{
	"cells" : 
	[
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Coordinate to~}\\left(r, \\linebreak[0] t\\right).\\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 Depends to~}\\rho.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Depends to~}\\chi.\\end{dmath*}"
				}
			],
			"source" : "{r,t}::Coordinate;\n\\partial{#}::PartialDerivative;\n\\rho::Depends(r,t);\n\\chi::Depends(r);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\rho+\\rho^{2}+\\partial_{t r}{\\rho}+\\partial_{r}{\\chi}\\end{dmath*}"
				}
			],
			"source" : "ex:= \\rho+\\rho**2 +\\partial_{t r}{\\rho} + \\partial_{r}{\\chi};"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\rho^{2}+\\rho+\\partial_{r}{\\chi}+\\partial_{r t}{\\rho}\\end{dmath*}"
				}
			],
			"source" : "res=scas(ex, \"\");"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "We need to strip off the arguments again."
				}
			],
			"hidden" : true,
			"source" : "We need to strip off the arguments again."
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "output",
					"source" : "\\begin{verbatim}{\\sum}  (0x7f6a280272f8)\n  1:{\\pow}  (0x7f6a28021078)\n  2:  {\\rho}  (0x7f6a280236c8)\n  3:  {1}  2  (0x7f6a28020fd8)\n  4:{\\rho}  (0x7f6a28023718)\n  5:{\\partial}  (0x7f6a28025c38)\n  6:  _{r}  (0x7f6a2801de28)\n  7:  {\\chi}  (0x7f6a2801ddd8)\n  8:{\\partial}  (0x7f6a28010c28)\n  9:  _{r}  (0x7f6a280274d8)\n 10:  _{t}  (0x7f6a2800a698)\n 11:  {\\rho}  (0x7f6a2800a6e8)\n\n\\end{verbatim}"
				}
			],
			"source" : "print(tree(res))"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Coordinate to~}\\left(r, \\linebreak[0] t\\right).\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Indices(position=free) to~}\\left(m, \\linebreak[0] n\\right).\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Depends to~}\\Delta.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Metric to~}g_{m n}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property TableauSymmetry to~}g^{m n}.\\end{dmath*}"
				}
			],
			"source" : "{r,t}::Coordinate;\n{m,n}::Indices(values={r,t});\n\\Delta::Depends(r);\n\\partial{#}::PartialDerivative;\ng_{m n}::Metric;\ng^{m n}::InverseMetric;"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\left(g_{t t} = \\Delta, \\linebreak[0] g_{r r} = \\sin\\left(t\\right)\\right)\\end{dmath*}"
				}
			],
			"source" : "rl:= g_{t t} = \\Delta, g_{r r} = \\sin(t);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\left(g_{t t} = \\Delta, \\linebreak[0] g_{r r} = \\sin\\left(t\\right), \\linebreak[0] g^{r r} = \\frac{1}{\\sin\\left(t\\right)}, \\linebreak[0] g^{t t} = \\frac{1}{\\Delta}\\right)\\end{dmath*}"
				}
			],
			"source" : "complete(rl, $g^{m n}$);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\partial_{\\mu}\\left(g_{\\mu \\nu}\\right)\\end{dmath*}"
				}
			],
			"source" : "ex2:=\\partial_{\\mu}{ g_{\\mu\\nu} };"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\left\\{\\begin{aligned}\\end{aligned}\\right.\n\\end{dmath*}"
				}
			],
			"source" : "evaluate(ex2, rl);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "output",
					"source" : "\\begin{verbatim}{\\components}  (0x7fcdb0001048)\n  1:_{\\mu}  (0x7fcdb00096d8)\n  2:{\\comma}  (0x7fcdb0003648)\n\n\\end{verbatim}"
				}
			],
			"source" : "print(tree(ex2))"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : ""
		}
	],
	"description" : "Cadabra JSON notebook format",
	"version" : 1
}
