{
	"cell_id": 12201017813844474228,
	"cells": [
		{
			"cell_id": 11200548926868858386,
			"cell_origin": "client",
			"cell_type": "latex",
			"cells": [
				{
					"cell_id": 706940583944905291,
					"cell_origin": "client",
					"cell_type": "latex_view",
					"source": "\\algorithm{eliminate_metric}{Eliminate metrics by raising or lowering indices.}\n\nEliminate metric and inverse metric objects by raising or lowering indices."
				}
			],
			"hidden": true,
			"source": "\\algorithm{eliminate_metric}{Eliminate metrics by raising or lowering indices.}\n\nEliminate metric and inverse metric objects by raising or lowering indices."
		},
		{
			"cell_id": 9501239282791426272,
			"cell_origin": "client",
			"cell_type": "input",
			"cells": [
				{
					"cell_id": 15552618808454340805,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"cells": [
						{
							"cell_id": 17909960130070292947,
							"cell_origin": "server",
							"cell_type": "input_form",
							"source": "g_{m p} g^{p m}"
						}
					],
					"source": "\\begin{dmath*}{}g_{m p} g^{p m}\\end{dmath*}"
				},
				{
					"cell_id": 346245979832968625,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"cells": [
						{
							"cell_id": 18301710340624209207,
							"cell_origin": "server",
							"cell_type": "input_form",
							"source": "g^{p}_{p}"
						}
					],
					"source": "\\begin{dmath*}{}g^{p}\\,_{p}\\end{dmath*}"
				}
			],
			"source": "{m, n, p, q, r}::Indices(vector, position=fixed).\n{m, n, p, q, r}::Integer(0..9).\ng_{m n}::Metric.\ng^{m n}::InverseMetric.\ng_{m}^{n}::KroneckerDelta.\ng^{m}_{n}::KroneckerDelta.\nex:=g_{m p} g^{p m};\neliminate_metric(_);"
		},
		{
			"cell_id": 7815987119515900884,
			"cell_origin": "client",
			"cell_type": "input",
			"cells": [
				{
					"cell_id": 692499475391029252,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"cells": [
						{
							"cell_id": 12623500600163379539,
							"cell_origin": "server",
							"cell_type": "input_form",
							"source": "10"
						}
					],
					"source": "\\begin{dmath*}{}10\\end{dmath*}"
				}
			],
			"source": "eliminate_kronecker(_);"
		},
		{
			"cell_id": 11136087069753532813,
			"cell_origin": "client",
			"cell_type": "latex",
			"cells": [
				{
					"cell_id": 10975080456446455892,
					"cell_origin": "client",
					"cell_type": "latex_view",
					"source": "Related algorithms are \\algo{eliminate_kronecker} and \\algo{eliminate_vielbein}."
				}
			],
			"hidden": true,
			"source": "Related algorithms are \\algo{eliminate_kronecker} and \\algo{eliminate_vielbein}."
		},
		{
			"cell_id": 668070063135773764,
			"cell_origin": "client",
			"cell_type": "latex",
			"cells": [
				{
					"cell_id": 2955225009111573646,
					"cell_origin": "client",
					"cell_type": "latex_view",
					"source": "It is sometimes useful to eliminate only those metrics which have two\ndummy indices (so as to avoid changing indices on non-metric factors),\nas in the following example:"
				}
			],
			"hidden": true,
			"source": "It is sometimes useful to eliminate only those metrics which have two\ndummy indices (so as to avoid changing indices on non-metric factors),\nas in the following example:"
		},
		{
			"cell_id": 7674476649362588094,
			"cell_origin": "client",
			"cell_type": "input",
			"cells": [
				{
					"cell_id": 934843099193461823,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"source": "\\begin{dmath*}{}\\text{Property Indices(position=fixed) attached to~}\\left[a, \\discretionary{}{}{}b, \\discretionary{}{}{}c, \\discretionary{}{}{}d, \\discretionary{}{}{}e, \\discretionary{}{}{}f\\right].\\end{dmath*}"
				},
				{
					"cell_id": 816358059307477494,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"source": "\\begin{dmath*}{}\\text{Property Metric attached to~}g_{a b}.\\end{dmath*}"
				},
				{
					"cell_id": 2839007278772691664,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"source": "\\begin{dmath*}{}\\text{Property TableauSymmetry attached to~}g^{a b}.\\end{dmath*}"
				},
				{
					"cell_id": 13817763760227715534,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"cells": [
						{
							"cell_id": 10707513932396855145,
							"cell_origin": "server",
							"cell_type": "input_form",
							"source": "X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f}"
						}
					],
					"source": "\\begin{dmath*}{}X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f}\\end{dmath*}"
				},
				{
					"cell_id": 15694279202429955163,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"cells": [
						{
							"cell_id": 16096105714669192847,
							"cell_origin": "server",
							"cell_type": "input_form",
							"source": "X_{e} g^{e f}"
						}
					],
					"source": "\\begin{dmath*}{}X_{e} g^{e f}\\end{dmath*}"
				}
			],
			"source": "{a,b,c,d,e,f}::Indices(position=fixed);\ng_{a b}::Metric;\ng^{a b}::InverseMetric;\nex:=X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f};\neliminate_metric(ex, repeat=True, redundant=True);"
		},
		{
			"cell_id": 10177437379030071371,
			"cell_origin": "client",
			"cell_type": "latex",
			"cells": [
				{
					"cell_id": 1237014864296849726,
					"cell_origin": "client",
					"cell_type": "latex_view",
					"source": "Without the \\verb|redundant=True| option, this would have reduced the \nexpression to $X^{f}$."
				}
			],
			"hidden": true,
			"source": "Without the \\verb|redundant=True| option, this would have reduced the \nexpression to $X^{f}$."
		},
		{
			"cell_id": 8153574234349350675,
			"cell_origin": "client",
			"cell_type": "input",
			"source": ""
		}
	],
	"description": "Cadabra JSON notebook format",
	"version": 1.0
}