{
	"cells" : 
	[
		
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "\\algorithm{eliminate_kronecker}{Eliminate Kronecker delta symbols.}\n\nEliminates Kronecker delta symbols by performing index\ncontractions. Also replaces contracted Kronecker delta symbols with\nthe range over which the index runs, if known. "
				}
			],
			"hidden" : true,
			"source" : "\\algorithm{eliminate_kronecker}{Eliminate Kronecker delta symbols.}\n\nEliminates Kronecker delta symbols by performing index\ncontractions. Also replaces contracted Kronecker delta symbols with\nthe range over which the index runs, if known. "
		},
		
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}A_{m p} \\delta_{p q} B_{q n}\\end{dmath*}"
				},
				
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}A_{m q} B_{q n}\\end{dmath*}"
				}
			],
			"source" : "\\delta_{m n}::KroneckerDelta.\nex:=A_{m p} \\delta_{p q} B_{q n};\neliminate_kronecker(_);"
		},
		
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "The index range is set as usual with \\prop{Integer},"
				}
			],
			"hidden" : true,
			"source" : "The index range is set as usual with \\prop{Integer},"
		},
		
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\delta_{p q} \\delta_{p q}\\end{dmath*}"
				},
				
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}d\\end{dmath*}"
				}
			],
			"source" : "{m,n,p,q}::Integer(0..d-1).\n\\delta_{m n}::KroneckerDelta.\nex:=\\delta_{p q} \\delta_{p q};\neliminate_kronecker(_);"
		},
		
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "In order to eliminate metric factors (i.e.~to `raise' and 'lower'\nindices) use the algorithm \\algo{eliminate_metric}."
				}
			],
			"hidden" : true,
			"source" : "In order to eliminate metric factors (i.e.~to `raise' and 'lower'\nindices) use the algorithm \\algo{eliminate_metric}."
		},
		
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : ""
		}
	],
	"description" : "Cadabra JSON notebook format",
	"version" : 1.0
}