{
	"cells" : 
	[
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "\\section*{Default simplification}\n\nBy default, Cadabra does very few things ``by itself'' with your\nexpressions. It only collects equal terms, but even that can be turned\noff if you want to. The logic is that all simplification steps are contained\nin a function \\verb|post_process|, which is executed on every new input and on every completion of\nan algorithm. It can contain arbitrary code, but by default it reads"
				}
			],
			"hidden" : true,
			"source" : "\\section*{Default simplification}\n\nBy default, Cadabra does very few things ``by itself'' with your\nexpressions. It only collects equal terms, but even that can be turned\noff if you want to. The logic is that all simplification steps are contained\nin a function \\verb|post_process|, which is executed on every new input and on every completion of\nan algorithm. It can contain arbitrary code, but by default it reads"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : "def post_process(ex):\n    collect_terms(ex)"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "which simply collects equal terms. You can for instance apply a substitution on every input automatically,"
				}
			],
			"hidden" : true,
			"source" : "which simply collects equal terms. You can for instance apply a substitution on every input automatically,"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : "def post_process(ex):\n    distribute(ex)\n    substitute(ex, $A_{m n} -> B_{m q} B_{q n}$)\n    collect_terms(ex)"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Indices(position=free) to~}\\left[m,~\\discretionary{}{}{} n,~\\discretionary{}{}{} p,~\\discretionary{}{}{} q\\right].\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Symmetric to~}B_{m q} B_{q n}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"cells" : 
					[
						{
							"cell_origin" : "server",
							"cell_type" : "input_form",
							"source" : "B_{m q} B_{q n} B_{n p} B_{p m} + B_{m q} B_{q n} C_{n m}"
						}
					],
					"source" : "\\begin{dmath*}{}B_{m q} B_{q n} B_{n p} B_{p m}+B_{m q} B_{q n} C_{n m}\\end{dmath*}"
				}
			],
			"source" : "{m,n,p,q}::Indices(vector);\nA_{m n}::Symmetric;\nex:=A_{m n} ( A_{n m} + C_{n m});"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "As usual dummy indices have been relabelled appropriately."
				}
			],
			"hidden" : true,
			"source" : "As usual dummy indices have been relabelled appropriately."
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "The \\verb|post_process| function can be redefined on-the-fly in the middle of a notebook."
				}
			],
			"hidden" : true,
			"source" : "The \\verb|post_process| function can be redefined on-the-fly in the middle of a notebook."
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : ""
		}
	],
	"description" : "Cadabra JSON notebook format",
	"version" : 1
}