{
	"cells" : 
	[
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : "def post_process(ex):\n   eliminate_kronecker(ex)\n   sort_product(ex)\n   collect_terms(ex)"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "It is easier to keep track of various parts of the computation if we disable automatic\nindex raising/lowering, so we use \\verb|position=independent| on the indices. "
				}
			],
			"hidden" : true,
			"source" : "It is easier to keep track of various parts of the computation if we disable automatic\nindex raising/lowering, so we use \\verb|position=independent| on the indices. "
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Derivative to~}D{\\#}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property PartialDerivative to~}\\partial{\\#}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property DiracBar to~}\\bar{\\#}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Derivative to~}\\delta\\left(A??\\right).\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Indices(position=independent) to~}\\left[m,~\\discretionary{}{}{} n,~\\discretionary{}{}{} p,~\\discretionary{}{}{} q,~\\discretionary{}{}{} r,~\\discretionary{}{}{} s,~\\discretionary{}{}{} t,~\\discretionary{}{}{} u\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Integer to~}\\left[m,~\\discretionary{}{}{} n,~\\discretionary{}{}{} p,~\\discretionary{}{}{} q,~\\discretionary{}{}{} r,~\\discretionary{}{}{} s,~\\discretionary{}{}{} t,~\\discretionary{}{}{} u\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Indices(position=independent) to~}\\left[\\mu,~\\discretionary{}{}{} \\nu,~\\discretionary{}{}{} \\rho,~\\discretionary{}{}{} \\sigma,~\\discretionary{}{}{} \\kappa,~\\discretionary{}{}{} \\lambda,~\\discretionary{}{}{} \\alpha,~\\discretionary{}{}{} \\beta\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Integer to~}\\left[\\mu,~\\discretionary{}{}{} \\nu,~\\discretionary{}{}{} \\rho,~\\discretionary{}{}{} \\sigma,~\\discretionary{}{}{} \\kappa,~\\discretionary{}{}{} \\lambda,~\\discretionary{}{}{} \\alpha,~\\discretionary{}{}{} \\beta\\right].\\end{dmath*}"
				}
			],
			"source" : "D{#}::Derivative;\n\\partial{#}::PartialDerivative;\n\\bar{#}::DiracBar;\n\\delta{A??}::Derivative;\n{m,n,p,q,r,s,t,u}::Indices(flat, position=independent);\n{m,n,p,q,r,s,t,u}::Integer(0..3);\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\alpha,\\beta}::Indices(curved,position=independent);\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\alpha,\\beta}::Integer(0..3);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Vielbein to~}e^{m \\mu}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property InverseVielbein to~}e_{m \\mu}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property TableauSymmetry to~}g^{\\mu \\nu}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Metric to~}g_{\\mu \\nu}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Metric to~}\\delta_{m n}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property TableauSymmetry to~}\\delta^{m n}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property KroneckerDelta to~}\\delta^{s}\\,_{r}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property TableauSymmetry to~}\\omega_{\\mu m n}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Depends to~}\\left[e_{m}\\,^{\\mu},~\\discretionary{}{}{} \\psi_{\\mu},~\\discretionary{}{}{} e,~\\discretionary{}{}{} T^{\\mu}\\,_{\\nu \\rho},~\\discretionary{}{}{} \\omega_{\\mu m n}\\right].\\end{dmath*}"
				}
			],
			"source" : "e^{m \\mu}::Vielbein;\ne_{m \\mu}::InverseVielbein;\ng^{\\mu\\nu}::InverseMetric;\ng_{\\mu\\nu}::Metric;\n\\delta_{m n}::Metric;\n\\delta^{m n}::InverseMetric;\n\\delta^{s}_{r}::KroneckerDelta;\n\\omega_{\\mu m n}::TableauSymmetry( indices={1,2}, shape={1,1} );\n{ e_{m}^{\\mu}, \\psi_{\\mu}, e, T^{\\mu}_{\\nu\\rho}, \\omega_{\\mu m n} }::Depends(\\partial{#});"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Spinor to~}\\left[\\epsilon,~\\discretionary{}{}{} \\psi_{\\mu},~\\discretionary{}{}{} \\psi_{\\mu \\nu}\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property GammaMatrix to~}\\Gamma_{\\#}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property AntiCommuting to~}\\left[\\psi_{\\mu \\nu},~\\discretionary{}{}{} \\psi_{\\mu},~\\discretionary{}{}{} \\epsilon\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property SelfAntiCommuting to~}\\left[\\psi_{\\mu},~\\discretionary{}{}{} \\psi_{\\mu \\nu}\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property SortOrder to~}\\left[\\epsilon,~\\discretionary{}{}{} \\psi_{\\mu},~\\discretionary{}{}{} \\psi_{\\mu \\nu}\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Depends to~}\\Gamma_{\\#}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property AntiSymmetric to~}\\psi_{\\mu \\nu}.\\end{dmath*}"
				}
			],
			"source" : "{ \\epsilon,\\psi_{\\mu},\\psi_{\\mu\\nu} }::Spinor(dimension=4, type=Majorana);\n\\Gamma_{#}::GammaMatrix(metric=\\delta);\n{ \\psi_{\\mu\\nu}, \\psi_{\\mu}, \\epsilon }::AntiCommuting;\n{ \\psi_{\\mu}, \\psi_{\\mu\\nu} }::SelfAntiCommuting;\n{ \\epsilon, \\psi_{\\mu}, \\psi_{\\mu\\nu} }::SortOrder;\n\\Gamma_{#}::Depends(\\bar{#});\n\\psi_{\\mu\\nu}::AntiSymmetric;"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\int \\left( - \\frac{1}{2}R_{\\mu \\nu r s} \\delta^{m s} \\delta^{n r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} - \\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{\\mu \\nu \\rho} D_{\\nu}{\\psi_{\\rho}} e\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\int \\left( - \\frac{1}{2}R_{\\mu \\nu r s} \\delta^{m s} \\delta^{n r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} - \\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "L:= \\int{-1/2 e e_{n}^{\\nu} e_{m}^{\\mu} R_{\\mu\\nu r s} \\delta^{n r} \\delta^{m s}\n                 - 1/2 e \\bar{\\psi_\\mu} \\Gamma^{\\mu\\nu\\rho} D_{\\nu}{\\psi_{\\rho}} }{x};\nrewrite_indices(_, $\\Gamma^{m n p}$, $e_{n}^{\\mu}$ );"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\left[e_{n}\\,^{\\mu} \\rightarrow -\\bar{\\epsilon} \\Gamma^{m} \\psi_{\\nu} e_{m}\\,^{\\mu} e_{n}\\,^{\\nu},~\\discretionary{}{}{} e \\rightarrow \\bar{\\epsilon} \\Gamma^{n} \\psi_{\\mu} e e_{n}\\,^{\\mu},~\\discretionary{}{}{} \\psi_{\\mu} \\rightarrow D_{\\mu}{\\epsilon}\\right]\\end{dmath*}"
				}
			],
			"source" : "susy:= { e_{n}^{\\mu} -> -\\bar{\\epsilon} \\Gamma^m \\psi_\\nu e_{m}^{\\mu} e_{n}^{\\nu},\n         e           -> e \\bar{\\epsilon} \\Gamma^n \\psi_\\mu e_{n}^{\\mu},\n         \\psi_\\mu    -> D_{\\mu}{\\epsilon} };"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\int \\left( - \\frac{1}{2}R_{\\mu \\nu r s} \\bar{\\epsilon} \\Gamma^{p} \\delta^{m s} \\delta^{n r} \\psi_{\\rho} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}+\\frac{1}{2}R_{\\mu \\nu r s} \\bar{\\epsilon} \\Gamma^{p} \\delta^{m s} \\delta^{n r} \\psi_{\\rho} e e_{m}\\,^{\\rho} e_{n}\\,^{\\nu} e_{p}\\,^{\\mu}+\\frac{1}{2}R_{\\mu \\nu r s} \\bar{\\epsilon} \\Gamma^{p} \\delta^{m s} \\delta^{n r} \\psi_{\\rho} e e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} - \\frac{1}{2}\\bar{D_{\\mu}{\\epsilon}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} - \\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{D_{\\rho}{\\epsilon}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} - \\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} e_{q}\\,^{\\sigma}+\\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\sigma} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} e_{q}\\,^{\\mu}+\\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\mu} e_{n}\\,^{\\sigma} e_{p}\\,^{\\rho} e_{q}\\,^{\\nu}+\\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\sigma} e_{q}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "vary(L, susy);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\int \\left( - \\frac{1}{2}R_{\\mu \\nu r s} \\bar{\\epsilon} \\Gamma^{p} \\delta^{m s} \\delta^{n r} \\psi_{\\rho} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}+\\frac{1}{2}R_{\\mu \\nu r s} \\bar{\\epsilon} \\Gamma^{p} \\delta^{m s} \\delta^{n r} \\psi_{\\rho} e e_{m}\\,^{\\rho} e_{n}\\,^{\\nu} e_{p}\\,^{\\mu}+\\frac{1}{2}R_{\\mu \\nu r s} \\bar{\\epsilon} \\Gamma^{p} \\delta^{m s} \\delta^{n r} \\psi_{\\rho} e e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} - \\frac{1}{2}\\bar{D_{\\mu}{\\epsilon}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} - \\frac{1}{8}R_{\\nu \\rho q r} \\bar{\\psi_{\\mu}} \\Gamma^{m n p} \\Gamma^{q r} \\epsilon e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} - \\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} e_{q}\\,^{\\sigma}+\\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\sigma} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} e_{q}\\,^{\\mu}+\\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\mu} e_{n}\\,^{\\sigma} e_{p}\\,^{\\rho} e_{q}\\,^{\\nu}+\\frac{1}{2}\\bar{\\psi_{\\mu}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\bar{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\sigma} e_{q}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "substitute(_, $D_{\\nu}{ D_{\\rho}{ \\epsilon } } -> 1/4 R_{\\nu\\rho m n} \\Gamma^{m n} \\epsilon$ );"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\bar{D_{\\mu}{\\epsilon}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "take_match(_, $\\bar{D_{\\mu}{\\epsilon}}*A??$);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\bar{D_{\\mu}{\\epsilon}} = \\partial_{\\mu}\\left(\\bar{\\epsilon}\\right) - \\frac{1}{4}\\bar{\\epsilon} \\Gamma^{m n} \\omega_{\\mu m n}\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left(\\partial_{\\mu}\\left(\\bar{\\epsilon}\\right) \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} - \\frac{1}{4}\\bar{\\epsilon} \\Gamma^{q r} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\omega_{\\mu q r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "covD:= \\bar{D_{\\mu}{\\epsilon}} = \\partial_{\\mu}{\\bar{\\epsilon}} \n                                  - 1/4 \\bar{\\epsilon}\\omega_{\\mu m n} \\Gamma^{m n} ):\nsubstitute(L, covD)\ndistribute(L);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left(-\\bar{\\epsilon} \\partial_{\\mu}\\left(\\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right) - \\frac{1}{4}\\bar{\\epsilon} \\Gamma^{q r} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\omega_{\\mu q r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "integrate_by_parts(L, $\\bar{\\epsilon}$);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left(-\\bar{\\epsilon} \\left(\\partial_{\\mu}{\\Gamma^{m n p}} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}+\\Gamma^{m n p} \\partial_{\\mu}{D_{\\nu}{\\psi_{\\rho}}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}+\\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e} e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}+\\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}+\\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{n}\\,^{\\nu}} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho}+\\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{p}\\,^{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu}\\right) - \\frac{1}{4}\\bar{\\epsilon} \\Gamma^{q r} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\omega_{\\mu q r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "product_rule(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left(-\\bar{\\epsilon} \\partial_{\\mu}{\\Gamma^{m n p}} D_{\\nu}{\\psi_{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} \\partial_{\\mu}{D_{\\nu}{\\psi_{\\rho}}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e} e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{n}\\,^{\\nu}} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{p}\\,^{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} - \\frac{1}{4}\\bar{\\epsilon} \\Gamma^{q r} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\omega_{\\mu q r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "distribute(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left(-\\bar{\\epsilon} \\Gamma^{m n p} \\partial_{\\mu}{D_{\\nu}{\\psi_{\\rho}}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e} e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{n}\\,^{\\nu}} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{p}\\,^{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} - \\frac{1}{4}\\bar{\\epsilon} \\Gamma^{q r} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\omega_{\\mu q r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "unwrap(_, $\\partial{#}$);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left(-\\bar{\\epsilon} \\Gamma^{m n p} \\partial_{\\mu}{D_{\\nu}{\\psi_{\\rho}}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e} e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{n}\\,^{\\nu}} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} \\partial_{\\mu}{e_{p}\\,^{\\rho}} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} - \\frac{1}{4}\\bar{\\epsilon} \\left(\\Gamma^{q n p} \\delta^{m r}-\\Gamma^{q n m} \\delta^{p r}+\\Gamma^{q p m} \\delta^{n r}-\\Gamma^{r n p} \\delta^{m q}+\\Gamma^{r n m} \\delta^{p q}-\\Gamma^{r p m} \\delta^{n q}+\\Gamma^{p} \\delta^{m r} \\delta^{n q}-\\Gamma^{m} \\delta^{n q} \\delta^{p r}+\\Gamma^{n} \\delta^{m q} \\delta^{p r}-\\Gamma^{p} \\delta^{m q} \\delta^{n r}+\\Gamma^{m} \\delta^{n r} \\delta^{p q}-\\Gamma^{n} \\delta^{m r} \\delta^{p q}\\right) D_{\\nu}{\\psi_{\\rho}} \\omega_{\\mu q r} e e_{m}\\,^{\\mu} e_{n}\\,^{\\nu} e_{p}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "join_gamma(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left(-\\bar{\\epsilon} \\Gamma^{m n p} \\partial_{\\nu}{D_{\\mu}{\\psi_{\\rho}}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e} e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\nu}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\rho}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "distribute(_)\ncanonicalise(_)\nrename_dummies(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "Is the following correct, or do we miss a spin connection term here?"
				}
			],
			"hidden" : true,
			"source" : "Is the following correct, or do we miss a spin connection term here?"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\nu \\mu q r} \\bar{\\epsilon} \\Gamma^{m n p} \\Gamma^{q r} \\psi_{\\rho} e e_{m}\\,^{\\nu} e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e} e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\nu}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\rho}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "substitute(_,  $\\partial_{\\mu}{D_{\\nu}{\\psi_{\\rho}}} -> 1/4 R_{\\mu\\nu m n}\\Gamma^{m n} \\psi_{\\rho}$ );"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\nu \\mu q r} \\bar{\\epsilon} \\Gamma^{m n p} \\Gamma^{q r} \\psi_{\\rho} e e_{m}\\,^{\\nu} e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{q}\\,^{\\sigma}} e e^{q}\\,_{\\sigma} e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\nu}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\rho}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "substitute(L, $\\partial_{\\rho}{e} -> - e e^{n}_{\\mu} \\partial_{\\rho}{ e_{n}^{\\mu} }$ );"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\mu \\nu m n} \\bar{\\epsilon} \\Gamma^{p q r} \\Gamma^{m n} \\psi_{\\rho} e e_{p}\\,^{\\mu} e_{q}\\,^{\\nu} e_{r}\\,^{\\rho}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{q}\\,^{\\sigma}} e e^{q}\\,_{\\sigma} e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\nu}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\mu}} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\partial_{\\nu}{e_{m}\\,^{\\rho}} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "canonicalise(_)\nrename_dummies(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "Last three terms disappeared in the original computation, but that did a weird join... Is that based\non a trick in vNh?\nWe now need to replace the derivative of the vielbein using the fact that it is covariantly constant. So we can trade\nthe derivative for a term with the spin connection and a term with the torsion."
				}
			],
			"hidden" : true,
			"source" : "Last three terms disappeared in the original computation, but that did a weird join... Is that based\non a trick in vNh?\nWe now need to replace the derivative of the vielbein using the fact that it is covariantly constant. So we can trade\nthe derivative for a term with the spin connection and a term with the torsion."
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\mu \\nu m n} \\bar{\\epsilon} \\Gamma^{p q r} \\Gamma^{m n} \\psi_{\\rho} e e_{p}\\,^{\\mu} e_{q}\\,^{\\nu} e_{r}\\,^{\\rho}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{s r} \\omega_{\\nu q s} e e_{r}\\,^{\\sigma} e^{q}\\,_{\\sigma} e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}-C^{\\sigma}\\,_{\\nu \\kappa} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} e e_{q}\\,^{\\kappa} e^{q}\\,_{\\sigma} e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{r q} \\omega_{\\nu m r} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{q}\\,^{\\nu}+C^{\\nu}\\,_{\\nu \\sigma} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} e e_{m}\\,^{\\sigma} e_{n}\\,^{\\mu} e_{p}\\,^{\\rho}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{r q} \\omega_{\\nu m r} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{q}\\,^{\\mu}+C^{\\mu}\\,_{\\nu \\sigma} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} e e_{m}\\,^{\\sigma} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}-\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{r q} \\omega_{\\nu m r} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{q}\\,^{\\rho}-C^{\\rho}\\,_{\\nu \\sigma} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} e e_{m}\\,^{\\sigma} e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "substitute(_, $\\partial_{\\mu}{e_{m}^{\\nu}} -> -\\omega_{\\mu m p} \\delta^{p n} e_{n}^{\\nu} - C^{\\nu}_{\\mu\\rho} e_{m}^{\\rho}$ )\ndistribute(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\mu \\nu m n} \\bar{\\epsilon} \\Gamma^{p q r} \\Gamma^{m n} \\psi_{\\rho} e e_{p}\\,^{\\mu} e_{q}\\,^{\\nu} e_{r}\\,^{\\rho}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu q s} e e_{m}\\,^{\\mu} e^{s}\\,_{\\sigma} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\sigma}-C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\sigma}{\\psi_{\\kappa}} e e_{m}\\,^{\\nu} e^{q}\\,_{\\mu} e_{n}\\,^{\\sigma} e_{p}\\,^{\\kappa} e_{q}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+C^{\\mu}\\,_{\\mu \\nu} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\rho}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu}+C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho}-C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\sigma}{\\psi_{\\mu}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "canonicalise(_)\nrename_dummies(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "The gamma3 omega terms should have gone now, or after eliminate of vielbeine. First indeed goes. 2,3,4 not sure?"
				}
			],
			"hidden" : true,
			"source" : "The gamma3 omega terms should have gone now, or after eliminate of vielbeine. First indeed goes. 2,3,4 not sure?"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\mu \\nu m n} \\bar{\\epsilon} \\Gamma^{p q r} \\Gamma^{m n} \\psi_{\\rho} e e_{p}\\,^{\\mu} e_{q}\\,^{\\nu} e_{r}\\,^{\\rho}+\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q s} \\omega_{\\nu q s} e e_{m}\\,^{\\mu} e_{n}\\,^{\\rho} e_{p}\\,^{\\nu}-C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\sigma}{\\psi_{\\kappa}} e e_{m}\\,^{\\nu} e^{q}\\,_{\\mu} e_{n}\\,^{\\sigma} e_{p}\\,^{\\kappa} e_{q}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+C^{\\mu}\\,_{\\mu \\nu} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\rho}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu}+C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho}-C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\sigma}{\\psi_{\\mu}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "substitute(_, $e^{s}_{\\sigma} e_{r}^{\\sigma} = \\delta^{s}_{r}$ );"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\mu \\nu m n} \\bar{\\epsilon} \\Gamma^{p q r} \\Gamma^{m n} \\psi_{\\rho} e e_{p}\\,^{\\mu} e_{q}\\,^{\\nu} e_{r}\\,^{\\rho}-C^{\\kappa}\\,_{\\mu \\nu} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\rho}{\\psi_{\\sigma}} e e_{m}\\,^{\\mu} e^{q}\\,_{\\kappa} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} e_{q}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\nu}} \\delta^{q r} \\omega_{\\rho m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho}+C^{\\mu}\\,_{\\mu \\nu} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\rho}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\nu}} \\delta^{q r} \\omega_{\\rho m q} e e_{n}\\,^{\\nu} e_{p}\\,^{\\rho} e_{r}\\,^{\\mu}+C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\nu}} \\delta^{q r} \\omega_{\\rho m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}-C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\sigma}{\\psi_{\\mu}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\nu}} \\delta^{n p} \\delta^{q r} \\omega_{\\rho n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\nu}} \\delta^{n p} \\delta^{q r} \\omega_{\\rho n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\nu}} \\delta^{n p} \\delta^{q r} \\omega_{\\rho n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "canonicalise(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{} - \\frac{1}{2}\\int \\left( - \\frac{1}{4}R_{\\mu \\nu m n} \\bar{\\epsilon} \\Gamma^{p q r} \\Gamma^{m n} \\psi_{\\rho} e e_{p}\\,^{\\mu} e_{q}\\,^{\\nu} e_{r}\\,^{\\rho}-C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\sigma}{\\psi_{\\kappa}} e e_{m}\\,^{\\nu} e^{q}\\,_{\\mu} e_{n}\\,^{\\sigma} e_{p}\\,^{\\kappa} e_{q}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}+C^{\\mu}\\,_{\\mu \\nu} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\rho}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\rho} e_{p}\\,^{\\nu} e_{r}\\,^{\\mu}+C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\sigma}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m n p} D_{\\mu}{\\psi_{\\rho}} \\delta^{q r} \\omega_{\\nu m q} e e_{n}\\,^{\\mu} e_{p}\\,^{\\nu} e_{r}\\,^{\\rho}-C^{\\mu}\\,_{\\nu \\rho} \\bar{\\epsilon} \\Gamma^{m n p} D_{\\sigma}{\\psi_{\\mu}} e e_{m}\\,^{\\nu} e_{n}\\,^{\\rho} e_{p}\\,^{\\sigma} - \\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\rho} e_{p}\\,^{\\mu} e_{r}\\,^{\\nu}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\nu} e_{p}\\,^{\\mu} e_{r}\\,^{\\rho}+\\frac{1}{2}\\bar{\\epsilon} \\Gamma^{m} D_{\\mu}{\\psi_{\\rho}} \\delta^{n p} \\delta^{q r} \\omega_{\\nu n q} e e_{m}\\,^{\\mu} e_{p}\\,^{\\rho} e_{r}\\,^{\\nu}\\right)\\,\\,{\\rm d}x\\end{dmath*}"
				}
			],
			"source" : "rename_dummies(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "\\hrule\n\\subsection*{Curvature}"
				}
			],
			"hidden" : true,
			"source" : "\\hrule\n\\subsection*{Curvature}"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "A few quick computations to ensure that we have the right normalisations for curvatures and covariant derivatives."
				}
			],
			"hidden" : true,
			"source" : "A few quick computations to ensure that we have the right normalisations for curvatures and covariant derivatives."
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D_{\\mu}{D_{\\nu}{\\psi_{\\rho}}}-D_{\\nu}{D_{\\mu}{\\psi_{\\rho}}}\\end{dmath*}"
				}
			],
			"source" : "riem:= D_{\\mu}{D_{\\nu}{\\psi_{\\rho}}} - D_{\\nu}{D_{\\mu}{\\psi_{\\rho}}};"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D_{\\mu}\\left(A??\\right) = \\partial_{\\mu}\\left(A??\\right)+\\frac{1}{4}\\omega_{\\mu m n} \\Gamma^{m n} A??\\end{dmath*}"
				}
			],
			"source" : "covd:= D_{\\mu}{A??} = \\partial_{\\mu}{A??} + 1/4 \\omega_{\\mu m n} \\Gamma^{m n} A??;"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\partial_{\\mu}\\left(\\partial_{\\nu}{\\psi_{\\rho}}+\\frac{1}{4}\\Gamma^{m n} \\omega_{\\nu m n} \\psi_{\\rho}\\right)+\\frac{1}{4}\\Gamma^{p q} \\omega_{\\mu p q} \\left(\\partial_{\\nu}{\\psi_{\\rho}}+\\frac{1}{4}\\Gamma^{m n} \\omega_{\\nu m n} \\psi_{\\rho}\\right)-\\partial_{\\nu}\\left(\\partial_{\\mu}{\\psi_{\\rho}}+\\frac{1}{4}\\Gamma^{m n} \\omega_{\\mu m n} \\psi_{\\rho}\\right) - \\frac{1}{4}\\Gamma^{p q} \\omega_{\\nu p q} \\left(\\partial_{\\mu}{\\psi_{\\rho}}+\\frac{1}{4}\\Gamma^{m n} \\omega_{\\mu m n} \\psi_{\\rho}\\right)\\end{dmath*}"
				}
			],
			"source" : "substitute(riem, covd);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\frac{1}{4}\\Gamma^{m n} \\partial_{\\mu}{\\omega_{\\nu m n}} \\psi_{\\rho} - \\frac{1}{2}\\Gamma^{m n} \\delta^{p q} \\omega_{\\mu m p} \\omega_{\\nu n q} \\psi_{\\rho} - \\frac{1}{4}\\Gamma^{m n} \\partial_{\\nu}{\\omega_{\\mu m n}} \\psi_{\\rho}\\end{dmath*}"
				}
			],
			"source" : "distribute(_)\nproduct_rule(_)\njoin_gamma(_)\ndistribute(_)\nunwrap(_)\ncanonicalise(_)\nrename_dummies(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\frac{1}{4}\\Gamma^{m n} \\left(\\partial_{\\mu}{\\omega_{\\nu m n}}-\\partial_{\\nu}{\\omega_{\\mu m n}}+\\delta^{p q} \\omega_{\\mu m p} \\omega_{\\nu q n}-\\delta^{p q} \\omega_{\\mu q n} \\omega_{\\nu m p}\\right)\\end{dmath*}"
				}
			],
			"source" : "goal:= \\frac{1}{4} \\Gamma^{m n} ( \\partial_{\\mu}{\\omega_{\\nu m n}} - \\partial_{\\nu}{\\omega_{\\mu m n}} + \n                                 \\omega_{\\mu m p} \\omega_{\\nu q n} \\delta^{p q} - \\omega_{\\nu m p} \\omega_{\\mu q n} \\delta^{p q});"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\frac{1}{4}\\Gamma^{m n} \\partial_{\\mu}{\\omega_{\\nu m n}} - \\frac{1}{4}\\Gamma^{m n} \\partial_{\\nu}{\\omega_{\\mu m n}}+\\frac{1}{4}\\Gamma^{m n} \\delta^{p q} \\omega_{\\mu m p} \\omega_{\\nu q n} - \\frac{1}{4}\\Gamma^{m n} \\delta^{p q} \\omega_{\\mu q n} \\omega_{\\nu m p}\\end{dmath*}"
				}
			],
			"source" : "distribute(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\left(\\frac{1}{4}\\Gamma^{m n} \\partial_{\\mu}{\\omega_{\\nu m n}} - \\frac{1}{4}\\Gamma^{m n} \\partial_{\\nu}{\\omega_{\\mu m n}}+\\frac{1}{4}\\Gamma^{m n} \\delta^{p q} \\omega_{\\mu m p} \\omega_{\\nu q n} - \\frac{1}{4}\\Gamma^{m n} \\delta^{p q} \\omega_{\\mu q n} \\omega_{\\nu m p}\\right) \\psi_{\\rho} - \\frac{1}{4}\\Gamma^{m n} \\partial_{\\mu}{\\omega_{\\nu m n}} \\psi_{\\rho}+\\frac{1}{2}\\Gamma^{m n} \\delta^{p q} \\omega_{\\mu m p} \\omega_{\\nu n q} \\psi_{\\rho}+\\frac{1}{4}\\Gamma^{m n} \\partial_{\\nu}{\\omega_{\\mu m n}} \\psi_{\\rho}\\end{dmath*}"
				}
			],
			"source" : "tst:= @(goal) \\psi_{\\rho} - @(riem);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}0\\end{dmath*}"
				}
			],
			"source" : "distribute(_)\ncanonicalise(_)\nrename_dummies(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : ""
		}
	],
	"description" : "Cadabra JSON notebook format",
	"version" : 1
}