 2] + Perm[3, 1, 5, 2, 4] + Perm[3, 1, 5, 4, 2] + Perm[3, \ 2, 1, 4, 5] + Perm[3, 2, 1, 5, 4] + Perm[3, 2, 4, 1, 5] + Perm[3, 2, 4, 5, 1] + Perm[3, \ 2, 5, 1, 4] + Perm[3, 2, 5, 4, 1] + Perm[3, 4, 1, 2, 5] + Perm[3, 4, 1, 5, 2] + Perm[3, \ 4, 2, 1, 5] + Perm[3, 4, 2, 5, 1] + Perm[3, 4, 5, 1, 2] + Perm[3, 4, 5, 2, 1] + Perm[3, \ 5, 1, 2, 4] + Perm[3, 5, 1, 4, 2] + Perm[3, 5, 2, 1, 4] + Perm[3, 5, 2, 4, 1] + Perm[3, \ 5, 4, 1, 2] + Perm[3, 5, 4, 2, 1] + Perm[4, 1, 2, 3, 5] + Perm[4, 1, 2, 5, 3] + Perm[4, \ 1, 3, 2, 5] + Perm[4, 1, 3, 5, 2] + Perm[4, 1, 5, 2, 3] + Perm[4, 1, 5, 3, 2] + Perm[4, \ 2, 1, 3, 5] + Perm[4, 2, 1, 5, 3] + Perm[4, 2, 3, 1, 5] + Perm[4, 2, 3, 5, 1] + Perm[4, \ 2, 5, 1, 3] + Perm[4, 2, 5, 3, 1] + Perm[4, 3, 1, 2, 5] + Perm[4, 3, 1, 5, 2] + Perm[4, \ 3, 2, 1, 5] + Perm[4, 3, 2, 5, 1] + Perm[4, 3, 5, 1, 2] + Perm[4, 3, 5, 2, 1] + Perm[4, \ 5, 1, 2, 3] + Perm[4, 5, 1, 3, 2] + Perm[4, 5, 2, 1, 3] + Perm[4, 5, 2, 3, 1] + Perm[4, \ 5, 3, 1, 2] + Perm[4, 5, 3, 2, 1] + Perm[5, 1, 2, 3, 4] + Perm[5, 1, 2, 4, 3] + Perm[5, \ 1, 3, 2, 4] + Perm[5, 1, 3, 4, 2] + Perm[5, 1, 4, 2, 3] + Perm[5, 1, 4, 3, 2] + Perm[5, \ 2, 1, 3, 4] + Perm[5, 2, 1, 4, 3] + Perm[5, 2, 3, 1, 4] + Perm[5, 2, 3, 4, 1] + Perm[5, \ 2, 4, 1, 3] + Perm[5, 2, 4, 3, 1] + Perm[5, 3, 1, 2, 4] + Perm[5, 3, 1, 4, 2] + Perm[5, \ 3, 2, 1, 4] + Perm[5, 3, 2, 4, 1] + Perm[5, 3, 4, 1, 2] + Perm[5, 3, 4, 2, 1] + Perm[5, \ 4, 1, 2, 3] + Perm[5, 4, 1, 3, 2] + Perm[5, 4, 2, 1, 3] + Perm[5, 4, 2, 3, 1] + Perm[5, \ 4, 3, 1, 2] + Perm[5, 4, 3, 2, 1]]\ \>", "\<\ {( 1 2 3 4 5 ) - ( 1 2 3 5 4 ) - ( 1 2 4 3 5 ) + ( 1 2 4 5 3 ) + ( 1 2 5 3 4 \ ) - ( 1 2 5 4 3 ) - ( 1 3 2 4 5 ) + ( 1 3 2 5 4 ) + ( 1 3 4 2 5 ) - ( 1 3 4 5 \ 2 ) - ( 1 3 5 2 4 ) + ( 1 3 5 4 2 ) + ( 1 4 2 3 5 ) - ( 1 4 2 5 3 ) - ( 1 4 3 2 \ 5 ) + ( 1 4 3 5 2 ) + ( 1 4 5 2 3 ) - ( 1 4 5 3 2 ) - ( 1 5 2 3 4 ) + ( 1 5 2 4 \ 3 ) + ( 1 5 3 2 4 ) - ( 1 5 3 4 2 ) - ( 1 5 4 2 3 ) + ( 1 5 4 3 2 ) - ( 2 1 3 4 \ 5 ) + ( 2 1 3 5 4 ) + ( 2 1 4 3 5 ) - ( 2 1 4 5 3 ) - ( 2 1 5 3 4 ) + ( 2 1 5 4 \ 3 ) + ( 2 3 1 4 5 ) - ( 2 3 1 5 4 ) - ( 2 3 4 1 5 ) + ( 2 3 4 5 1 ) + ( 2 3 5 1 \ 4 ) - ( 2 3 5 4 1 ) - ( 2 4 1 3 5 ) + ( 2 4 1 5 3 ) + ( 2 4 3 1 5 ) - ( 2 4 3 5 \ 1 ) - ( 2 4 5 1 3 ) + ( 2 4 5 3 1 ) + ( 2 5 1 3 4 ) - ( 2 5 1 4 3 ) - ( 2 5 3 1 \ 4 ) + ( 2 5 3 4 1 ) + ( 2 5 4 1 3 ) - ( 2 5 4 3 1 ) + ( 3 1 2 4 5 ) - ( 3 1 2 5 \ 4 ) - ( 3 1 4 2 5 ) + ( 3 1 4 5 2 ) + ( 3 1 5 2 4 ) - ( 3 1 5 4 2 ) - ( 3 2 1 4 \ 5 ) + ( 3 2 1 5 4 ) + ( 3 2 4 1 5 ) - ( 3 2 4 5 1 ) - ( 3 2 5 1 4 ) + ( 3 2 5 4 \ 1 ) + ( 3 4 1 2 5 ) - ( 3 4 1 5 2 ) - ( 3 4 2 1 5 ) + ( 3 4 2 5 1 ) + ( 3 4 5 1 \ 2 ) - ( 3 4 5 2 1 ) - ( 3 5 1 2 4 ) + ( 3 5 1 4 2 ) + ( 3 5 2 1 4 ) - ( 3 5 2 4 \ 1 ) - ( 3 5 4 1 2 ) + ( 3 5 4 2 1 ) - ( 4 1 2 3 5 ) + ( 4 1 2 5 3 ) + ( 4 1 3 2 \ 5 ) - ( 4 1 3 5 2 ) - ( 4 1 5 2 3 ) + ( 4 1 5 3 2 ) + ( 4 2 1 3 5 ) - ( 4 2 1 5 \ 3 ) - ( 4 2 3 1 5 ) + ( 4 2 3 5 1 ) + ( 4 2 5 1 3 ) - ( 4 2 5 3 1 ) - ( 4 3 1 2 \ 5 ) + ( 4 3 1 5 2 ) + ( 4 3 2 1 5 ) - ( 4 3 2 5 1 ) - ( 4 3 5 1 2 ) + ( 4 3 5 2 \ 1 ) + ( 4 5 1 2 3 ) - ( 4 5 1 3 2 ) - ( 4 5 2 1 3 ) + ( 4 5 2 3 1 ) + ( 4 5 3 1 \ 2 ) - ( 4 5 3 2 1 ) + ( 5 1 2 3 4 ) - ( 5 1 2 4 3 ) - ( 5 1 3 2 4 ) + ( 5 1 3 4 \ 2 ) + ( 5 1 4 2 3 ) - ( 5 1 4 3 2 ) - ( 5 2 1 3 4 ) + ( 5 2 1 4 3 ) + ( 5 2 3 1 \ 4 ) - ( 5 2 3 4 1 ) - ( 5 2 4 1 3 ) + ( 5 2 4 3 1 ) + ( 5 3 1 2 4 ) - ( 5 3 1 4 \ 2 ) - ( 5 3 2 1 4 ) + ( 5 3 2 4 1 ) + ( 5 3 4 1 2 ) - ( 5 3 4 2 1 ) - ( 5 4 1 2 \ 3 ) + ( 5 4 1 3 2 ) + ( 5 4 2 1 3 ) - ( 5 4 2 3 1 ) - ( 5 4 3 1 2 ) + ( 5 4 3 2 \ 1 ), ( 1 2 3 4 5 ) - ( 1 2 3 5 4 ) - ( 1 2 4 3 5 ) + ( 1 2 4 5 3 ) + ( 1 2 5 3 4 \ ) - 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( 2 4 3 1 5 ) - ( 2 4 5 1 3 ) + ( 2 5 1 4 \ 3 ) - ( 2 5 3 1 4 ) + ( 2 5 3 4 1 ) - ( 2 5 4 1 3 ) + ( 3 1 2 4 5 ) + ( 3 1 5 4 \ 2 ) + ( 3 2 1 4 5 ) - ( 3 2 4 1 5 ) - ( 3 2 5 1 4 ) + ( 3 2 5 4 1 ) - ( 3 4 2 1 \ 5 ) - ( 3 4 5 1 2 ) + ( 3 5 1 4 2 ) - ( 3 5 2 1 4 ) + ( 3 5 2 4 1 ) - ( 3 5 4 1 \ 2 ) - ( 4 2 3 1 5 ) - ( 4 2 5 1 3 ) - ( 4 3 2 1 5 ) - ( 4 3 5 1 2 ) - ( 4 5 2 1 \ 3 ) - ( 4 5 3 1 2 ) + ( 5 1 2 4 3 ) + ( 5 1 3 4 2 ) + ( 5 2 1 4 3 ) - ( 5 2 3 1 \ 4 ) + ( 5 2 3 4 1 ) - ( 5 2 4 1 3 ) + ( 5 3 1 4 2 ) - ( 5 3 2 1 4 ) + ( 5 3 2 4 \ 1 ) - ( 5 3 4 1 2 ) - ( 5 4 2 1 3 ) - ( 5 4 3 1 2 ), ( 1 2 3 4 5 ) + ( 1 2 3 5 4 ) + ( 1 4 3 2 5 ) + ( 1 4 3 5 2 ) + ( 1 5 3 2 4 \ ) + ( 1 5 3 4 2 ) + ( 2 1 3 4 5 ) + ( 2 1 3 5 4 ) - ( 2 3 1 4 5 ) - ( 2 3 1 5 \ 4 ) - ( 2 4 1 3 5 ) - ( 2 4 1 5 3 ) + ( 2 4 3 1 5 ) + ( 2 4 3 5 1 ) - ( 2 5 1 3 \ 4 ) - ( 2 5 1 4 3 ) + ( 2 5 3 1 4 ) + ( 2 5 3 4 1 ) - ( 3 2 1 4 5 ) - ( 3 2 1 5 \ 4 ) - ( 3 4 1 2 5 ) - ( 3 4 1 5 2 ) - ( 3 5 1 2 4 ) - ( 3 5 1 4 2 ) + ( 4 1 3 2 \ 5 ) + ( 4 1 3 5 2 ) - ( 4 2 1 3 5 ) - ( 4 2 1 5 3 ) + ( 4 2 3 1 5 ) + ( 4 2 3 5 \ 1 ) - ( 4 3 1 2 5 ) - ( 4 3 1 5 2 ) - ( 4 5 1 2 3 ) - ( 4 5 1 3 2 ) + ( 4 5 3 1 \ 2 ) + ( 4 5 3 2 1 ) + ( 5 1 3 2 4 ) + ( 5 1 3 4 2 ) - ( 5 2 1 3 4 ) - ( 5 2 1 4 \ 3 ) + ( 5 2 3 1 4 ) + ( 5 2 3 4 1 ) - ( 5 3 1 2 4 ) - ( 5 3 1 4 2 ) - ( 5 4 1 2 \ 3 ) - ( 5 4 1 3 2 ) + ( 5 4 3 1 2 ) + ( 5 4 3 2 1 ), ( 1 2 3 4 5 ) + ( 1 2 3 5 4 ) + ( 1 2 4 3 5 ) + ( 1 2 4 5 3 ) + ( 1 2 5 3 4 \ ) + ( 1 2 5 4 3 ) - ( 2 1 3 4 5 ) - ( 2 1 3 5 4 ) - ( 2 1 4 3 5 ) - ( 2 1 4 5 \ 3 ) - ( 2 1 5 3 4 ) - ( 2 1 5 4 3 ) - ( 3 1 2 4 5 ) - ( 3 1 2 5 4 ) - ( 3 1 4 2 \ 5 ) - ( 3 1 4 5 2 ) - ( 3 1 5 2 4 ) - ( 3 1 5 4 2 ) + ( 3 2 1 4 5 ) + ( 3 2 1 5 \ 4 ) + ( 3 2 4 1 5 ) + ( 3 2 4 5 1 ) + ( 3 2 5 1 4 ) + ( 3 2 5 4 1 ) - ( 4 1 2 3 \ 5 ) - ( 4 1 2 5 3 ) - ( 4 1 3 2 5 ) - ( 4 1 3 5 2 ) - ( 4 1 5 2 3 ) - ( 4 1 5 3 \ 2 ) + ( 4 2 1 3 5 ) + ( 4 2 1 5 3 ) + ( 4 2 3 1 5 ) + ( 4 2 3 5 1 ) + ( 4 2 5 1 \ 3 ) + ( 4 2 5 3 1 ) - ( 5 1 2 3 4 ) - ( 5 1 2 4 3 ) - ( 5 1 3 2 4 ) - ( 5 1 3 4 \ 2 ) - ( 5 1 4 2 3 ) - ( 5 1 4 3 2 ) + ( 5 2 1 3 4 ) + ( 5 2 1 4 3 ) + ( 5 2 3 1 \ 4 ) + ( 5 2 3 4 1 ) + ( 5 2 4 1 3 ) + ( 5 2 4 3 1 ), ( 1 2 3 4 5 ) + ( 1 2 3 5 4 ) + ( 1 2 4 3 5 ) + ( 1 2 4 5 3 ) + ( 1 2 5 3 4 \ ) + ( 1 2 5 4 3 ) + ( 1 3 2 4 5 ) + ( 1 3 2 5 4 ) + ( 1 3 4 2 5 ) + ( 1 3 4 5 \ 2 ) + ( 1 3 5 2 4 ) + ( 1 3 5 4 2 ) + ( 1 4 2 3 5 ) + ( 1 4 2 5 3 ) + ( 1 4 3 2 \ 5 ) + ( 1 4 3 5 2 ) + ( 1 4 5 2 3 ) + ( 1 4 5 3 2 ) + ( 1 5 2 3 4 ) + ( 1 5 2 4 \ 3 ) + ( 1 5 3 2 4 ) + ( 1 5 3 4 2 ) + ( 1 5 4 2 3 ) + ( 1 5 4 3 2 ) + ( 2 1 3 4 \ 5 ) + ( 2 1 3 5 4 ) + ( 2 1 4 3 5 ) + ( 2 1 4 5 3 ) + ( 2 1 5 3 4 ) + ( 2 1 5 4 \ 3 ) + ( 2 3 1 4 5 ) + ( 2 3 1 5 4 ) + ( 2 3 4 1 5 ) + ( 2 3 4 5 1 ) + ( 2 3 5 1 \ 4 ) + ( 2 3 5 4 1 ) + ( 2 4 1 3 5 ) + ( 2 4 1 5 3 ) + ( 2 4 3 1 5 ) + ( 2 4 3 5 \ 1 ) + ( 2 4 5 1 3 ) + ( 2 4 5 3 1 ) + ( 2 5 1 3 4 ) + ( 2 5 1 4 3 ) + ( 2 5 3 1 \ 4 ) + ( 2 5 3 4 1 ) + ( 2 5 4 1 3 ) + ( 2 5 4 3 1 ) + ( 3 1 2 4 5 ) + ( 3 1 2 5 \ 4 ) + ( 3 1 4 2 5 ) + ( 3 1 4 5 2 ) + ( 3 1 5 2 4 ) + ( 3 1 5 4 2 ) + ( 3 2 1 4 \ 5 ) + ( 3 2 1 5 4 ) + ( 3 2 4 1 5 ) + ( 3 2 4 5 1 ) + ( 3 2 5 1 4 ) + ( 3 2 5 4 \ 1 ) + ( 3 4 1 2 5 ) + ( 3 4 1 5 2 ) + ( 3 4 2 1 5 ) + ( 3 4 2 5 1 ) + ( 3 4 5 1 \ 2 ) + ( 3 4 5 2 1 ) + ( 3 5 1 2 4 ) + ( 3 5 1 4 2 ) + ( 3 5 2 1 4 ) + ( 3 5 2 4 \ 1 ) + ( 3 5 4 1 2 ) + ( 3 5 4 2 1 ) + ( 4 1 2 3 5 ) + ( 4 1 2 5 3 ) + ( 4 1 3 2 \ 5 ) + ( 4 1 3 5 2 ) + ( 4 1 5 2 3 ) + ( 4 1 5 3 2 ) + ( 4 2 1 3 5 ) + ( 4 2 1 5 \ 3 ) + ( 4 2 3 1 5 ) + ( 4 2 3 5 1 ) + ( 4 2 5 1 3 ) + ( 4 2 5 3 1 ) + ( 4 3 1 2 \ 5 ) + ( 4 3 1 5 2 ) + ( 4 3 2 1 5 ) + ( 4 3 2 5 1 ) + ( 4 3 5 1 2 ) + ( 4 3 5 2 \ 1 ) + ( 4 5 1 2 3 ) + ( 4 5 1 3 2 ) + ( 4 5 2 1 3 ) + ( 4 5 2 3 1 ) + ( 4 5 3 1 \ 2 ) + ( 4 5 3 2 1 ) + ( 5 1 2 3 4 ) + ( 5 1 2 4 3 ) + ( 5 1 3 2 4 ) + ( 5 1 3 4 \ 2 ) + ( 5 1 4 2 3 ) + ( 5 1 4 3 2 ) + ( 5 2 1 3 4 ) + ( 5 2 1 4 3 ) + ( 5 2 3 1 \ 4 ) + ( 5 2 3 4 1 ) + ( 5 2 4 1 3 ) + ( 5 2 4 3 1 ) + ( 5 3 1 2 4 ) + ( 5 3 1 4 \ 2 ) + ( 5 3 2 1 4 ) + ( 5 3 2 4 1 ) + ( 5 3 4 1 2 ) + ( 5 3 4 2 1 ) + ( 5 4 1 2 \ 3 ) + ( 5 4 1 3 2 ) + ( 5 4 2 1 3 ) + ( 5 4 2 3 1 ) + ( 5 4 3 1 2 ) + ( 5 4 3 2 \ 1 )}\ \>"], "Output"] }, Open ]], Cell[TextData[{ "Now we symmetrize the derivative of the Riemannian curvature tensor by \ means of all these ", Cell[BoxData[ \(TraditionalForm\`\(y\^\[Star]\)\)]], "." }], "Text"], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = List @@ (Symmetrize[#,driemfunc,{i,j,k,l,s}]& /@ allyy)\ \>", "Input"], Cell[OutputFormData["\<\ {8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 8*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 8*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 8*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ + 8*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 8*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 8*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 8*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 8*Rm[L[i], L[s], L[j], L[l]] [L[k]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 8*Rm[L[j], L[k], L[l], L[s]] [L[i]] - 8*Rm[L[j], L[l], L[k], L[s]] [L[i]] \ + 8*Rm[L[j], L[s], L[k], L[l]] [L[i]], 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 2*Rm[L[i], L[j], L[k], L[s]] [L[l]] - \ 2*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 8*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ - 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ + 8*Rm[L[i], L[l], L[j], L[k]] [L[s]] + 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] + 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ - 2*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 2*Rm[L[j], L[k], L[l], L[s]] [L[i]] + 2*Rm[L[j], L[l], L[k], L[s]] [L[i]] \ - 2*Rm[L[j], L[s], L[k], L[l]] [L[i]], 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] + \ 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ - 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 4*Rm[L[j], L[k], L[l], L[s]] [L[i]] + 4*Rm[L[j], L[l], L[k], L[s]] [L[i]] \ + 8*Rm[L[j], L[s], L[k], L[l]] [L[i]], -4*Rm[L[i], L[j], L[k], L[s]] [L[l]] - 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] \ + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ + 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 2*Rm[L[j], L[k], L[l], L[s]] [L[i]] - 4*Rm[L[j], L[l], L[k], L[s]] [L[i]] \ - 2*Rm[L[j], L[s], L[k], L[l]] [L[i]], 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] + \ 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ - 2*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 4*Rm[L[j], L[k], L[l], L[s]] [L[i]] + 2*Rm[L[j], L[l], L[k], L[s]] [L[i]] \ - 2*Rm[L[j], L[s], L[k], L[l]] [L[i]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] - \ 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 2*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 4*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 2*Rm[L[j], L[k], L[l], L[s]] [L[i]] - 2*Rm[L[j], L[l], L[k], L[s]] [L[i]] \ - 4*Rm[L[j], L[s], L[k], L[l]] [L[i]], 0, 0, 0, 0, 0}\ \>", "\<\ {8 Rm - 8 Rm + 8 Rm - 8 Rm + 8 Rm \ - i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k j s ;l 8 Rm + 8 Rm - 8 Rm + 8 Rm - 8 \ Rm + i k l s ;j i l j k ;s i l j s ;k i l k s ;j \ i s j k ;l 8 Rm - 8 Rm + 8 Rm - 8 Rm + 8 \ Rm , 0, i s j l ;k i s k l ;j j k l s ;i j l k s ;i \ j s k l ;i 0, 0, 8 Rm + 2 Rm - 2 Rm - 8 Rm \ - i j k l ;s i j k s ;l i j l s ;k i k j l ;s 2 Rm + 2 Rm + 8 Rm + 2 Rm - 2 \ Rm + i k j s ;l i k l s ;j i l j k ;s i l j s ;k \ i l k s ;j 2 Rm - 2 Rm + 2 Rm - 2 Rm + 2 \ Rm - i s j k ;l i s j l ;k i s k l ;j j k l s ;i \ j l k s ;i 2 Rm , 0, 0, 8 Rm + 4 Rm + 4 Rm \ - j s k l ;i i j k l ;s i k j l ;s i k l s ;j 4 Rm - 4 Rm - 8 Rm - 4 Rm + 4 \ Rm + i l j k ;s i l k s ;j i s k l ;j j k l s ;i \ j l k s ;i 8 Rm , -4 Rm - 2 Rm + 2 Rm + 4 \ Rm + j s k l ;i i j k s ;l i k j s ;l i k l s ;j \ i l k s ;j 2 Rm + 2 Rm - 2 Rm - 4 Rm - 2 \ Rm , i s j k ;l i s k l ;j j k l s ;i j l k s ;i \ j s k l ;i 4 Rm - 4 Rm + 2 Rm - 2 Rm - 2 \ Rm + i j l s ;k i k l s ;j i l j s ;k i l k s ;j \ i s j l ;k 2 Rm + 4 Rm + 2 Rm - 2 Rm , 0, \ 0, 0, 0, 0, 0, 0, i s k l ;j j k l s ;i j l k s ;i j s k l ;i 0, 0, 0, 8 Rm + 4 Rm - 4 Rm + 4 Rm \ + i j k l ;s i j k s ;l i j l s ;k i k j l \ ;s 2 Rm - 2 Rm - 4 Rm - 2 Rm + 2 \ Rm - i k j s ;l i k l s ;j i l j k ;s i l j s ;k \ i l k s ;j 2 Rm + 2 Rm + 4 Rm + 2 Rm - 2 \ Rm - i s j k ;l i s j l ;k i s k l ;j j k l s ;i \ j l k s ;i 4 Rm , 0, 0, 0, 0, 0} j s k l ;i\ \>"], "Output"] }, Open ]], Cell[TextData[{ "Now we apply the first and the second Bianchi identity to the above \ results to find out which of these results are equal to zero. To this end we \ use the following strategy:\n\n1. If we find a term ", Cell[BoxData[ \(TraditionalForm\`R\_\(\(****\)\ ; \ i\)\)]], ", then we use Bianchi II to move", StyleBox[" i", FontSlant->"Italic"], " to the positions 3 or 4. Then Ricci moves ", StyleBox["i ", FontSlant->"Italic"], "automatically to position 1.\n\n2. If ", StyleBox["i", FontSlant->"Italic"], " has position 1 in all terms and we find", StyleBox[" s", FontSlant->"Italic"], " on position 2, then we move ", StyleBox["s", FontSlant->"Italic"], " to positions 3 and 4 by means of Bianchi I." }], "Text"], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[k],L[l],L[i]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 8*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 8*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ - 8*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 8*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ + 8*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 8*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 8*Rm[L[i], L[s], L[j], L[l]] [L[k]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 8*Rm[L[j], L[k], L[l], L[s]] [L[i]] - 8*Rm[L[j], L[l], L[k], L[s]] [L[i]], \ 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 2*Rm[L[i], L[j], L[k], L[s]] [L[l]] - \ 2*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 8*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 8*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] + 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ - 2*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 2*Rm[L[j], L[k], L[l], L[s]] [L[i]] + 2*Rm[L[j], L[l], L[k], L[s]] [L[i]], \ 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] - \ 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] + 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] + 8*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ - 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 4*Rm[L[j], L[k], L[l], L[s]] [L[i]] + 4*Rm[L[j], L[l], L[k], L[s]] [L[i]], \ -4*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] + 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ + 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 2*Rm[L[j], L[k], L[l], L[s]] [L[i]] - 4*Rm[L[j], L[l], L[k], L[s]] [L[i]], \ 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] - \ 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ - 2*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 4*Rm[L[j], L[k], L[l], L[s]] [L[i]] + 2*Rm[L[j], L[l], L[k], L[s]] [L[i]], \ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[j], L[k], \ L[s]] [L[l]] - 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 2*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 4*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 2*Rm[L[j], L[k], L[l], L[s]] [L[i]] - 2*Rm[L[j], L[l], L[k], L[s]] [L[i]], \ 0, 0, 0, 0, 0}\ \>", "\<\ {8 Rm - 8 Rm + 8 Rm - 8 Rm - 8 Rm \ + i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k l s ;j 8 Rm + 8 Rm - 8 Rm + 8 Rm - 8 \ Rm + i l j k ;s i l k s ;j i s j k ;l i s j l ;k \ i s k l ;j 8 Rm - 8 Rm , 0, 0, 0, j k l s ;i j l k s ;i 8 Rm + 2 Rm - 2 Rm - 8 Rm + 2 \ Rm + i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k l s ;j 8 Rm - 2 Rm + 2 Rm - 2 Rm + 2 \ Rm - i l j k ;s i l k s ;j i s j k ;l i s j l ;k \ i s k l ;j 2 Rm + 2 Rm , 0, 0, j k l s ;i j l k s ;i 8 Rm + 4 Rm - 8 Rm + 4 Rm - 4 \ Rm + i j k l ;s i k j l ;s i k j s ;l i k l s ;j \ i l j k ;s 8 Rm - 4 Rm - 8 Rm - 4 Rm + 4 \ Rm , i l j s ;k i l k s ;j i s k l ;j j k l s ;i \ j l k s ;i -4 Rm + 2 Rm - 2 Rm + 4 Rm + 2 \ Rm + i j k s ;l i k l s ;j i l j s ;k i l k s ;j \ i s j k ;l 2 Rm - 2 Rm - 4 Rm , i s k l ;j j k l s ;i j l k s ;i 4 Rm + 2 Rm - 4 Rm - 2 Rm - 2 \ Rm + i j l s ;k i k j s ;l i k l s ;j i l k s ;j \ i s j l ;k 2 Rm + 4 Rm + 2 Rm , 0, 0, 0, 0, 0, 0, 0, \ 0, 0, 0, i s k l ;j j k l s ;i j l k s ;i 8 Rm + 4 Rm - 4 Rm + 4 Rm + 6 \ Rm - i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k j s ;l 2 Rm - 4 Rm - 6 Rm + 2 Rm - 2 \ Rm + i k l s ;j i l j k ;s i l j s ;k i l k s ;j \ i s j k ;l 2 Rm + 4 Rm + 2 Rm - 2 Rm , 0, \ 0, 0, 0, 0} i s j l ;k i s k l ;j j k l s ;i j l k s ;i\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[k],L[s],L[i]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 8*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 8*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ + 8*Rm[L[i], L[l], L[j], L[k]] [L[s]] + 8*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ - 8*Rm[L[i], L[s], L[j], L[k]] [L[l]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 8*Rm[L[j], L[k], L[l], L[s]] [L[i]], 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 2*Rm[L[i], L[j], L[k], L[s]] [L[l]] - \ 2*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 10*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 8*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] + 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] - 2*Rm[L[j], L[k], L[l], L[s]] [L[i]], \ 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] + \ 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ + 8*Rm[L[i], L[l], L[j], L[s]] [L[k]] - 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ + 4*Rm[L[i], L[s], L[j], L[l]] [L[k]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 4*Rm[L[j], L[k], L[l], L[s]] [L[i]], -4*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] + 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ - 4*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ - 2*Rm[L[j], L[k], L[l], L[s]] [L[i]], 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 2*Rm[L[i], L[k], L[j], L[l]] [L[s]] + \ 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]] \ + 4*Rm[L[j], L[k], L[l], L[s]] [L[i]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] - \ 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 2*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 4*Rm[L[i], L[s], L[k], L[l]] [L[j]] + 2*Rm[L[j], L[k], L[l], L[s]] [L[i]], \ 0, 0, 0, 0, 0}\ \>", "\<\ {8 Rm - 8 Rm + 8 Rm - 8 Rm + 8 Rm \ + i j k l ;s i j k s ;l i j l s ;k i k l s ;j \ i l j k ;s 8 Rm - 8 Rm - 8 Rm + 8 Rm , 0, \ 0, 0, i l k s ;j i s j k ;l i s k l ;j j k l s ;i 8 Rm + 2 Rm - 2 Rm - 10 Rm + 2 \ Rm + i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k l s ;j 8 Rm - 2 Rm + 2 Rm + 2 Rm - 2 \ Rm , 0, i l j k ;s i l k s ;j i s j k ;l i s k l ;j \ j k l s ;i 0, 8 Rm - 8 Rm + 4 Rm - 4 Rm + \ 8 Rm - i j k l ;s i k j s ;l i k l s ;j i l j k ;s \ i l j s ;k 4 Rm + 4 Rm - 8 Rm - 4 Rm , i l k s ;j i s j l ;k i s k l ;j j k l s ;i -4 Rm + 4 Rm + 2 Rm - 2 Rm + 4 \ Rm + i j k s ;l i k j l ;s i k l s ;j i l j s ;k \ i l k s ;j 2 Rm - 4 Rm + 2 Rm - 2 Rm , i s j k ;l i s j l ;k i s k l ;j j k l s ;i 4 Rm - 2 Rm + 2 Rm - 4 Rm - 2 \ Rm + i j l s ;k i k j l ;s i k j s ;l i k l s ;j \ i l k s ;j 2 Rm + 4 Rm , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, i s k l ;j j k l s ;i 8 Rm + 4 Rm - 4 Rm + 6 Rm + 6 \ Rm - i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k j s ;l 2 Rm - 4 Rm - 6 Rm + 2 Rm - 2 \ Rm + i k l s ;j i l j k ;s i l j s ;k i l k s ;j \ i s j k ;l 4 Rm + 2 Rm , 0, 0, 0, 0, 0} i s k l ;j j k l s ;i\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[l],L[s],L[i]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 8*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 8*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ + 8*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]], \ 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 2*Rm[L[i], L[j], L[k], L[s]] [L[l]] - \ 2*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 10*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 10*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]], \ 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] + \ 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 8*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ - 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 4*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 4*Rm[L[i], L[s], L[j], L[l]] [L[k]] - 8*Rm[L[i], L[s], L[k], L[l]] [L[j]], \ -4*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 2*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ - 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] + 4*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ - 4*Rm[L[i], L[s], L[j], L[l]] [L[k]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]], \ 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 2*Rm[L[i], L[k], L[j], L[l]] [L[s]] + \ 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 4*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ + 4*Rm[L[i], L[s], L[j], L[k]] [L[l]] + 2*Rm[L[i], L[s], L[k], L[l]] [L[j]], \ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[j], L[k], \ L[s]] [L[l]] - 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 2*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 6*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 2*Rm[L[i], L[l], L[k], L[s]] [L[j]] + 4*Rm[L[i], L[s], L[k], L[l]] [L[j]], \ 0, 0, 0, 0, 0}\ \>", "\<\ {8 Rm - 8 Rm + 8 Rm - 8 Rm + 8 Rm \ - i j k l ;s i j k s ;l i j l s ;k i k l s ;j \ i l k s ;j 8 Rm , 0, 0, 0, 8 Rm + 2 Rm - 2 Rm \ - i s k l ;j i j k l ;s i j k s ;l i j l s \ ;k 10 Rm + 2 Rm + 10 Rm - 2 Rm + \ 2 Rm , i k j l ;s i k l s ;j i l j k ;s i l k s ;j \ i s k l ;j 0, 0, 8 Rm - 8 Rm + 4 Rm + 8 Rm \ - i j k l ;s i k j s ;l i k l s ;j i l j s ;k 4 Rm - 4 Rm + 4 Rm - 8 Rm , i l k s ;j i s j k ;l i s j l ;k i s k l ;j -4 Rm + 4 Rm + 2 Rm + 2 Rm - 2 \ Rm + i j k s ;l i k j l ;s i k l s ;j i l j k ;s \ i l j s ;k 4 Rm - 4 Rm + 2 Rm , i l k s ;j i s j l ;k i s k l ;j 4 Rm - 2 Rm + 2 Rm - 4 Rm - 4 \ Rm - i j l s ;k i k j l ;s i k j s ;l i k l s ;j \ i l j k ;s 2 Rm + 4 Rm + 2 Rm , 0, 0, 0, 0, 0, 0, 0, \ 0, 0, 0, i l k s ;j i s j k ;l i s k l ;j 8 Rm + 4 Rm - 4 Rm + 6 Rm + 6 \ Rm - i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k j s ;l 2 Rm - 6 Rm - 6 Rm + 2 Rm + 4 \ Rm , 0, i k l s ;j i l j k ;s i l j s ;k i l k s ;j \ i s k l ;j 0, 0, 0, 0}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[s],L[k],L[l]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 8*Rm[L[i], L[j], L[l], L[s]] [L[k]], 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 2*Rm[L[i], L[j], L[k], L[s]] [L[l]] - \ 2*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 10*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 10*Rm[L[i], L[l], L[j], L[k]] [L[s]], 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] + \ 12*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 8*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ - 12*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 4*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 4*Rm[L[i], L[s], L[j], L[l]] [L[k]], -4*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 4*Rm[L[i], L[s], L[j], L[l]] [L[k]], \ 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 2*Rm[L[i], L[k], L[j], L[l]] [L[s]] + \ 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] + 4*Rm[L[i], L[s], L[j], L[k]] [L[l]], \ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[j], L[k], \ L[s]] [L[l]] - 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 6*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], 0, 0, 0, 0, 0}\ \>", "\<\ {8 Rm - 8 Rm + 8 Rm , 0, 0, 0, i j k l ;s i j k s ;l i j l s ;k 8 Rm + 2 Rm - 2 Rm - 10 Rm + 10 \ Rm , i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i l j k ;s 0, 0, 8 Rm - 8 Rm + 12 Rm + 8 Rm \ - i j k l ;s i k j s ;l i k l s ;j i l j s ;k \ 12 Rm - 4 Rm + 4 Rm , i l k s ;j i s j k ;l i s j l ;k -4 Rm + 4 Rm + 2 Rm - 2 Rm + 6 \ Rm - i j k s ;l i k j l ;s i l j k ;s i l j s ;k \ i l k s ;j 4 Rm , 4 Rm - 2 Rm + 2 Rm - 6 \ Rm - i s j l ;k i j l s ;k i k j l ;s i k j s ;l \ i k l s ;j 4 Rm + 4 Rm , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, i l j k ;s i s j k ;l 8 Rm + 4 Rm - 4 Rm + 6 Rm + 6 \ Rm - i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i k j s ;l 6 Rm - 6 Rm - 6 Rm + 6 Rm , 0, \ 0, 0, 0, 0} i k l s ;j i l j k ;s i l j s ;k i l k s ;j\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[l],L[s],L[k]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 10*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 10*Rm[L[i], L[k], L[j], \ L[l]] [L[s]] + 10*Rm[L[i], L[l], L[j], L[k]] [L[s]], 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] + \ 12*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 8*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ - 12*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 4*Rm[L[i], L[s], L[j], L[k]] [L[l]] \ + 4*Rm[L[i], L[s], L[j], L[l]] [L[k]], -4*Rm[L[i], L[j], L[k], L[s]] [L[l]] + 4*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 2*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 4*Rm[L[i], L[s], L[j], L[l]] [L[k]], \ -4*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] \ - 2*Rm[L[i], L[k], L[j], L[l]] [L[s]] + 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] \ - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 4*Rm[L[i], L[l], L[j], L[k]] [L[s]] \ + 4*Rm[L[i], L[s], L[j], L[k]] [L[l]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ - 6*Rm[L[i], L[l], L[j], L[k]] [L[s]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 10 Rm - 10 Rm + 10 Rm , 0, 0, i j k l ;s i k j l ;s i l j k ;s 8 Rm - 8 Rm + 12 Rm + 8 Rm - 12 \ Rm - i j k l ;s i k j s ;l i k l s ;j i l j s ;k \ i l k s ;j 4 Rm + 4 Rm , -4 Rm + 4 Rm + 2 \ Rm - i s j k ;l i s j l ;k i j k s ;l i k j l ;s \ i l j k ;s 2 Rm + 6 Rm - 4 Rm , i l j s ;k i l k s ;j i s j l ;k -4 Rm + 4 Rm - 2 Rm + 2 Rm - 6 \ Rm - i j k l ;s i j k s ;l i k j l ;s i k j s ;l \ i k l s ;j 4 Rm + 4 Rm , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, i l j k ;s i s j k ;l 12 Rm + 6 Rm + 6 Rm - 6 Rm - 6 \ Rm - i j k l ;s i k j l ;s i k j s ;l i k l s ;j \ i l j k ;s 6 Rm + 6 Rm , 0, 0, 0, 0, 0} i l j s ;k i l k s ;j\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[l],L[j],L[k]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] + 12*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ + 8*Rm[L[i], L[l], L[j], L[s]] [L[k]] - 12*Rm[L[i], L[l], L[k], L[s]] [L[j]] \ - 4*Rm[L[i], L[s], L[j], L[k]] [L[l]] + 4*Rm[L[i], L[s], L[j], L[l]] [L[k]], \ -2*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] \ + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] - 2*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 4*Rm[L[i], L[s], L[j], L[l]] [L[k]], \ 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] - 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] + \ 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ + 4*Rm[L[i], L[s], L[j], L[k]] [L[l]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] \ - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 0, 0, 0, 8 Rm - 8 Rm + 12 Rm + \ 8 Rm - i j k l ;s i k j s ;l i k l s ;j \ i l j s ;k 12 Rm - 4 Rm + 4 Rm , i l k s ;j i s j k ;l i s j l ;k -2 Rm - 4 Rm + 6 Rm - 2 Rm + 6 \ Rm - i j k l ;s i j k s ;l i k j l ;s i l j s ;k \ i l k s ;j 4 Rm , 4 Rm - 6 Rm + 2 Rm - 6 \ Rm + i s j l ;k i j k s ;l i k j l ;s i k j s ;l \ i k l s ;j 4 Rm , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, i s j k ;l 18 Rm + 6 Rm - 6 Rm - 6 Rm + 6 \ Rm , 0, i j k l ;s i k j s ;l i k l s ;j i l j s ;k \ i l k s ;j 0, 0, 0, 0}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[s],L[j],L[l]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] - 8*Rm[L[i], L[k], L[j], L[s]] [L[l]] \ + 12*Rm[L[i], L[k], L[l], L[s]] [L[j]] + 12*Rm[L[i], L[l], L[j], L[s]] \ [L[k]] - 12*Rm[L[i], L[l], L[k], L[s]] [L[j]] - 4*Rm[L[i], L[s], L[j], L[k]] \ [L[l]], -2*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] \ + 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], \ 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] - 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] + \ 2*Rm[L[i], L[k], L[j], L[s]] [L[l]] - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] \ + 4*Rm[L[i], L[s], L[j], L[k]] [L[l]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] \ - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 0, 0, 0, 8 Rm - 4 Rm - 8 Rm + \ 12 Rm + i j k l ;s i j l s ;k i k j s ;l \ i k l s ;j 12 Rm - 12 Rm - 4 Rm , i l j s ;k i l k s ;j i s j k ;l -2 Rm - 4 Rm + 4 Rm + 6 Rm - 6 \ Rm + i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i l j s ;k 6 Rm , 4 Rm - 6 Rm + 2 Rm - 6 \ Rm + i l k s ;j i j k s ;l i k j l ;s i k j s ;l \ i k l s ;j 4 Rm , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, i s j k ;l 18 Rm + 6 Rm - 6 Rm - 6 Rm + 6 \ Rm , 0, i j k l ;s i k j s ;l i k l s ;j i l j s ;k \ i l k s ;j 0, 0, 0, 0}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[s],L[j],L[k]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 0, 0, 0, 8*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] - 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] \ - 12*Rm[L[i], L[k], L[j], L[s]] [L[l]] + 12*Rm[L[i], L[k], L[l], L[s]] \ [L[j]] + 12*Rm[L[i], L[l], L[j], L[s]] [L[k]] - 12*Rm[L[i], L[l], L[k], L[s]] \ [L[j]], -2*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 4*Rm[L[i], L[j], L[k], L[s]] [L[l]] \ + 4*Rm[L[i], L[j], L[l], L[s]] [L[k]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], \ -6*Rm[L[i], L[k], L[j], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] \ - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[s]] [L[l]] \ - 6*Rm[L[i], L[k], L[l], L[s]] [L[j]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 0, 0, 0, 8 Rm + 4 Rm - 4 Rm - \ 12 Rm + i j k l ;s i j k s ;l i j l s ;k \ i k j s ;l 12 Rm + 12 Rm - 12 Rm , i k l s ;j i l j s ;k i l k s ;j -2 Rm - 4 Rm + 4 Rm + 6 Rm - 6 \ Rm + i j k l ;s i j k s ;l i j l s ;k i k j l ;s \ i l j s ;k 6 Rm , -6 Rm + 6 Rm - 6 Rm , 0, \ 0, 0, 0, 0, 0, 0, i l k s ;j i k j l ;s i k j s ;l i k l s ;j 0, 0, 0, 18 Rm + 6 Rm - 6 Rm - 6 Rm \ + i j k l ;s i k j s ;l i k l s ;j i l j s \ ;k 6 Rm , 0, 0, 0, 0, 0} i l k s ;j\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["symmetrizeddriem = symmetrizeddriem /. SecondBianchiRule", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 0, 0, 0, 12*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 12*Rm[L[i], L[k], L[j], L[s]] [L[l]] + 12*Rm[L[i], L[k], L[l], L[s]] \ [L[j]] + 12*Rm[L[i], L[l], L[j], L[s]] [L[k]] - 12*Rm[L[i], L[l], L[k], L[s]] \ [L[j]], -6*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], \ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] - 6*Rm[L[i], L[l], L[j], L[s]] [L[k]] \ + 6*Rm[L[i], L[l], L[k], L[s]] [L[j]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 0, 0, 0, 12 Rm - 12 Rm + 12 Rm \ + i j k l ;s i k j s ;l i k l s ;j 12 Rm - 12 Rm , i l j s ;k i l k s ;j -6 Rm + 6 Rm - 6 Rm + 6 Rm , 0, \ 0, 0, 0, 0, 0, 0, i j k l ;s i k j l ;s i l j s ;k i l k s ;j 0, 0, 0, 0, 18 Rm + 6 Rm - 6 Rm + 6 Rm \ , 0, 0, 0, i j k l ;s i k j l ;s i l j s ;k i l \ k s ;j 0, 0}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["symmetrizeddriem = symmetrizeddriem /. SecondBianchiRule", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 0, 0, 0, 12*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 12*Rm[L[i], L[k], L[j], L[l]] [L[s]] + 12*Rm[L[i], L[l], L[j], L[s]] \ [L[k]] - 12*Rm[L[i], L[l], L[k], L[s]] [L[j]], -6*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ - 6*Rm[L[i], L[l], L[j], L[k]] [L[s]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18*Rm[L[i], L[j], L[k], L[l]] [L[s]] + 6*Rm[L[i], L[k], L[j], L[l]] [L[s]] \ - 6*Rm[L[i], L[l], L[j], L[k]] [L[s]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 0, 0, 0, 12 Rm - 12 Rm + 12 Rm \ - i j k l ;s i k j l ;s i l j s ;k 12 Rm , -6 Rm + 6 Rm - 6 Rm , 0, \ 0, 0, 0, 0, 0, i l k s ;j i j k l ;s i k j l ;s i l j k ;s 0, 0, 0, 0, 0, 18 Rm + 6 Rm - 6 Rm , 0, 0, \ 0, 0, 0} i j k l ;s i k j l ;s i l j k ;s\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ symmetrizeddriem = symmetrizeddriem /. BianchiRules[L[l],L[j],L[k]] \ //Expand\ \>", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 0, 0, 0, 12*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 12*Rm[L[i], L[k], L[j], L[l]] [L[s]] + 12*Rm[L[i], L[l], L[j], L[s]] \ [L[k]] - 12*Rm[L[i], L[l], L[k], L[s]] [L[j]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24*Rm[L[i], L[j], L[k], L[l]] [L[s]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 0, 0, 0, 12 Rm - 12 Rm + 12 Rm \ - i j k l ;s i k j l ;s i l j s ;k 12 Rm , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24 Rm , 0, \ 0, 0, 0, 0} i l k s ;j i j k l ;s\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["symmetrizeddriem = symmetrizeddriem /. SecondBianchiRule", "Input"], Cell[OutputFormData["\<\ {0, 0, 0, 0, 0, 0, 0, 12*Rm[L[i], L[j], L[k], L[l]] [L[s]] - 12*Rm[L[i], L[k], L[j], L[l]] [L[s]] + 12*Rm[L[i], L[l], L[j], L[k]] \ [L[s]], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24*Rm[L[i], L[j], L[k], L[l]] [L[s]], 0, 0, 0, 0, 0}\ \>", "\<\ {0, 0, 0, 0, 0, 0, 0, 12 Rm - 12 Rm + 12 Rm , \ 0, 0, 0, 0, 0, i j k l ;s i k j l ;s i l j k ;s 0, 0, 0, 0, 0, 0, 0, 24 Rm , 0, 0, 0, 0, 0} i j k l ;s\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["symmetrizeddriem = symmetrizeddriem /. 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